Publications

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2016

F. Berkenkamp, A. P. Schoellig, and A. Krause, “Safe controller optimization for quadrotors with Gaussian processes,” in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2016, pp. 493-496.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [View 2nd Video]
One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be tuned manually on the real system to achieve the best performance. To avoid this manual tuning step, methods from machine learning, such as Bayesian optimization, have been used. However, as these methods evaluate different controller parameters on the real system, safety-critical system failures may happen. In this paper, we overcome this problem by applying, for the first time, a recently developed safe optimization algorithm, SafeOpt, to the problem of automatic controller parameter tuning. Given an initial, low-performance controller, SafeOpt automatically optimizes the parameters of a control law while guaranteeing safety. It models the underlying performance measure as a Gaussian process and only explores new controller parameters whose performance lies above a safe performance threshold with high probability. Experimental results on a quadrotor vehicle indicate that the proposed method enables fast, automatic, and safe optimization of controller parameters without human intervention.

@inproceedings{berkenkamp-icra16,
author = {Felix Berkenkamp and Angela P. Schoellig and Andreas Krause},
title = {Safe controller optimization for quadrotors with {G}aussian processes},
booktitle = {{Proc. of the IEEE International Conference on Robotics and Automation (ICRA)}},
year = {2016},
month = {May},
pages = {493--496},
url = {\href{http://arxiv.org/abs/1509.01066}{arXiv:1509.01066 [cs.RO]}},
abstract = {One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be tuned manually on the real system to achieve the best performance. To avoid this manual tuning step, methods from machine learning, such as Bayesian optimization, have been used. However, as these methods evaluate different controller parameters on the real system, safety-critical system failures may happen. In this paper, we overcome this problem by applying, for the first time, a recently developed safe optimization algorithm, SafeOpt, to the problem of automatic controller parameter tuning. Given an initial, low-performance controller, SafeOpt automatically optimizes the parameters of a control law while guaranteeing safety. It models the underlying performance measure as a Gaussian process and only explores new controller parameters whose performance lies above a safe performance threshold with high probability. Experimental results on a quadrotor vehicle indicate that the proposed method enables fast, automatic, and safe optimization of controller parameters without human intervention.},
urlvideo = {https://www.youtube.com/watch?v=GiqNQdzc5TI},
urlvideo2 = {https://www.youtube.com/watch?v=IYi8qMnt0yU},
code = {https://github.com/befelix/SafeOpt},
}

2015

F. Berkenkamp and A. P. Schoellig, “Safe and robust learning control with Gaussian processes,” in Proc. of the European Control Conference (ECC), 2015, pp. 2501-2506.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides]
This paper introduces a learning-based robust control algorithm that provides robust stability and performance guarantees during learning. The approach uses Gaussian process (GP) regression based on data gathered during operation to update an initial model of the system and to gradually decrease the uncertainty related to this model. Embedding this data-based update scheme in a robust control framework guarantees stability during the learning process. Traditional robust control approaches have not considered online adaptation of the model and its uncertainty before. As a result, their controllers do not improve performance during operation. Typical machine learning algorithms that have achieved similar high-performance behavior by adapting the model and controller online do not provide the guarantees presented in this paper. In particular, this paper considers a stabilization task, linearizes the nonlinear, GP-based model around a desired operating point, and solves a convex optimization problem to obtain a linear robust controller. The resulting performance improvements due to the learning-based controller are demonstrated in experiments on a quadrotor vehicle.

@INPROCEEDINGS{berkenkamp-ecc15,
author = {Felix Berkenkamp and Angela P. Schoellig},
title = {Safe and robust learning control with {G}aussian processes},
booktitle = {{Proc. of the European Control Conference (ECC)}},
pages = {2501--2506},
year = {2015},
urlvideo={https://youtu.be/YqhLnCm0KXY?list=PLC12E387419CEAFF2},
urlslides={../../wp-content/papercite-data/slides/berkenkamp-ecc15-slides.pdf},
abstract = {This paper introduces a learning-based robust control algorithm that provides robust stability and performance guarantees during learning. The approach uses Gaussian process (GP) regression based on data gathered during operation to update an initial model of the system and to gradually decrease the uncertainty related to this model. Embedding this data-based update scheme in a robust control framework guarantees stability during the learning process. Traditional robust control approaches have not considered online adaptation of the model and its uncertainty before. As a result, their controllers do not improve performance during operation. Typical machine learning algorithms that have achieved similar high-performance behavior by adapting the model and controller online do not provide the guarantees presented in this paper. In particular, this paper considers a stabilization task, linearizes the nonlinear, GP-based model around a desired operating point, and solves a convex optimization problem to obtain a linear robust controller. The resulting performance improvements due to the learning-based controller are demonstrated in experiments on a quadrotor vehicle.}
}

C. J. Ostafew, A. P. Schoellig, and T. D. Barfoot, “Conservative to confident: treating uncertainty robustly within learning-based control,” in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2015. To appear.
[View BibTeX] [View Abstract] [Download PDF]

Robust control algorithms maintain performance and stability despite model uncertainty but lack the ability to reduce model uncertainty. Learning-based control algorithms, on the other hand, reduce modelling errors and uncertainty over time but often are not robust to model uncertainty during the learning process. This paper proposes a novel combination of both ideas: a robust Min-Max Learning-based Nonlinear Model Predictive Control (MM-LB-NMPC) algorithm. Based on an existing LB-NMPC algorithm, we present an efficient and robust extension, altering the MPC performance objective to optimize for the worst-case scenario. The algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modelled as a Gaussian Process (GP) based on experience collected during previous trials as a function of system state, input, and other relevant variables. Nominal state sequences are predicted using an Unscented Transform and worst-case scenarios are defined as sequences bounding the 3 confidence region. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results from testing on a 50 kg skid-steered robot executing a path-tracking task. The results show reductions in maximum lateral and heading path-tracking errors by to 30 per cent and a clear transition from robust control, when the model uncertainty is high, to optimal control, when model uncertainty is reduced.

@INPROCEEDINGS{ostafew-icra15,
author = {Chris J. Ostafew and Angela P. Schoellig and Timothy D. Barfoot},
title = {Conservative to confident: treating uncertainty robustly within learning-based control},
booktitle = {{Proc. of the IEEE International Conference on Robotics and Automation (ICRA)}},
year = {2015},
note = {To appear},
abstract = {Robust control algorithms maintain performance and stability despite model uncertainty but lack the ability to reduce model uncertainty. Learning-based control algorithms, on the other hand, reduce modelling errors and uncertainty over time but often are not robust to model uncertainty during the learning process. This paper proposes a novel combination of both ideas: a robust Min-Max Learning-based Nonlinear Model Predictive Control (MM-LB-NMPC) algorithm. Based on an existing LB-NMPC algorithm, we present an efficient and robust extension, altering the MPC performance objective to optimize for the worst-case scenario. The algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modelled as a Gaussian Process (GP) based on experience collected during previous trials as a function of system state, input, and other relevant variables. Nominal state sequences are predicted using an Unscented Transform and worst-case scenarios are defined as sequences bounding the 3 confidence region. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results from testing on a 50 kg skid-steered robot executing a path-tracking task. The results show reductions in maximum lateral and heading path-tracking errors by to 30 per cent and a clear transition from robust control, when the model uncertainty is high, to optimal control, when model uncertainty is reduced.}
}

X. Wang, N. Dalal, T. Laidlow, and A. P. Schoellig, “A flying drum machine,” in Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015. Submitted.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

This paper proposes the use of a quadrotor aerial vehicle as a musical instrument. Using the idea of interactions based on physical contact, a system is developed that enables humans to engage in artistic expression with a flying robot and produce music. A robotic user interface that uses physical interactions was created for a quadcopter. The interactive quadcopter was then programmed to drive playback of drum sounds in real-time in response to physical interaction. An intuitive mapping was developed between machine movement and art/creative composition. Challenges arose in meeting realtime latency requirements mainly due to delays in input detection. They were overcome through the development of a quick input detection method, which relies on accurate yet fast digital filtering. Successful experiments were conducted with a professional musician who used the interface to compose complex rhythm patterns. A video accompanying this paper demonstrates his performance.

@INPROCEEDINGS{wang-iros15,
author = {Xingbo Wang and Natasha Dalal and Tristan Laidlow and Angela P. Schoellig},
title = {A Flying Drum Machine},
booktitle = {{Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
year = {2015},
note = {Submitted},
urlvideo={https://youtu.be/d5zG-BWB7lE?list=PLD6AAACCBFFE64AC5},
abstract = {This paper proposes the use of a quadrotor aerial vehicle as a musical instrument. Using the idea of interactions based on physical contact, a system is developed that enables humans to engage in artistic expression with a flying robot and produce music. A robotic user interface that uses physical interactions was created for a quadcopter. The interactive quadcopter was then programmed to drive playback of drum sounds in real-time in response to physical interaction. An intuitive mapping was developed between machine movement and art/creative composition. Challenges arose in meeting realtime latency requirements mainly due to delays in input detection. They were overcome through the development of a quick input detection method, which relies on accurate yet fast digital filtering. Successful experiments were conducted with a professional musician who used the interface to compose complex rhythm patterns. A video accompanying this paper demonstrates his performance.}
}

K. V. Raimalwala, B. A. Francis, and A. P. Schoellig, “An upper bound on the error of alignment-based transfer learning between two linear, time-invariant, scalar systems,” in Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015. Submitted.
[View BibTeX] [View Abstract] [Download PDF]

Methods from machine learning have successfully been used to improve the performance of control systems in cases when accurate models of the system or the environment are not available. These methods require the use of data generated from physical trials. Transfer Learning (TL) allows for this data to come from a different, similar system. This paper studies a simplified TL scenario with the goal of understanding in which cases a simple alignment-based transfer of data is possible and beneficial. Two linear, time-invariant (LTI), scalar systems are tasked to follow the same reference signal. A scalar, LTI transformation is applied to the output from a source system to align with the output from a target system. An upper bound on the 2-norm of the transformation error is derived for a large set of reference signals and is minimized with respect to the transformation scalar. Analysis indicates that the minimized bound depends on the systems’ poles and gains. It is reduced for systems with poles that have a larger negative real part (i.e., for stable systems with low response time). The bound is shown to be zero when the poles of the two systems are equal, independent of the gains of the system. Furthermore, the bound is shown to grow exponentially as the pole of the target system approaches the imaginary axis. Additionally, numerical results show that using the reference signal as input to the transformation reduces the upper bound on the error 2-norm further.

@INPROCEEDINGS{raimalwala-iros15,
author = {Kaizad V. Raimalwala and Bruce A. Francis and Angela P. Schoellig},
title = {An upper bound on the error of alignment-based transfer learning between two linear, time-invariant, scalar systems},
booktitle = {{Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
year = {2015},
note = {Submitted},
abstract = {Methods from machine learning have successfully been used to improve the performance of control systems in cases when accurate models of the system or the environment are not available. These methods require the use of data generated from physical trials. Transfer Learning (TL) allows for this data to come from a different, similar system. This paper studies a simplified TL scenario with the goal of understanding in which cases a simple alignment-based transfer of data is possible and beneficial. Two linear, time-invariant (LTI), scalar systems are tasked to follow the same reference signal. A scalar, LTI transformation is applied to the output from a source system to align with the output from a target system. An upper bound on the 2-norm of the transformation error is derived for a large set of reference signals and is minimized with respect to the transformation scalar. Analysis indicates that the minimized bound depends on the systems' poles and gains. It is reduced for systems with poles that have a larger negative real part (i.e., for stable systems with low response time). The bound is shown to be zero when the poles of the two systems are equal, independent of the gains of the system. Furthermore, the bound is shown to grow exponentially as the pole of the target system approaches the imaginary axis. Additionally, numerical results show that using the reference signal as input to the transformation reduces the upper bound on the error 2-norm further.}
}

M. Vukosavljev, I. Jansen, M. E. Broucke, and A. P. Schoellig, “Safe and robust quadrotor maneuvers based on reach control,” in Proc. of the IEEE Conference on Decision and Control (CDC), 2015. Submitted.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

In this paper, we investigate the synthesis of piecewise affine feedback controllers to execute safe and robust quadrocopter maneuvers. The methodology is based on formulating the problem as a reach control problem on a polytopic state space. Reach control has so far only been developed in theory and has not been tested experimentally in a real system before. We demonstrate that these theoretical tools can achieve aggressive, albeit safe and robust, quadrocopter maneuvers without the need for a predefined open-loop reference trajectory. In a proof-of-concept demonstration, the reach controller is implemented in one translational direction while the other degrees of freedom are stabilized by separate controllers. Experimental results on a quadrocopter show the effectiveness and robustness of this control approach.

@INPROCEEDINGS{vukosavljev-cdc15,
author = {Marijan Vukosavljev and Ivo Jansen and Mireille E. Broucke and Angela P. Schoellig},
title = {Safe and robust quadrotor maneuvers based on reach control},
booktitle = {{Proc. of the IEEE Conference on Decision and Control (CDC)}},
year = {2015},
note = {Submitted},
urlvideo={https://youtu.be/l4vdxdmd2xc?list=PLuLKX4lDsLIbqy0qr7qy-FHVpB7UUSq_B},
abstract = {In this paper, we investigate the synthesis of piecewise affine feedback controllers to execute safe and robust quadrocopter maneuvers. The methodology is based on formulating the problem as a reach control problem on a polytopic state space. Reach control has so far only been developed in theory and has not been tested experimentally in a real system before. We demonstrate that these theoretical tools can achieve aggressive, albeit safe and robust, quadrocopter maneuvers without the need for a predefined open-loop reference trajectory. In a proof-of-concept demonstration, the reach controller is implemented in one translational direction while the other degrees of freedom are stabilized by separate controllers. Experimental results on a quadrocopter show the effectiveness and robustness of this control approach.}
}

C. J. Ostafew, J. Collier, A. P. Schoellig, and T. D. Barfoot, “Learning-based nonlinear model predictive control to improve vision-based mobile robot path tracking,” Journal of Field Robotics, 2015. To appear.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [View 2nd Video] [View 3rd Video] [View 4th Video]

This paper presents a Learning-based Nonlinear Model Predictive Control (LB-NMPC) algorithm to achieve high-performance path tracking in challenging off-road terrain through learning. The LB-NMPC algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modelled as a Gaussian Process (GP) as a function of system state, input, and other relevant variables. The GP is updated based on experience collected during previous trials. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results including over 3.0 km of travel by three significantly different robot platforms with masses ranging from 50 kg to 600 kg and at speeds ranging from 0.35 m/s to 1.2 m/s. Planned speeds are generated by a novel experience-based speed scheduler that balances overall travel time, path-tracking errors, and localization reliability. The results show that the controller can start from a generic a priori vehicle model and subsequently learn to reduce vehicle- and trajectory-specific path-tracking errors based on experience.

@ARTICLE{ostafew-jfr15,
author = {Chris J. Ostafew and Jack Collier and Angela P. Schoellig and Timothy D. Barfoot},
title = {Learning-based nonlinear model predictive control to improve vision-based mobile robot path tracking},
year = {2015},
note = {To appear},
journal = {{Journal of Field Robotics}},
urlvideo={https://youtu.be/lxm-2A6yOY0?list=PLC12E387419CEAFF2},
urlvideo2={https://youtu.be/M9xhkHCzpMo?list=PL0F1AD87C0266A961},
urlvideo3={http://youtu.be/MwVElAn95-M?list=PLC0E5EB919968E507},
urlvideo4={http://youtu.be/Pu3_F6k6Fa4?list=PLC0E5EB919968E507},
abstract = {This paper presents a Learning-based Nonlinear Model Predictive Control (LB-NMPC)
algorithm to achieve high-performance path tracking in challenging off-road terrain through
learning. The LB-NMPC algorithm uses a simple a priori vehicle model and a learned
disturbance model. Disturbances are modelled as a Gaussian Process (GP) as a function of
system state, input, and other relevant variables. The GP is updated based on experience
collected during previous trials. Localization for the controller is provided by an on-board,
vision-based mapping and navigation system enabling operation in large-scale, GPS-denied
environments. The paper presents experimental results including over 3.0 km of travel by
three significantly different robot platforms with masses ranging from 50 kg to 600 kg and
at speeds ranging from 0.35 m/s to 1.2 m/s. Planned speeds are generated by a novel
experience-based speed scheduler that balances overall travel time, path-tracking errors,
and localization reliability. The results show that the controller can start from a generic
a priori vehicle model and subsequently learn to reduce vehicle- and trajectory-specific
path-tracking errors based on experience.}
}

2014

[DOI] C. J. Ostafew, A. P. Schoellig, and T. D. Barfoot, “Learning-based nonlinear model predictive control to improve vision-based mobile robot path-tracking in challenging outdoor environments,” in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2014, pp. 4029-4036.
[View BibTeX] [View Abstract] [Download PDF] [View Video]
This paper presents a Learning-based Nonlinear Model Predictive Control (LB-NMPC) algorithm for an autonomous mobile robot to reduce path-tracking errors over repeated traverses along a reference path. The LB-NMPC algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modelled as a Gaussian Process (GP) based on experience collected during previous traversals as a function of system state, input and other relevant variables. Modelling the disturbance as a GP enables interpolation and extrapolation of learned disturbances, a key feature of this algorithm. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results including over 1.8 km of travel by a four-wheeled, 50 kg robot travelling through challenging terrain (including steep, uneven hills) and by a six-wheeled, 160 kg robot learning disturbances caused by unmodelled dynamics at speeds ranging from 0.35 m/s to 1.0 m/s. The speed is scheduled to balance trial time, path-tracking errors, and localization reliability based on previous experience. The results show that the system can start from a generic a priori vehicle model and subsequently learn to reduce vehicle- and trajectory-specific path-tracking errors based on experience.

@INPROCEEDINGS{ostafew-icra14,
author = {Chris J. Ostafew and Angela P. Schoellig and Timothy D. Barfoot},
title = {Learning-based nonlinear model predictive control to improve vision-based mobile robot path-tracking in challenging outdoor environments},
booktitle = {{Proc. of the IEEE International Conference on Robotics and Automation (ICRA)}},
pages = {4029-4036},
year = {2014},
doi = {10.1109/ICRA.2014.6907444},
urlvideo = {https://youtu.be/MwVElAn95-M?list=PLC12E387419CEAFF2},
abstract = {This paper presents a Learning-based Nonlinear Model Predictive Control (LB-NMPC) algorithm for an autonomous mobile robot to reduce path-tracking errors over repeated traverses along a reference path. The LB-NMPC algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modelled as a Gaussian Process (GP) based on experience collected during previous traversals as a function of system state, input and other relevant variables. Modelling the disturbance as a GP enables interpolation and extrapolation of learned disturbances, a key feature of this algorithm. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results including over 1.8 km of travel by a four-wheeled, 50 kg robot travelling through challenging terrain (including steep, uneven hills) and by a six-wheeled, 160 kg robot learning disturbances caused by unmodelled dynamics at speeds ranging from 0.35 m/s to 1.0 m/s. The speed is scheduled to balance trial time, path-tracking errors, and localization reliability based on previous experience. The results show that the system can start from a generic a priori vehicle model and subsequently learn to reduce vehicle- and trajectory-specific path-tracking errors based on experience.}
}

[DOI] C. J. Ostafew, A. P. Schoellig, T. D. Barfoot, and J. Collier, “Speed daemon: experience-based mobile robot speed scheduling,” in Proc. of the International Conference on Computer and Robot Vision (CRV), 2014, pp. 56-62. Best Robotics Paper Award.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

A time-optimal speed schedule results in a mobile robot driving along a planned path at or near the limits of the robot’s capability. However, deriving models to predict the effect of increased speed can be very difficult. In this paper, we present a speed scheduler that uses previous experience, instead of complex models, to generate time-optimal speed schedules. The algorithm is designed for a vision-based, path-repeating mobile robot and uses experience to ensure reliable localization, low path-tracking errors, and realizable control inputs while maximizing the speed along the path. To our knowledge, this is the first speed scheduler to incorporate experience from previous path traversals in order to address system constraints. The proposed speed scheduler was tested in over 4 km of path traversals in outdoor terrain using a large Ackermann-steered robot travelling between 0.5 m/s and 2.0 m/s. The approach to speed scheduling is shown to generate fast speed schedules while remaining within the limits of the robot’s capability.

@INPROCEEDINGS{ostafew-crv14,
author = {Chris J. Ostafew and Angela P. Schoellig and Timothy D. Barfoot and J. Collier},
title = {Speed daemon: experience-based mobile robot speed scheduling},
booktitle = {{Proc. of the International Conference on Computer and Robot Vision (CRV)}},
pages = {56-62},
year = {2014},
doi = {10.1109/CRV.2014.16},
urlvideo = {https://youtu.be/Pu3_F6k6Fa4?list=PLC12E387419CEAFF2},
abstract = {A time-optimal speed schedule results in a mobile robot driving along a planned path at or near the limits of the robot's capability. However, deriving models to predict the effect of increased speed can be very difficult. In this paper, we present a speed scheduler that uses previous experience, instead of complex models, to generate time-optimal speed schedules. The algorithm is designed for a vision-based, path-repeating mobile robot and uses experience to ensure reliable localization, low path-tracking errors, and realizable control inputs while maximizing the speed along the path. To our knowledge, this is the first speed scheduler to incorporate experience from previous path traversals in order to address system constraints. The proposed speed scheduler was tested in over 4 km of path traversals in outdoor terrain using a large Ackermann-steered robot travelling between 0.5 m/s and 2.0 m/s. The approach to speed scheduling is shown to generate fast speed schedules while remaining within the limits of the robot's capability.},
note = {Best Robotics Paper Award}
}

[DOI] A. Pfrunder, A. P. Schoellig, and T. D. Barfoot, “A proof-of-concept demonstration of visual teach and repeat on a quadrocopter using an altitude sensor and a monocular camera,” in Proc. of the International Conference on Computer and Robot Vision (CRV), 2014, pp. 238-245.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides]

This paper applies an existing vision-based navigation algorithm to a micro aerial vehicle (MAV). The algorithm has previously been used for long-range navigation of ground robots based on on-board 3D vision sensors such as a stereo or Kinect cameras. A teach-and-repeat operational strategy enables a robot to autonomously repeat a manually taught route without relying on an external positioning system such as GPS. For MAVs we show that a monocular downward looking camera combined with an altitude sensor can be used as 3D vision sensor replacing other resource-expensive 3D vision solutions. The paper also includes a simple path tracking controller that uses feedback from the visual and inertial sensors to guide the vehicle along a straight and level path. Preliminary experimental results demonstrate reliable, accurate and fully autonomous flight of an 8-m-long (straight and level) route, which was taught with the quadrocopter fixed to a cart. Finally, we present the successful flight of a more complex, 16-m-long route.

@INPROCEEDINGS{pfrunder-crv14,
author = {Andreas Pfrunder and Angela P. Schoellig and Timothy D. Barfoot},
title = {A proof-of-concept demonstration of visual teach and repeat on a quadrocopter using an altitude sensor and a monocular camera},
booktitle = {{Proc. of the International Conference on Computer and Robot Vision (CRV)}},
pages = {238-245},
year = {2014},
doi = {10.1109/CRV.2014.40},
urlvideo = {https://youtu.be/BRDvK4xD8ZY?list=PLuLKX4lDsLIaJEVTsuTAVdDJDx0xmzxXr},
urlslides = {../../wp-content/papercite-data/slides/pfrunder-crv14-slides.pdf},
abstract = {This paper applies an existing vision-based navigation algorithm to a micro aerial vehicle (MAV). The algorithm has previously been used for long-range navigation of ground robots based on on-board 3D vision sensors such as a stereo or Kinect cameras. A teach-and-repeat operational strategy enables a robot to autonomously repeat a manually taught route without relying on an external positioning system such as GPS. For MAVs we show that a monocular downward looking camera combined with an altitude sensor can be used as 3D vision sensor replacing other resource-expensive 3D vision solutions. The paper also includes a simple path tracking controller that uses feedback from the visual and inertial sensors to guide the vehicle along a straight and level path. Preliminary experimental results demonstrate reliable, accurate and fully autonomous flight of an 8-m-long (straight and level) route, which was taught with the quadrocopter fixed to a cart. Finally, we present the successful flight of a more complex, 16-m-long route.}
}

[DOI] N. Degen and A. P. Schoellig, “Design of norm-optimal iterative learning controllers: the effect of an iteration-domain Kalman filter for disturbance estimation,” in Proc. of the IEEE Conference on Decision and Control (CDC), 2014, pp. 3590-3596.
[View BibTeX] [View Abstract] [Download PDF] [Download Slides]

Iterative learning control (ILC) has proven to be an effective method for improving the performance of repetitive control tasks. This paper revisits two optimization-based ILC algorithms: (i) the widely used quadratic-criterion ILC law (QILC) and (ii) an estimation-based ILC law using an iteration-domain Kalman filter (K-ILC). The goal of this paper is to analytically compare both algorithms and to highlight the advantages of the Kalman-filter-enhanced algorithm. We first show that for an iteration-constant estimation gain and an appropriate choice of learning parameters both algorithms are identical. We then show that the estimation-enhanced algorithm with its iteration-varying optimal Kalman gains can achieve both fast initial convergence and good noise rejection by (optimally) adapting the learning update rule over the course of an experiment. We conclude that the clear separation of disturbance estimation and input update of the K-ILC algorithm provides an intuitive architecture to design learning schemes that achieve both low noise sensitivity and fast convergence. To benchmark the algorithms we use a simulation of a single-input, single-output mass-spring-damper system.

@INPROCEEDINGS{degen-cdc14,
author = {Nicolas Degen and Angela P. Schoellig},
title = {Design of norm-optimal iterative learning controllers: the effect of an iteration-domain {K}alman filter for disturbance estimation},
booktitle = {{Proc. of the IEEE Conference on Decision and Control (CDC)}},
pages = {3590-3596},
year = {2014},
doi = {10.1109/CDC.2014.7039947},
urlslides = {../../wp-content/papercite-data/slides/degen-cdc14-slides.pdf},
abstract = {Iterative learning control (ILC) has proven to be an effective method for improving the performance of repetitive control tasks. This paper revisits two optimization-based ILC algorithms: (i) the widely used quadratic-criterion ILC law (QILC) and (ii) an estimation-based ILC law using an iteration-domain Kalman filter (K-ILC). The goal of this paper is to analytically compare both algorithms and to highlight the advantages of the Kalman-filter-enhanced algorithm. We first show that for an iteration-constant estimation gain and an appropriate choice of learning parameters both algorithms are identical. We then show that the estimation-enhanced algorithm with its iteration-varying optimal Kalman gains can achieve both fast initial convergence and good noise rejection by (optimally) adapting the learning update rule over the course of an experiment. We conclude that the clear separation of disturbance estimation and input update of the K-ILC algorithm provides an intuitive architecture to design learning schemes that achieve both low noise sensitivity and fast convergence. To benchmark the algorithms we use a simulation of a single-input, single-output mass-spring-damper system.}
}

F. Berkenkamp and A. P. Schoellig, “Learning-based robust control: guaranteeing stability while improving performance,” in Proc. of the Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2014.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides] [More Information]

To control dynamic systems, modern control theory relies on accurate mathematical models that describe the system behavior. Machine learning methods have proven to be an effective method to compensate for initial errors in these models and to achieve high-performance maneuvers by adapting the system model and control online. However, these methods usually do not guarantee stability during the learning process. On the other hand, the control community has traditionally accounted for model uncertainties by designing robust controllers. Robust controllers use a mathematical description of the uncertainty in the dynamic system derived prior to operation and guarantee robust stability for all uncertainties. Unlike machine learning methods, robust control does not improve the control performance by adapting the model online. This paper combines machine learning and robust control theory for the first time with the goal of improving control performance while guaranteeing stability. Data gathered during operation is used to reduce the uncertainty in the model and to learn systematic errors. Specifically, a nonlinear, nonparametric model of the unknown dynamics is learned with a Gaussian Process. This model is used for the computation of a linear robust controller, which guarantees stability around an operating point for all uncertainties. As a result, the robust controller improves its performance online while guaranteeing robust stability. A simulation example illustrates the performance improvements due to the learning-based robust controller.

@INPROCEEDINGS{berkenkamp-iros14,
author = {Felix Berkenkamp and Angela P. Schoellig},
title = {Learning-based robust control: guaranteeing stability while improving performance},
booktitle = {{Proc. of the Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
year = {2014},
urllink = {http://www.cs.unm.edu/amprg/mlpc14Workshop/},
urlvideo={https://youtu.be/YqhLnCm0KXY?list=PLC12E387419CEAFF2},
urlslides={../../wp-content/papercite-data/slides/berkenkamp-iros14-slides.pdf},
abstract = {To control dynamic systems, modern control theory relies on accurate mathematical models that describe the system behavior. Machine learning methods have proven to be an effective method to compensate for initial errors in these models and to achieve high-performance maneuvers by adapting the system model and control online. However, these methods usually do not guarantee stability during the learning process. On the other hand, the control community has traditionally accounted for model uncertainties by designing robust controllers. Robust controllers use a mathematical description of the uncertainty in the dynamic system derived prior to operation and guarantee robust stability for all uncertainties. Unlike machine learning methods, robust control does not improve the control performance by adapting the model online. This paper combines machine learning and robust control theory for the first time with the goal of improving control performance while guaranteeing stability. Data gathered during operation is used to reduce the uncertainty in the model and to learn systematic errors. Specifically, a nonlinear, nonparametric model of the unknown dynamics is learned with a Gaussian Process. This model is used for the computation of a linear robust controller, which guarantees stability around an operating point for all uncertainties. As a result, the robust controller improves its performance online while guaranteeing robust stability. A simulation example illustrates the performance improvements due to the learning-based robust controller.}
}

[DOI] T. Andre, K. A. Hummel, A. P. Schoellig, E. Yanmaz, M. Asedpour, C. Bettstetter, P. Grippa, H. Hellwagner, S. Sand, and S. Zhang, “Application-driven design of aerial communication networks,” IEEE Communications Magazine, vol. 52, iss. 5, pp. 129-137, 2014. Authors 1 to 4 contributed equally.
[View BibTeX] [View Abstract] [Download PDF] [More Information]

Networks of micro aerial vehicles (MAVs) equipped with various sensors are increasingly used for civil applications, such as monitoring, surveillance, and disaster management. In this article, we discuss the communication requirements raised by applications in MAV networks. We propose a novel system representation that can be used to specify different application demands. To this end, we extract key functionalities expected in an MAV network. We map these functionalities into building blocks to characterize the expected communication needs. Based on insights from our own and related real-world experiments, we discuss the capabilities of existing communications technologies and their limitations to implement the proposed building blocks. Our findings indicate that while certain requirements of MAV applications are met with available technologies, further research and development is needed to address the scalability, heterogeneity, safety, quality of service, and security aspects of multi-MAV systems.

@ARTICLE{andre-com14,
author = {Torsten Andre and Karin A. Hummel and Angela P. Schoellig and Evsen Yanmaz and Mahdi Asedpour and Christian Bettstetter and Pasquale Grippa and Hermann Hellwagner and Stephan Sand and Siwei Zhang},
title = {Application-driven design of aerial communication networks},
journal = {{IEEE Communications Magazine}},
note={Authors 1 to 4 contributed equally},
volume = {52},
number = {5},
pages = {129-137},
year = {2014},
doi = {10.1109/MCOM.2014.6815903},
urllink = {http://nes.aau.at/?p=1176},
abstract = {Networks of micro aerial vehicles (MAVs) equipped with various sensors are increasingly used for civil applications, such as monitoring, surveillance, and disaster management. In this article, we discuss the communication requirements raised by applications in MAV networks. We propose a novel system representation that can be used to specify different application demands. To this end, we extract key functionalities expected in an MAV network. We map these functionalities into building blocks to characterize the expected communication needs. Based on insights from our own and related real-world experiments, we discuss the capabilities of existing communications technologies and their limitations to implement the proposed building blocks. Our findings indicate that while certain requirements of MAV applications are met with available technologies, further research and development is needed to address the scalability, heterogeneity, safety, quality of service, and security aspects of multi-MAV systems.}
}

[DOI] A. P. Schoellig, H. Siegel, F. Augugliaro, and R. D’Andrea, “So you think you can dance? Rhythmic flight performances with quadrocopters,” in Controls and Art, A. LaViers and M. Egerstedt, Eds., Springer International Publishing, 2014, pp. 73-105.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Additional Material] [Download Slides] [More Information]

This chapter presents a set of algorithms that enable quadrotor vehicles to "fly with the music"; that is, to perform rhythmic motions that are aligned with the beat of a given music piece.

@INCOLLECTION{schoellig-springer14,
author = {Angela P. Schoellig and Hallie Siegel and Federico Augugliaro and Raffaello D'Andrea},
title = {So you think you can dance? {Rhythmic} flight performances with quadrocopters},
booktitle = {{Controls and Art}},
editor = {Amy LaViers and Magnus Egerstedt},
publisher = {Springer International Publishing},
pages = {73-105},
year = {2014},
doi = {10.1007/978-3-319-03904-6_4},
urldata={../../wp-content/papercite-data/data/schoellig-springer14-files.zip},
urlslides={../../wp-content/papercite-data/slides/schoellig-springer14-slides.pdf},
urllink = {http://www.tiny.cc/MusicInMotionSite},
urlvideo={https://www.youtube.com/playlist?list=PLD6AAACCBFFE64AC5},
abstract = {This chapter presents a set of algorithms that enable quadrotor vehicles to "fly with the music"; that is, to perform rhythmic motions that are aligned with the beat of a given music piece.}
}

[DOI] S. Lupashin, M. Hehn, M. W. Mueller, A. P. Schoellig, and R. D’Andrea, “A platform for aerial robotics research and demonstration: The Flying Machine Arena,” Mechatronics, vol. 24, iss. 1, pp. 41-54, 2014.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [More Information]

The Flying Machine Arena is a platform for experiments and demonstrations with fleets of small flying vehicles. It utilizes a distributed, modular architecture linked by robust communication layers. An estimation and control framework along with built-in system protection components enable prototyping of new control systems concepts and implementation of novel demonstrations. More recently, a mobile version has been featured at several eminent public events. We describe the architecture of the Arena from the viewpoint of system robustness and its capability as a dual-purpose research and demonstration platform.

@ARTICLE{lupashin-mech14,
author = {Sergei Lupashin and Markus Hehn and Mark W. Mueller and Angela P. Schoellig and Raffaello D'Andrea},
title = {A platform for aerial robotics research and demonstration: {The Flying Machine Arena}},
journal = {{Mechatronics}},
volume = {24},
number = {1},
pages = {41-54},
year = {2014},
doi = {10.1016/j.mechatronics.2013.11.006},
urllink = {http://flyingmachinearena.org/},
urlvideo={https://youtu.be/pcgvWhu8Arc?list=PLuLKX4lDsLIaVjdGsZxNBKLcogBnVVFQr},
abstract = {The Flying Machine Arena is a platform for experiments and demonstrations with fleets of small flying vehicles. It utilizes a distributed, modular architecture linked by robust communication layers. An estimation and control framework along with built-in system protection components enable prototyping of new control systems concepts and implementation of novel demonstrations. More recently, a mobile version has been featured at several eminent public events. We describe the architecture of the Arena from the viewpoint of system robustness and its capability as a dual-purpose research and demonstration platform.}
}

2013

[DOI] A. P. Schoellig, “Improving tracking performance by learning from past data,” PhD Thesis, Diss. ETH No. 20593, Institute for Dynamic Systems and Control, ETH Zurich, Switzerland, 2013. Awards: ETH Medal, Dimitris N. Chorafas Foundation Prize.
[View BibTeX] [Download Abstract] [Download PDF] [View Video] [View 2nd Video] [Download Slides]
@PHDTHESIS{schoellig-eth13,
author = {Angela P. Schoellig},
title = {Improving tracking performance by learning from past data},
school = {Diss. ETH No. 20593, Institute for Dynamic Systems and Control, ETH Zurich},
doi = {10.3929/ethz-a-009758916},
year = {2013},
address = {Switzerland},
urlabstract = {../../wp-content/papercite-data/pdf/schoellig-eth13-abstract.pdf},
urlslides = {../../wp-content/papercite-data/slides/schoellig-eth13-slides.pdf},
urlvideo = {https://youtu.be/zHTCsSkmADo?list=PLC12E387419CEAFF2},
urlvideo2 = {https://youtu.be/7r281vgfotg?list=PLD6AAACCBFFE64AC5},
note = {Awards: ETH Medal, Dimitris N. Chorafas Foundation Prize}
}

[DOI] C. J. Ostafew, A. P. Schoellig, and T. D. Barfoot, “Visual teach and repeat, repeat, repeat: iterative learning control to improve mobile robot path tracking in challenging outdoor environments,” in Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2013, pp. 176-181.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

This paper presents a path-repeating, mobile robot controller that combines a feedforward, proportional Iterative Learning Control (ILC) algorithm with a feedback-linearized path-tracking controller to reduce path-tracking errors over repeated traverses along a reference path. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied, extreme environments. The paper presents experimental results including over 600 m of travel by a four-wheeled, 50 kg robot travelling through challenging terrain including steep hills and sandy turns and by a six-wheeled, 160 kg robot at gradually-increased speeds up to three times faster than the nominal, safe speed. In the absence of a global localization system, ILC is demonstrated to reduce path-tracking errors caused by unmodelled robot dynamics and terrain challenges.

@INPROCEEDINGS{ostafew-iros13,
author = {Chris J. Ostafew and Angela P. Schoellig and Timothy D. Barfoot},
title = {Visual teach and repeat, repeat, repeat: Iterative learning control to improve mobile robot path tracking in challenging outdoor environments},
booktitle = {{Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
pages = {176-181},
year = {2013},
doi = {10.1109/IROS.2013.6696350},
urlvideo = {https://youtu.be/08_d1HSPADA?list=PLC12E387419CEAFF2},
abstract = {This paper presents a path-repeating, mobile robot controller that combines a feedforward, proportional Iterative Learning Control (ILC) algorithm with a feedback-linearized path-tracking controller to reduce path-tracking errors over repeated traverses along a reference path. Localization for the controller is provided by an on-board, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied, extreme environments. The paper presents experimental results including over 600 m of travel by a four-wheeled, 50 kg robot travelling through challenging terrain including steep hills and sandy turns and by a six-wheeled, 160 kg robot at gradually-increased speeds up to three times faster than the nominal, safe speed. In the absence of a global localization system, ILC is demonstrated to reduce path-tracking errors caused by unmodelled robot dynamics and terrain challenges.}
}

[DOI] F. Augugliaro, A. P. Schoellig, and R. D’Andrea, “Dance of the flying machines: methods for designing and executing an aerial dance choreography,” IEEE Robotics Automation Magazine, vol. 20, iss. 4, pp. 96-104, 2013.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides]

Imagine a troupe of dancers flying together across a big open stage, their movement choreographed to the rhythm of the music. Their performance is both coordinated and skilled; the dancers are well rehearsed, and the choreography well suited to their abilities. They are no ordinary dancers, however, and this is not an ordinary stage. The performers are quadrocopters, and the stage is the ETH Zurich Flying Machine Arena, a state-of-the-art mobile testbed for aerial motion control research.

@ARTICLE{augugliaro-ram13,
author = {Federico Augugliaro and Angela P. Schoellig and Raffaello D'Andrea},
title = {Dance of the Flying Machines: Methods for Designing and Executing an Aerial Dance Choreography},
journal = {{IEEE Robotics Automation Magazine}},
volume = {20},
number = {4},
pages = {96-104},
year = {2013},
doi = {10.1109/MRA.2013.2275693},
urlvideo={http://youtu.be/NRL_1ozDQCA?t=21s},
urlslides={../../wp-content/papercite-data/slides/augugliaro-ram13-slides.pdf},
abstract = {Imagine a troupe of dancers flying together across a big open stage, their movement choreographed to the rhythm of the music. Their performance is both coordinated and skilled; the dancers are well rehearsed, and the choreography well suited to their abilities. They are no ordinary dancers, however, and this is not an ordinary stage. The performers are quadrocopters, and the stage is the ETH Zurich Flying Machine Arena, a state-of-the-art mobile testbed for aerial motion control research.}
}

2012

[DOI] A. P. Schoellig, C. Wiltsche, and R. D’Andrea, “Feed-forward parameter identification for precise periodic quadrocopter motions,” in Proc. of the American Control Conference (ACC), 2012, pp. 4313-4318.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides]
This paper presents an approach for precisely tracking periodic trajectories with a quadrocopter. In order to improve temporal and spatial tracking performance, we propose a feed-forward strategy that adapts the motion parameters sent to the vehicle controller. The motion parameters are either adjusted on the fly or, in order to avoid initial transients, identified prior to the flight performance. We outline an identification scheme that tunes parameters for a large class of periodic motions, and requires only a small number of identification experiments prior to flight. This reduced identification is based on analysis and experiments showing that the quadrocopter’s closed-loop dynamics can be approximated by three directionally decoupled linear systems. We show the effectiveness of this approach by performing a sequence of periodic motions on real quadrocopters using the tuned parameters obtained by the reduced identification.

@INPROCEEDINGS{schoellig-acc12,
author = {Angela P. Schoellig and Clemens Wiltsche and Raffaello D'Andrea},
title = {Feed-forward parameter identification for precise periodic quadrocopter motions},
booktitle = {{Proc. of the American Control Conference (ACC)}},
pages = {4313-4318},
year = {2012},
doi = {10.1109/ACC.2012.6315248},
urlvideo = {http://tiny.cc/MusicInMotion},
urlslides = {../../wp-content/papercite-data/slides/schoellig-acc12-slides.pdf},
abstract = {This paper presents an approach for precisely tracking periodic trajectories with a quadrocopter. In order to improve temporal and spatial tracking performance, we propose a feed-forward strategy that adapts the motion parameters sent to the vehicle controller. The motion parameters are either adjusted on the fly or, in order to avoid initial transients, identified prior to the flight performance. We outline an identification scheme that tunes parameters for a large class of periodic motions, and requires only a small number of identification experiments prior to flight. This reduced identification is based on analysis and experiments showing that the quadrocopter's closed-loop dynamics can be approximated by three directionally decoupled linear systems. We show the effectiveness of this approach by performing a sequence of periodic motions on real quadrocopters using the tuned parameters obtained by the reduced identification.}
}

A. P. Schoellig, F. L. Mueller, and R. D’Andrea, “Quadrocopter slalom learning”, Video Submission, AI and Robotics Multimedia Fair, Conference on Artificial Intelligence (AI), Assn. of the Advancement of Artificial Intelligence (AAAI), 2012.
[View BibTeX] [View Video]

@MISC{schoellig-aaai12,
author = {Angela P. Schoellig and Fabian L. Mueller and Raffaello D'Andrea},
title = {Quadrocopter Slalom Learning},
howpublished = {Video Submission, AI and Robotics Multimedia Fair, Conference on Artificial Intelligence (AI), Assn. of the Advancement of Artificial Intelligence (AAAI)},
urlvideo = {https://youtu.be/zHTCsSkmADo?list=PLC12E387419CEAFF2},
year = {2012},
}

[DOI] F. L. Mueller, A. P. Schoellig, and R. D’Andrea, “Iterative learning of feed-forward corrections for high-performance tracking,” in Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2012, pp. 3276-3281.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides]

We revisit a recently developed iterative learning algorithm that enables systems to learn from a repeated operation with the goal of achieving high tracking performance of a given trajectory. The learning scheme is based on a coarse dynamics model of the system and uses past measurements to iteratively adapt the feed-forward input signal to the system. The novelty of this work is an identification routine that uses a numerical simulation of the system dynamics to extract the required model information. This allows the learning algorithm to be applied to any dynamic system for which a dynamics simulation is available (including systems with underlying feedback loops). The proposed learning algorithm is applied to a quadrocopter system that is guided by a trajectory-following controller. With the identification routine, we are able to extend our previous learning results to three-dimensional quadrocopter motions and achieve significantly higher tracking accuracy due to the underlying feedback control, which accounts for non-repetitive noise.

@INPROCEEDINGS{mueller-iros12,
author = {Fabian L. Mueller and Angela P. Schoellig and Raffaello D'Andrea},
title = {Iterative learning of feed-forward corrections for high-performance tracking},
booktitle = {{Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
pages = {3276-3281},
year = {2012},
doi = {10.1109/IROS.2012.6385647},
urlvideo = {https://youtu.be/zHTCsSkmADo?list=PLC12E387419CEAFF2},
urlslides = {../../wp-content/papercite-data/slides/mueller-iros12-slides.pdf},
abstract = {We revisit a recently developed iterative learning algorithm that enables systems to learn from a repeated operation with the goal of achieving high tracking performance of a given trajectory. The learning scheme is based on a coarse dynamics model of the system and uses past measurements to iteratively adapt the feed-forward input signal to the system. The novelty of this work is an identification routine that uses a numerical simulation of the system dynamics to extract the required model information. This allows the learning algorithm to be applied to any dynamic system for which a dynamics simulation is available (including systems with underlying feedback loops). The proposed learning algorithm is applied to a quadrocopter system that is guided by a trajectory-following controller. With the identification routine, we are able to extend our previous learning results to three-dimensional quadrocopter motions and achieve significantly higher tracking accuracy due to the underlying feedback control, which accounts for non-repetitive noise.}
}

[DOI] F. Augugliaro, A. P. Schoellig, and R. D’Andrea, “Generation of collision-free trajectories for a quadrocopter fleet: a sequential convex programming approach,” in Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2012, pp. 1917-1922.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

This paper presents an algorithm that generates collision-free trajectories in three dimensions for multiple vehicles within seconds. The problem is cast as a non-convex optimization problem, which is iteratively solved using sequential convex programming that approximates non-convex constraints by using convex ones. The method generates trajectories that account for simple dynamics constraints and is thus independent of the vehicle’s type. An extensive a posteriori vehicle-specific feasibility check is included in the algorithm. The algorithm is applied to a quadrocopter fleet. Experimental results are shown.

@INPROCEEDINGS{augugliaro-iros12,
author = {Federico Augugliaro and Angela P. Schoellig and Raffaello D'Andrea},
title = {Generation of collision-free trajectories for a quadrocopter fleet: A sequential convex programming approach},
booktitle = {{Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
pages = {1917-1922},
year = {2012},
doi = {10.1109/IROS.2012.6385823},
urlvideo = {https://youtu.be/wwK7WvvUvlI?list=PLD6AAACCBFFE64AC5},
abstract = {This paper presents an algorithm that generates collision-free trajectories in three dimensions for multiple vehicles within seconds. The problem is cast as a non-convex optimization problem, which is iteratively solved using sequential convex programming that approximates non-convex constraints by using convex ones. The method generates trajectories that account for simple dynamics constraints and is thus independent of the vehicle's type. An extensive a posteriori vehicle-specific feasibility check is included in the algorithm. The algorithm is applied to a quadrocopter fleet. Experimental results are shown.}
}

[DOI] A. P. Schoellig, J. Alonso-Mora, and R. D’Andrea, “Limited benefit of joint estimation in multi-agent iterative learning,” Asian Journal of Control, vol. 14, iss. 3, pp. 613-623, 2012.
[View BibTeX] [View Abstract] [Download PDF] [Download Additional Material] [Download Slides]

This paper studies iterative learning control (ILC) in a multi-agent framework, wherein a group of agents simultaneously and repeatedly perform the same task. Assuming similarity between the agents, we investigate whether exchanging information between the agents improves an individual’s learning performance. That is, does an individual agent benefit from the experience of the other agents? We consider the multi-agent iterative learning problem as a two-step process of: first, estimating the repetitive disturbance of each agent; and second, correcting for it. We present a comparison of an agent’s disturbance estimate in the case of (I) independent estimation, where each agent has access only to its own measurement, and (II) joint estimation, where information of all agents is globally accessible. When the agents are identical and noise comes from measurement only, joint estimation yields a noticeable improvement in performance. However, when process noise is encountered or when the agents have an individual disturbance component, the benefit of joint estimation is negligible.

@ARTICLE{schoellig-ajc12,
author = {Angela P. Schoellig and Javier Alonso-Mora and Raffaello D'Andrea},
title = {Limited benefit of joint estimation in multi-agent iterative learning},
journal = {{Asian Journal of Control}},
volume = {14},
number = {3},
pages = {613-623},
year = {2012},
doi = {10.1002/asjc.398},
urldata={../../wp-content/papercite-data/data/schoellig-ajc12-files.zip},
urlslides={../../wp-content/papercite-data/slides/schoellig-ajc12-slides.pdf},
abstract = {This paper studies iterative learning control (ILC) in a multi-agent framework, wherein a group of agents simultaneously and repeatedly perform the same task. Assuming similarity between the agents, we investigate whether exchanging information between the agents improves an individual's learning performance. That is, does an individual agent benefit from the experience of the other agents? We consider the multi-agent iterative learning problem as a two-step process of: first, estimating the repetitive disturbance of each agent; and second, correcting for it. We present a comparison of an agent's disturbance estimate in the case of (I) independent estimation, where each agent has access only to its own measurement, and (II) joint estimation, where information of all agents is globally accessible. When the agents are identical and noise comes from measurement only, joint estimation yields a noticeable improvement in performance. However, when process noise is encountered or when the agents have an individual disturbance component, the benefit of joint estimation is negligible.}
}

[DOI] A. P. Schoellig, F. L. Mueller, and R. D’Andrea, “Optimization-based iterative learning for precise quadrocopter trajectory tracking,” Autonomous Robots, vol. 33, iss. 1-2, pp. 103-127, 2012.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

Current control systems regulate the behavior of dynamic systems by reacting to noise and unexpected disturbances as they occur. To improve the performance of such control systems, experience from iterative executions can be used to anticipate recurring disturbances and proactively compensate for them. This paper presents an algorithm that exploits data from previous repetitions in order to learn to precisely follow a predefined trajectory. We adapt the feed-forward input signal to the system with the goal of achieving high tracking performance – even under the presence of model errors and other recurring disturbances. The approach is based on a dynamics model that captures the essential features of the system and that explicitly takes system input and state constraints into account. We combine traditional optimal filtering methods with state-of-the-art optimization techniques in order to obtain an effective and computationally efficient learning strategy that updates the feed-forward input signal according to a customizable learning objective. It is possible to define a termination condition that stops an execution early if the deviation from the nominal trajectory exceeds a given bound. This allows for a safe learning that gradually extends the time horizon of the trajectory. We developed a framework for generating arbitrary flight trajectories and for applying the algorithm to highly maneuverable autonomous quadrotor vehicles in the ETH Flying Machine Arena testbed. Experimental results are discussed for selected trajectories and different learning algorithm parameters.

@ARTICLE{schoellig-auro12,
author = {Angela P. Schoellig and Fabian L. Mueller and Raffaello D'Andrea},
title = {Optimization-based iterative learning for precise quadrocopter trajectory tracking},
journal = {{Autonomous Robots}},
volume = {33},
number = {1-2},
pages = {103-127},
year = {2012},
doi = {10.1007/s10514-012-9283-2},
urlvideo={http://youtu.be/goVuP5TJIUU?list=PLC12E387419CEAFF2},
abstract = {Current control systems regulate the behavior of dynamic systems by reacting to noise and unexpected disturbances as they occur. To improve the performance of such control systems, experience from iterative executions can be used to anticipate recurring disturbances and proactively compensate for them. This paper presents an algorithm that exploits data from previous repetitions in order to learn to precisely follow a predefined trajectory. We adapt the feed-forward input signal to the system with the goal of achieving high tracking performance - even under the presence of model errors and other recurring disturbances. The approach is based on a dynamics model that captures the essential features of the system and that explicitly takes system input and state constraints into account. We combine traditional optimal filtering methods with state-of-the-art optimization techniques in order to obtain an effective and computationally efficient learning strategy that updates the feed-forward input signal according to a customizable learning objective. It is possible to define a termination condition that stops an execution early if the deviation from the nominal trajectory exceeds a given bound. This allows for a safe learning that gradually extends the time horizon of the trajectory. We developed a framework for generating arbitrary flight trajectories and for applying the algorithm to highly maneuverable autonomous quadrotor vehicles in the ETH Flying Machine Arena testbed. Experimental results are discussed for selected trajectories and different learning algorithm parameters.}
}

2011

[DOI] S. Lupashin, A. P. Schoellig, M. Hehn, and R. D’Andrea, “The Flying Machine Arena as of 2010″, Video Submission, in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2011.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [More Information]
The Flying Machine Arena (FMA) is an indoor research space built specifically for the study of autonomous systems and aerial robotics. In this video, we give an overview of this testbed and some of its capabilities. We show the FMA infrastructure and hardware, which includes a fleet of quadrocopters and a motion capture system for vehicle localization. The physical components of the FMA are complemented by specialized software tools and components that facilitate the use of the space and provide a unified framework for communication and control. The flexibility and modularity of the experimental platform is highlighted by various research projects and demonstrations.

@MISC{lupashin-icra11,
author = {Sergei Lupashin and Angela P. Schoellig and Markus Hehn and Raffaello D'Andrea},
title = {The {Flying Machine Arena} as of 2010},
howpublished = {Video Submission, in Proc. of the IEEE International Conference on Robotics and Automation (ICRA)},
year = {2011},
pages = {2970-2971},
doi = {10.1109/ICRA.2011.5980308},
urlvideo = {https://youtu.be/pcgvWhu8Arc?list=PLuLKX4lDsLIaVjdGsZxNBKLcogBnVVFQr},
urllink = {http://www.flyingmachinearena.org},
abstract = {The Flying Machine Arena (FMA) is an indoor research space built specifically for the study of autonomous systems and aerial robotics. In this video, we give an overview of this testbed and some of its capabilities. We show the FMA infrastructure and hardware, which includes a fleet of quadrocopters and a motion capture system for vehicle localization. The physical components of the FMA are complemented by specialized software tools and components that facilitate the use of the space and provide a unified framework for communication and control. The flexibility and modularity of the experimental platform is highlighted by various research projects and demonstrations.},
}

[DOI] A. P. Schoellig, M. Hehn, S. Lupashin, and R. D’Andrea, “Feasibility of motion primitives for choreographed quadrocopter flight,” in Proc. of the American Control Conference (ACC), 2011, pp. 3843-3849.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Additional Material] [Download Slides]

This paper describes a method for checking the feasibility of quadrocopter motions. The approach, meant as a validation tool for preprogrammed quadrocopter performances, is based on first principles models and ensures that a desired trajectory respects both vehicle dynamics and motor thrust limits. We apply this method towards the eventual goal of using parameterized motion primitives for expressive quadrocopter choreographies. First, we show how a large class of motion primitives can be formulated as truncated Fourier series. We then show how the feasibility check can be applied to such motions by deriving explicit parameter constraints for two particular parameterized primitives. The predicted feasibility constraints are compared against experimental results from quadrocopters in the ETH Flying Machine Arena.

@INPROCEEDINGS{schoellig-acc11,
author = {Angela P. Schoellig and Markus Hehn and Sergei Lupashin and Raffaello D'Andrea},
title = {Feasibility of motion primitives for choreographed quadrocopter flight},
booktitle = {{Proc. of the American Control Conference (ACC)}},
pages = {3843-3849},
year = {2011},
doi = {10.1109/ACC.2011.5991482},
urlvideo = {https://www.youtube.com/playlist?list=PLD6AAACCBFFE64AC5},
urlslides = {../../wp-content/papercite-data/slides/schoellig-acc11-slides.pdf},
urldata = {../../wp-content/papercite-data/data/schoellig-acc11-files.pdf},
abstract = {This paper describes a method for checking the feasibility of quadrocopter motions. The approach, meant as a validation tool for preprogrammed quadrocopter performances, is based on first principles models and ensures that a desired trajectory respects both vehicle dynamics and motor thrust limits. We apply this method towards the eventual goal of using parameterized motion primitives for expressive quadrocopter choreographies. First, we show how a large class of motion primitives can be formulated as truncated Fourier series. We then show how the feasibility check can be applied to such motions by deriving explicit parameter constraints for two particular parameterized primitives. The predicted feasibility constraints are compared against experimental results from quadrocopters in the ETH Flying Machine Arena.}
}

[DOI] A. P. Schoellig and R. D’Andrea, “Sensitivity of joint estimation in multi-agent iterative learning control,” in Proc. of the IFAC (International Federation of Automatic Control) World Congress, 2011, pp. 1204-1212.
[View BibTeX] [View Abstract] [Download PDF] [Download Additional Material] [Download Slides]

We consider a group of agents that simultaneously learn the same task, and revisit a previously developed algorithm, where agents share their information and learn jointly. We have already shown that, as compared to an independent learning model that disregards the information of the other agents, and when assuming similarity between the agents, a joint algorithm improves the learning performance of an individual agent. We now revisit the joint learning algorithm to determine its sensitivity to the underlying assumption of similarity between agents. We note that an incorrect assumption about the agents’ degree of similarity degrades the performance of the joint learning scheme. The degradation is particularly acute if we assume that the agents are more similar than they are in reality; in this case, a joint learning scheme can result in a poorer performance than the independent learning algorithm. In the worst case (when we assume that the agents are identical, but they are, in reality, not) the joint learning does not even converge to the correct value. We conclude that, when applying the joint algorithm, it is crucial not to overestimate the similarity of the agents; otherwise, a learning scheme that is independent of the similarity assumption is preferable.

@INPROCEEDINGS{schoellig-ifac11,
author = {Angela P. Schoellig and Raffaello D'Andrea},
title = {Sensitivity of joint estimation in multi-agent iterative learning control},
booktitle = {{Proc. of the IFAC (International Federation of Automatic Control) World Congress}},
pages = {1204-1212},
year = {2011},
doi = {10.3182/20110828-6-IT-1002.03687},
urlslides = {../../wp-content/papercite-data/slides/schoellig-ifac11-slides.pdf},
urldata = {../../wp-content/papercite-data/data/schoellig-ifac11-files.pdf},
abstract = {We consider a group of agents that simultaneously learn the same task, and revisit a previously developed algorithm, where agents share their information and learn jointly. We have already shown that, as compared to an independent learning model that disregards the information of the other agents, and when assuming similarity between the agents, a joint algorithm improves the learning performance of an individual agent. We now revisit the joint learning algorithm to determine its sensitivity to the underlying assumption of similarity between agents. We note that an incorrect assumption about the agents' degree of similarity degrades the performance of the joint learning scheme. The degradation is particularly acute if we assume that the agents are more similar than they are in reality; in this case, a joint learning scheme can result in a poorer performance than the independent learning algorithm. In the worst case (when we assume that the agents are identical, but they are, in reality, not) the joint learning does not even converge to the correct value. We conclude that, when applying the joint algorithm, it is crucial not to overestimate the similarity of the agents; otherwise, a learning scheme that is independent of the similarity assumption is preferable.}
}

2010

[DOI] A. P. Schoellig, F. Augugliaro, and R. D’Andrea, “Synchronizing the motion of a quadrocopter to music,” in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2010, pp. 3355-3360.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides]
This paper presents a quadrocopter flying in rhythm to music. The quadrocopter performs a periodic side-to-side motion in time to a musical beat. Underlying controllers are designed that stabilize the vehicle and produce a swinging motion. Synchronization is then achieved by using concepts from phase-locked loops. A phase comparator combined with a correction algorithm eliminate the phase error between the music reference and the actual quadrocopter motion. Experimental results show fast and effective synchronization that is robust to sudden changes in the reference amplitude and frequency. Changes in frequency and amplitude are tracked precisely when adding an additional feedforward component, based on an experimentally determined look-up table.

@INPROCEEDINGS{schoellig-icra10,
author = {Angela P. Schoellig and Federico Augugliaro and Raffaello D'Andrea},
title = {Synchronizing the motion of a quadrocopter to music},
booktitle = {{Proc. of the IEEE International Conference on Robotics and Automation (ICRA)}},
pages = {3355-3360},
year = {2010},
doi = {10.1109/ROBOT.2010.5509755},
urlslides = {../../wp-content/papercite-data/slides/schoellig-icra10-slides.pdf},
urlvideo = {https://youtu.be/Kx4DtXv_bPo?list=PLD6AAACCBFFE64AC5},
abstract = {This paper presents a quadrocopter flying in rhythm to music. The quadrocopter performs a periodic side-to-side motion in time to a musical beat. Underlying controllers are designed that stabilize the vehicle and produce a swinging motion. Synchronization is then achieved by using concepts from phase-locked loops. A phase comparator combined with a correction algorithm eliminate the phase error between the music reference and the actual quadrocopter motion. Experimental results show fast and effective synchronization that is robust to sudden changes in the reference amplitude and frequency. Changes in frequency and amplitude are tracked precisely when adding an additional feedforward component, based on an experimentally determined look-up table.}
}

A. P. Schoellig, F. Augugliaro, and R. D’Andrea, “A platform for dance performances with multiple quadrocopters,” in Proc. of the Workshop on Robots and Musical Expressions at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2010, pp. 1-8.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [View 2nd Video] [Download Slides]

This paper presents a platform for rhythmic flight with multiple quadrocopters. We envision an expressive multimedia dance performance that is automatically composed and controlled, given a random piece of music. Results in this paper prove the feasibility of audio-motion synchronization when precisely timing the side-to-side motion of a quadrocopter to the beat of the music. An illustration of the indoor flight space and the vehicles shows the characteristics and capabilities of the experimental setup. Prospective features of the platform are outlined and key challenges are emphasized. The paper concludes with a proof-of-concept demonstration showing three vehicles synchronizing their side-to-side motion to the music beat. Moreover, a dance performance to a remix of the sound track ‘Pirates of the Caribbean’ gives a first impression of the novel musical experience. Future steps include an appropriate multiscale music analysis and the development of algorithms for the automated generation of choreography based on a database of motion primitives.

@INPROCEEDINGS{schoellig-iros10,
author = {Angela P. Schoellig and Federico Augugliaro and Raffaello D'Andrea},
title = {A platform for dance performances with multiple quadrocopters},
booktitle = {{Proc. of the Workshop on Robots and Musical Expressions at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
pages = {1-8},
year = {2010},
urlvideo = {https://youtu.be/aaaGJKnJdrg?list=PLD6AAACCBFFE64AC5},
urlvideo2 = {https://www.youtube.com/playlist?list=PLD6AAACCBFFE64AC5},
urlslides = {../../wp-content/papercite-data/slides/schoellig-iros10-slides.pdf},
abstract = {This paper presents a platform for rhythmic flight with multiple quadrocopters. We envision an expressive multimedia dance performance that is automatically composed and controlled, given a random piece of music. Results in this paper prove the feasibility of audio-motion synchronization when precisely timing the side-to-side motion of a quadrocopter to the beat of the music. An illustration of the indoor flight space and the vehicles shows the characteristics and capabilities of the experimental setup. Prospective features of the platform are outlined and key challenges are emphasized. The paper concludes with a proof-of-concept demonstration showing three vehicles synchronizing their side-to-side motion to the music beat. Moreover, a dance performance to a remix of the sound track 'Pirates of the Caribbean' gives a first impression of the novel musical experience. Future steps include an appropriate multiscale music analysis and the development of algorithms for the automated generation of choreography based on a database of motion primitives.}
}

[DOI] A. P. Schoellig, J. Alonso-Mora, and R. D’Andrea, “Independent vs. joint estimation in multi-agent iterative learning control,” in Proc. of the IEEE Conference on Decision and Control (CDC), 2010, pp. 6949-6954.
[View BibTeX] [View Abstract] [Download PDF] [Download Additional Material] [Download Slides]

This paper studies iterative learning control (ILC) in a multi-agent framework, wherein a group of agents simultaneously and repeatedly perform the same task. The agents improve their performance by using the knowledge gained from previous executions. Assuming similarity between the agents, we investigate whether exchanging information between the agents improves an individual’s learning performance. That is, does an individual agent benefit from the experience of the other agents? We consider the multi-agent iterative learning problem as a two-step process of: first, estimating the repetitive disturbance of each agent; and second, correcting for it. We present a comparison of an agent’s disturbance estimate in the case of (I) independent estimation, where each agent has access only to its own measurement, and (II) joint estimation, where information of all agents is globally accessible. We analytically derive an upper bound of the performance improvement due to joint estimation. Results are obtained for two limiting cases: (i) pure process noise, and (ii) pure measurement noise. The benefits of information sharing are negligible in (i). For (ii), a performance improvement is observed when a high similarity between the agents is guaranteed.

@INPROCEEDINGS{schoellig-cdc10,
author = {Angela P. Schoellig and Javier Alonso-Mora and Raffaello D'Andrea},
title = {Independent vs. joint estimation in multi-agent iterative learning control},
booktitle = {{Proc. of the IEEE Conference on Decision and Control (CDC)}},
pages = {6949-6954},
year = {2010},
doi = {10.1109/CDC.2010.5717888},
urlslides = {../../wp-content/papercite-data/slides/schoellig-cdc10-slides.pdf},
urldata = {../../wp-content/papercite-data/data/schoellig-cdc10-files.pdf},
abstract = {This paper studies iterative learning control (ILC) in a multi-agent framework, wherein a group of agents simultaneously and repeatedly perform the same task. The agents improve their performance by using the knowledge gained from previous executions. Assuming similarity between the agents, we investigate whether exchanging information between the agents improves an individual's learning performance. That is, does an individual agent benefit from the experience of the other agents? We consider the multi-agent iterative learning problem as a two-step process of: first, estimating the repetitive disturbance of each agent; and second, correcting for it. We present a comparison of an agent's disturbance estimate in the case of (I) independent estimation, where each agent has access only to its own measurement, and (II) joint estimation, where information of all agents is globally accessible. We analytically derive an upper bound of the performance improvement due to joint estimation. Results are obtained for two limiting cases: (i) pure process noise, and (ii) pure measurement noise. The benefits of information sharing are negligible in (i). For (ii), a performance improvement is observed when a high similarity between the agents is guaranteed.}
}

[DOI] S. Lupashin, A. P. Schoellig, M. Sherback, and R. D’Andrea, “A simple learning strategy for high-speed quadrocopter multi-flips,” in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2010, pp. 1642-1648.
[View BibTeX] [View Abstract] [Download PDF] [View Video]

We describe a simple and intuitive policy gradient method for improving parametrized quadrocopter multi-flips by combining iterative experiments with information from a first-principles model. We start by formulating an N-flip maneuver as a five-step primitive with five adjustable parameters. Optimization using a low-order first-principles 2D vertical plane model of the quadrocopter yields an initial set of parameters and a corrective matrix. The maneuver is then repeatedly performed with the vehicle. At each iteration the state error at the end of the primitive is used to update the maneuver parameters via a gradient adjustment. The method is demonstrated at the ETH Zurich Flying Machine Arena testbed on quadrotor helicopters performing and improving on flips, double flips and triple flips.

@INPROCEEDINGS{lupashin-icra10,
author = {Sergei Lupashin and Angela P. Schoellig and Michael Sherback and Raffaello D'Andrea},
title = {A simple learning strategy for high-speed quadrocopter multi-flips},
booktitle = {{Proc. of the IEEE International Conference on Robotics and Automation (ICRA)}},
pages = {1642-1648},
year = {2010},
doi = {10.1109/ROBOT.2010.5509452},
urlvideo = {https://youtu.be/bWExDW9J9sA?list=PLC12E387419CEAFF2},
abstract = {We describe a simple and intuitive policy gradient method for improving parametrized quadrocopter multi-flips by combining iterative experiments with information from a first-principles model. We start by formulating an N-flip maneuver as a five-step primitive with five adjustable parameters. Optimization using a low-order first-principles 2D vertical plane model of the quadrocopter yields an initial set of parameters and a corrective matrix. The maneuver is then repeatedly performed with the vehicle. At each iteration the state error at the end of the primitive is used to update the maneuver parameters via a gradient adjustment. The method is demonstrated at the ETH Zurich Flying Machine Arena testbed on quadrotor helicopters performing and improving on flips, double flips and triple flips.}
}

2009

A. P. Schoellig and R. D’Andrea, “Optimization-based iterative learning control for trajectory tracking,” in Proc. of the European Control Conference (ECC), 2009, pp. 1505-1510.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides] [More Information]
In this paper, an optimization-based iterative learning control approach is presented. Given a desired trajectory to be followed, the proposed learning algorithm improves the system performance from trial to trial by exploiting the experience gained from previous repetitions. Taking advantage of the a-priori knowledge about the systems dominating dynamics, a data-based update rule is derived which adapts the feedforward input signal after each trial. By combining traditional model-based optimal filtering methods with state-of-the-art optimization techniques such as convex programming, an effective and computationally highly efficient learning strategy is obtained. Moreover, the derived formalism allows for the direct treatment of input and state constraints. Different (nonlinear) performance objectives can be specified defining the overall learning behavior. Finally, the proposed algorithm is successfully applied to the benchmark problem of swinging up a pendulum using open-loop control only.

@INPROCEEDINGS{schoellig-ecc09,
author = {Angela P. Schoellig and Raffaello D'Andrea},
title = {Optimization-based iterative learning control for trajectory tracking},
booktitle = {{Proc. of the European Control Conference (ECC)}},
pages = {1505-1510},
year = {2009},
urlslides = {../../wp-content/papercite-data/slides/schoellig-ecc09-slides.pdf},
urllink = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7074619},
urlvideo = {https://youtu.be/W2gCn6aAwz4?list=PLC12E387419CEAFF2},
abstract = {In this paper, an optimization-based iterative learning control approach is presented. Given a desired trajectory to be followed, the proposed learning algorithm improves the system performance from trial to trial by exploiting the experience gained from previous repetitions. Taking advantage of the a-priori knowledge about the systems dominating dynamics, a data-based update rule is derived which adapts the feedforward input signal after each trial. By combining traditional model-based optimal filtering methods with state-of-the-art optimization techniques such as convex programming, an effective and computationally highly efficient learning strategy is obtained. Moreover, the derived formalism allows for the direct treatment of input and state constraints. Different (nonlinear) performance objectives can be specified defining the overall learning behavior. Finally, the proposed algorithm is successfully applied to the benchmark problem of swinging up a pendulum using open-loop control only.}
}

2008

A. P. Schoellig and R. D’Andrea, “Learning through experience — Optimizing performance by repetition”, Abstract and Poster, in Proc. of the Robotics Challenges for Machine Learning Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2008.
[View BibTeX] [View Abstract] [Download PDF] [View Video] [Download Slides] [More Information]
The goal of our research is to develop a strategy which enables a system, executing the same task multiple times, to use the knowledge of the previous trials to learn more about its own dynamics and enhance its future performance. Our approach, which falls in the field of iterative learning control, combines methods from both areas, traditional model-based estimation and control and purely data-based learning.

@MISC{schoellig-iros08,
author = {Angela P. Schoellig and Raffaello D'Andrea},
title = {Learning through experience -- {O}ptimizing performance by repetition},
howpublished = {Abstract and Poster, in Proc. of the Robotics Challenges for Machine Learning Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
year = {2008},
urlvideo = {https://youtu.be/W2gCn6aAwz4?list=PLC12E387419CEAFF2},
urlslides = {../../wp-content/papercite-data/slides/schoellig-iros08-slides.pdf},
urllink = {http://www.learning-robots.de/pmwiki.php/TC/IROS2008},
abstract = {The goal of our research is to develop a strategy which enables a system, executing the same task multiple times, to use the knowledge of the previous trials to learn more about its own dynamics and enhance its future performance. Our approach, which falls in the field of iterative learning control, combines methods from both areas, traditional model-based estimation and control and purely data-based learning.},
}

P. F. Gath, D. Weise, T. Heinrich, A. P. Schoellig, and S. Otte, “Verification of the performance of selected subsystems for the LISA mission (in German),” in Proc. of the German Aerospace Congress, German Society for Aeronautics and Astronautics (DGLR), 2008.
[View BibTeX] [View Abstract] [Download PDF]

Im Rahmen der Untersuchung zur Systemleistung alternativer Nutzlastkonzepte fuer die LISA Mission (Laser Interferometer Space Antenna) werden bei Astrium derzeit einzelne Untersysteme der Nutzlast auf ihre Leistungsfaehigkeit hin ueberprueft. Dies geschieht sowohl durch theoretische Untersuchungen im Rahmen von Simulationen als auch durch experimentelle Laboruntersuchungen.

@INPROCEEDINGS{gath-gac08,
author = {Peter F. Gath and Dennis Weise and Thomas Heinrich and Angela P. Schoellig and S. Otte},
title = {Verification of the performance of selected subsystems for the {LISA} mission {(in German)}},
booktitle = {{Proc. of the German Aerospace Congress, German Society for Aeronautics and Astronautics (DGLR)}},
year = {2008},
abstract = {Im Rahmen der Untersuchung zur Systemleistung alternativer Nutzlastkonzepte fuer die LISA Mission (Laser Interferometer Space Antenna) werden bei Astrium derzeit einzelne Untersysteme der Nutzlast auf ihre Leistungsfaehigkeit hin ueberprueft. Dies geschieht sowohl durch theoretische Untersuchungen im Rahmen von Simulationen als auch durch experimentelle Laboruntersuchungen.}
}

2007

A. P. Schoellig, “Optimal control of hybrid systems with regional dynamics,” Master Thesis, Georgia Institute of Technology, USA, 2007.
[View BibTeX] [View Abstract] [Download PDF] [Download Slides] [More Information]
In this work, hybrid systems with regional dynamics are considered. These are systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, the attention is focused on the optimal control problem associated with such systems. More precisely, given a specific cost function, the goal is to determine the optimal path of going from a given starting point to a fixed final state during an a priori specified time horizon. The key characteristic of the approach presented in this thesis is a hierarchical decomposition of the hybrid optimal control problem, yielding to a framework which allows a solution on different levels of control. On the highest level of abstraction, the regional structure of the state space is taken into account and a discrete representation of the connections between the different regions provides global accessibility relations between regions. These are used on a lower level of control to formulate the main theorem of this work, namely, the Hybrid Bellman Equation for multimodal systems, which, in fact, provides a characterization of global optimality, given an upper bound on the number of transitions along a hybrid trajectory. Not surprisingly, the optimal solution is hybrid in nature, in that it depends on not only the continuous control signals, but also on discrete decisions as to what domains the system’s continuous state should go through in the first place. The main benefit with the proposed approach lies in the fact that a hierarchical Dynamic Programming algorithm can be used to representing both a theoretical characterization of the hybrid solution’s structural composition and, from a more application-driven point of view, a numerically implementable calculation rule yielding to globally optimal solutions in a regional dynamics framework. The operation of the recursive algorithm is highlighted by the consideration of numerous examples, among them, a heterogeneous multi-agent problem.

@MASTERSTHESIS{schoellig-gatech07,
author = {Angela P. Schoellig},
title = {Optimal control of hybrid systems with regional dynamics},
school = {Georgia Institute of Technology},
urllink = {http://hdl.handle.net/1853/19874},
urlslides = {../../wp-content/papercite-data/slides/schoellig-gatech07-slides.pdf},
year = {2007},
address = {USA},
abstract = {In this work, hybrid systems with regional dynamics are considered. These are systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, the attention is focused on the optimal control problem associated with such systems. More precisely, given a specific cost function, the goal is to determine the optimal path of going from a given starting point to a fixed final state during an a priori specified time horizon. The key characteristic of the approach presented in this thesis is a hierarchical decomposition of the hybrid optimal control problem, yielding to a framework which allows a solution on different levels of control. On the highest level of abstraction, the regional structure of the state space is taken into account and a discrete representation of the connections between the different regions provides global accessibility relations between regions. These are used on a lower level of control to formulate the main theorem of this work, namely, the Hybrid Bellman Equation for multimodal systems, which, in fact, provides a characterization of global optimality, given an upper bound on the number of transitions along a hybrid trajectory. Not surprisingly, the optimal solution is hybrid in nature, in that it depends on not only the continuous control signals, but also on discrete decisions as to what domains the system's continuous state should go through in the first place. The main benefit with the proposed approach lies in the fact that a hierarchical Dynamic Programming algorithm can be used to representing both a theoretical characterization of the hybrid solution's structural composition and, from a more application-driven point of view, a numerically implementable calculation rule yielding to globally optimal solutions in a regional dynamics framework. The operation of the recursive algorithm is highlighted by the consideration of numerous examples, among them, a heterogeneous multi-agent problem.},
}

A. P. Schoellig, U. Münz, and F. Allgöwer, “Topology-dependent stability of a network of dynamical systems with communication delays,” in Proc. of the European Control Conference (ECC), 2007, pp. 1197-1202.
[View BibTeX] [View Abstract] [Download PDF] [More Information]

In this paper, we analyze the stability of a network of first-order linear time-invariant systems with constant, identical communication delays. We investigate the influence of both system parameters and network characteristics on stability. In particular, a non-conservative stability bound for the delay is given such that the network is asymptotically stable for any delay smaller than this bound. We show how the network topology changes the stability bound. Exemplarily, we use these results to answer the question if a symmetric or skew-symmetric interconnection is preferable for a given set of subsystems.

@INPROCEEDINGS{schoellig-ecc07,
author = {Angela P. Schoellig and Ulrich M\"unz and Frank Allg\"ower},
title = {Topology-Dependent Stability of a Network of Dynamical Systems with Communication Delays},
booktitle = {{Proc. of the European Control Conference (ECC)}},
pages = {1197-1202},
year = {2007},
urllink = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7068977},
abstract = {In this paper, we analyze the stability of a network of first-order linear time-invariant systems with constant, identical communication delays. We investigate the influence of both system parameters and network characteristics on stability. In particular, a non-conservative stability bound for the delay is given such that the network is asymptotically stable for any delay smaller than this bound. We show how the network topology changes the stability bound. Exemplarily, we use these results to answer the question if a symmetric or skew-symmetric interconnection is preferable for a given set of subsystems.}
}

[DOI] A. P. Schoellig, P. E. Caines, M. Egerstedt, and R. P. Malhamé, “A hybrid Bellman equation for systems with regional dynamics,” in Proc.\ of the IEEE Conference on Decision and Control (CDC), 2007, pp. 3393-3398.
[View BibTeX] [View Abstract] [Download PDF]

In this paper, we study hybrid systems with regional dynamics, i.e., systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, we focus our attention on the optimal control problem associated with such systems, and we present a Hybrid Bellman Equation for such systems that provide a characterization of global optimality, given an upper bound on the number of switches. Not surprisingly, the solution will be hybrid in nature in that it will depend on not only the continuous control signals, but also on discrete decisions as to what domains the system should go through in the first place. A number of examples are presented to highlight the operation of the proposed approach.

@INPROCEEDINGS{schoellig-cdc07,
author = {Angela P. Schoellig and Peter E. Caines and Magnus Egerstedt and Roland P. Malham\'e},
title = {A hybrid {B}ellman equation for systems with regional dynamics},
booktitle = {{Proc.\ of the IEEE Conference on Decision and Control (CDC)}},
pages = {3393-3398},
year = {2007},
doi = {10.1109/CDC.2007.4434952},
abstract = {In this paper, we study hybrid systems with regional dynamics, i.e., systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, we focus our attention on the optimal control problem associated with such systems, and we present a Hybrid Bellman Equation for such systems that provide a characterization of global optimality, given an upper bound on the number of switches. Not surprisingly, the solution will be hybrid in nature in that it will depend on not only the continuous control signals, but also on discrete decisions as to what domains the system should go through in the first place. A number of examples are presented to highlight the operation of the proposed approach.}
}

[DOI] P. Caines, M. Egerstedt, R. Malhame, and A. P. Schoellig, “A hybrid Bellman equation for bimodal systems,” in Hybrid Systems: Computation and Control, A. Bemporad, A. Bicchi, and G. Buttazzo, Eds., Springer Berlin Heidelberg, 2007, vol. 4416, pp. 656-659.
[View BibTeX] [View Abstract] [Download PDF]

In this paper we present a dynamic programming formulation of a hybrid optimal control problem for bimodal systems with regional dynamics. In particular, based on optimality-zone computations, a framework is presented in which the resulting hybrid Bellman equation guides the design of optimal control programs with, at most, N discrete transitions.

@INCOLLECTION{caines-springer07,
author={Peter Caines and Magnus Egerstedt and Roland Malhame and Angela P. Schoellig},
title={A Hybrid {Bellman} Equation for Bimodal Systems},
booktitle={{Hybrid Systems: Computation and Control}},
editor={Bemporad, Alberto and Bicchi, Antonio and Buttazzo, Giorgio},
publisher={Springer Berlin Heidelberg},
pages={656-659},
year={2007},
volume={4416},
series={Lecture Notes in Computer Science},
doi={10.1007/978-3-540-71493-4_54},
abstract = {In this paper we present a dynamic programming formulation of a hybrid optimal control problem for bimodal systems with regional dynamics. In particular, based on optimality-zone computations,
a framework is presented in which the resulting hybrid Bellman equation guides the design of optimal control programs with, at most, N discrete transitions.}
}

2006

A. P. Schoellig, “Stability of a network of dynamical systems with communication delays (in German),” Bachelor Thesis , University of Stuttgart, Germany, 2006.
[View BibTeX] [Download PDF] [Download Slides]
@MASTERSTHESIS{schoellig-stuttgart06,
author = {Angela P. Schoellig},
title = {Stability of a network of dynamical systems with communication delays {(in German)}},
school = {University of Stuttgart},
type = {Bachelor Thesis},
urlslides = {../../wp-content/papercite-data/slides/schoellig-stuttgart06-slides.pdf},
year = {2006},
address = {Germany},
}

University of Toronto Institute for Aerospace Studies