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82 results (View BibTeX file of all listed publications)

2017

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Multi-Modal Imitation Learning from Unstructured Demonstrations using Generative Adversarial Nets

Hausman, K., Chebotar, Y., Schaal, S., Sukhatme, G., Lim, J.

In Proceedings from the conference "Neural Information Processing Systems 2017., (Editors: Guyon I. and Luxburg U.v. and Bengio S. and Wallach H. and Fergus R. and Vishwanathan S. and Garnett R.), Curran Associates, Inc., Advances in Neural Information Processing Systems 30 (NIPS), December 2017 (inproceedings)

pdf video [BibTex]

2017

Hausman, K., Chebotar, Y., Schaal, S., Sukhatme, G., Lim, J. Multi-Modal Imitation Learning from Unstructured Demonstrations using Generative Adversarial Nets In Proceedings from the conference "Neural Information Processing Systems 2017., (Editors: Guyon I. and Luxburg U.v. and Bengio S. and Wallach H. and Fergus R. and Vishwanathan S. and Garnett R.), Curran Associates, Inc., Advances in Neural Information Processing Systems 30 (NIPS), December 2017 (inproceedings)

pdf video [BibTex]

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On the Design of LQR Kernels for Efficient Controller Learning

Marco, A., Hennig, P., Schaal, S., Trimpe, S.

Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC), pages: 5193-5200, IEEE, IEEE Conference on Decision and Control, December 2017 (conference)

Abstract
Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.

arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]

Marco, A., Hennig, P., Schaal, S., Trimpe, S. On the Design of LQR Kernels for Efficient Controller Learning Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC), pages: 5193-5200, IEEE, IEEE Conference on Decision and Control, December 2017 (conference)

arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]

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Interactive Perception: Leveraging Action in Perception and Perception in Action

Bohg, J., Hausman, K., Sankaran, B., Brock, O., Kragic, D., Schaal, S., Sukhatme, G.

IEEE Transactions on Robotics, 33, pages: 1273-1291, December 2017 (article)

Abstract
Recent approaches in robotics follow the insight that perception is facilitated by interactivity with the environment. These approaches are subsumed under the term of Interactive Perception (IP). We argue that IP provides the following benefits: (i) any type of forceful interaction with the environment creates a new type of informative sensory signal that would otherwise not be present and (ii) any prior knowledge about the nature of the interaction supports the interpretation of the signal. This is facilitated by knowledge of the regularity in the combined space of sensory information and action parameters. The goal of this survey is to postulate this as a principle and collect evidence in support by analyzing and categorizing existing work in this area. We also provide an overview of the most important applications of Interactive Perception. We close this survey by discussing the remaining open questions. Thereby, we hope to define a field and inspire future work.

arXiv DOI Project Page [BibTex]

Bohg, J., Hausman, K., Sankaran, B., Brock, O., Kragic, D., Schaal, S., Sukhatme, G. Interactive Perception: Leveraging Action in Perception and Perception in Action IEEE Transactions on Robotics, 33, pages: 1273-1291, December 2017 (article)

arXiv DOI Project Page [BibTex]

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Optimizing Long-term Predictions for Model-based Policy Search

Doerr, A., Daniel, C., Nguyen-Tuong, D., Marco, A., Schaal, S., Toussaint, M., Trimpe, S.

Proceedings of 1st Annual Conference on Robot Learning (CoRL), 78, pages: 227-238, (Editors: Sergey Levine and Vincent Vanhoucke and Ken Goldberg), 1st Annual Conference on Robot Learning, November 2017 (conference)

Abstract
We propose a novel long-term optimization criterion to improve the robustness of model-based reinforcement learning in real-world scenarios. Learning a dynamics model to derive a solution promises much greater data-efficiency and reusability compared to model-free alternatives. In practice, however, modelbased RL suffers from various imperfections such as noisy input and output data, delays and unmeasured (latent) states. To achieve higher resilience against such effects, we propose to optimize a generative long-term prediction model directly with respect to the likelihood of observed trajectories as opposed to the common approach of optimizing a dynamics model for one-step-ahead predictions. We evaluate the proposed method on several artificial and real-world benchmark problems and compare it to PILCO, a model-based RL framework, in experiments on a manipulation robot. The results show that the proposed method is competitive compared to state-of-the-art model learning methods. In contrast to these more involved models, our model can directly be employed for policy search and outperforms a baseline method in the robot experiment.

PDF Project Page [BibTex]

Doerr, A., Daniel, C., Nguyen-Tuong, D., Marco, A., Schaal, S., Toussaint, M., Trimpe, S. Optimizing Long-term Predictions for Model-based Policy Search Proceedings of 1st Annual Conference on Robot Learning (CoRL), 78, pages: 227-238, (Editors: Sergey Levine and Vincent Vanhoucke and Ken Goldberg), 1st Annual Conference on Robot Learning, November 2017 (conference)

PDF Project Page [BibTex]

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Acquiring Target Stacking Skills by Goal-Parameterized Deep Reinforcement Learning

Li, W., Bohg, J., Fritz, M.

arXiv, November 2017 (article) Submitted

Abstract
Understanding physical phenomena is a key component of human intelligence and enables physical interaction with previously unseen environments. In this paper, we study how an artificial agent can autonomously acquire this intuition through interaction with the environment. We created a synthetic block stacking environment with physics simulation in which the agent can learn a policy end-to-end through trial and error. Thereby, we bypass to explicitly model physical knowledge within the policy. We are specifically interested in tasks that require the agent to reach a given goal state that may be different for every new trial. To this end, we propose a deep reinforcement learning framework that learns policies which are parametrized by a goal. We validated the model on a toy example navigating in a grid world with different target positions and in a block stacking task with different target structures of the final tower. In contrast to prior work, our policies show better generalization across different goals.

arXiv [BibTex]

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A New Data Source for Inverse Dynamics Learning

Kappler, D., Meier, F., Ratliff, N., Schaal, S.

In Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Piscataway, NJ, USA, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), September 2017 (inproceedings)

[BibTex]

Kappler, D., Meier, F., Ratliff, N., Schaal, S. A New Data Source for Inverse Dynamics Learning In Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Piscataway, NJ, USA, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), September 2017 (inproceedings)

[BibTex]

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Bayesian Regression for Artifact Correction in Electroencephalography

Fiebig, K., Jayaram, V., Hesse, T., Blank, A., Peters, J., Grosse-Wentrup, M.

Proceedings of the 7th Graz Brain-Computer Interface Conference 2017 - From Vision to Reality, pages: 131-136, (Editors: Müller-Putz G.R., Steyrl D., Wriessnegger S. C., Scherer R.), Graz University of Technology, Austria, Graz Brain-Computer Interface Conference, September 2017 (conference)

DOI [BibTex]

Fiebig, K., Jayaram, V., Hesse, T., Blank, A., Peters, J., Grosse-Wentrup, M. Bayesian Regression for Artifact Correction in Electroencephalography Proceedings of the 7th Graz Brain-Computer Interface Conference 2017 - From Vision to Reality, pages: 131-136, (Editors: Müller-Putz G.R., Steyrl D., Wriessnegger S. C., Scherer R.), Graz University of Technology, Austria, Graz Brain-Computer Interface Conference, September 2017 (conference)

DOI [BibTex]

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Investigating Music Imagery as a Cognitive Paradigm for Low-Cost Brain-Computer Interfaces

Grossberger, L., Hohmann, M. R., Peters, J., Grosse-Wentrup, M.

Proceedings of the 7th Graz Brain-Computer Interface Conference 2017 - From Vision to Reality, pages: 160-164, (Editors: Müller-Putz G.R., Steyrl D., Wriessnegger S. C., Scherer R.), Graz University of Technology, Austria, Graz Brain-Computer Interface Conference, September 2017 (conference)

DOI [BibTex]

Grossberger, L., Hohmann, M. R., Peters, J., Grosse-Wentrup, M. Investigating Music Imagery as a Cognitive Paradigm for Low-Cost Brain-Computer Interfaces Proceedings of the 7th Graz Brain-Computer Interface Conference 2017 - From Vision to Reality, pages: 160-164, (Editors: Müller-Putz G.R., Steyrl D., Wriessnegger S. C., Scherer R.), Graz University of Technology, Austria, Graz Brain-Computer Interface Conference, September 2017 (conference)

DOI [BibTex]

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On the relevance of grasp metrics for predicting grasp success

Rubert, C., Kappler, D., Morales, A., Schaal, S., Bohg, J.

In Proceedings of the IEEE/RSJ International Conference of Intelligent Robots and Systems, September 2017 (inproceedings) Accepted

Abstract
We aim to reliably predict whether a grasp on a known object is successful before it is executed in the real world. There is an entire suite of grasp metrics that has already been developed which rely on precisely known contact points between object and hand. However, it remains unclear whether and how they may be combined into a general purpose grasp stability predictor. In this paper, we analyze these questions by leveraging a large scale database of simulated grasps on a wide variety of objects. For each grasp, we compute the value of seven metrics. Each grasp is annotated by human subjects with ground truth stability labels. Given this data set, we train several classification methods to find out whether there is some underlying, non-trivial structure in the data that is difficult to model manually but can be learned. Quantitative and qualitative results show the complexity of the prediction problem. We found that a good prediction performance critically depends on using a combination of metrics as input features. Furthermore, non-parametric and non-linear classifiers best capture the structure in the data.

Project Page [BibTex]

Rubert, C., Kappler, D., Morales, A., Schaal, S., Bohg, J. On the relevance of grasp metrics for predicting grasp success In Proceedings of the IEEE/RSJ International Conference of Intelligent Robots and Systems, September 2017 (inproceedings) Accepted

Project Page [BibTex]

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Local Bayesian Optimization of Motor Skills

Akrour, R., Sorokin, D., Peters, J., Neumann, G.

Proceedings of the 34th International Conference on Machine Learning, 70, pages: 41-50, Proceedings of Machine Learning Research, (Editors: Doina Precup, Yee Whye Teh), PMLR, International Conference on Machine Learning (ICML), August 2017 (conference)

link (url) Project Page [BibTex]

Akrour, R., Sorokin, D., Peters, J., Neumann, G. Local Bayesian Optimization of Motor Skills Proceedings of the 34th International Conference on Machine Learning, 70, pages: 41-50, Proceedings of Machine Learning Research, (Editors: Doina Precup, Yee Whye Teh), PMLR, International Conference on Machine Learning (ICML), August 2017 (conference)

link (url) Project Page [BibTex]

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Combining Model-Based and Model-Free Updates for Trajectory-Centric Reinforcement Learning

Chebotar, Y., Hausman, K., Zhang, M., Sukhatme, G., Schaal, S., Levine, S.

Proceedings of the 34th International Conference on Machine Learning, 70, Proceedings of Machine Learning Research, (Editors: Doina Precup, Yee Whye Teh), PMLR, International Conference on Machine Learning (ICML), August 2017 (conference)

pdf video [BibTex]

Chebotar, Y., Hausman, K., Zhang, M., Sukhatme, G., Schaal, S., Levine, S. Combining Model-Based and Model-Free Updates for Trajectory-Centric Reinforcement Learning Proceedings of the 34th International Conference on Machine Learning, 70, Proceedings of Machine Learning Research, (Editors: Doina Precup, Yee Whye Teh), PMLR, International Conference on Machine Learning (ICML), August 2017 (conference)

pdf video [BibTex]

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Event-based State Estimation: An Emulation-based Approach

Trimpe, S.

IET Control Theory & Applications, 11(11):1684-1693, July 2017 (article)

Abstract
An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor agents observe a dynamic process and sporadically transmit their measurements to estimator agents over a shared bus network. Local event-triggering protocols ensure that data is transmitted only when necessary to meet a desired estimation accuracy. The event-based design is shown to emulate the performance of a centralised state observer design up to guaranteed bounds, but with reduced communication. The stability results for state estimation are extended to the distributed control system that results when the local estimates are used for feedback control. Results from numerical simulations and hardware experiments illustrate the effectiveness of the proposed approach in reducing network communication.

arXiv Supplementary material PDF DOI Project Page [BibTex]

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Model-Based Policy Search for Automatic Tuning of Multivariate PID Controllers

Doerr, A., Nguyen-Tuong, D., Marco, A., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 5295-5301, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

PDF arXiv DOI Project Page [BibTex]

Doerr, A., Nguyen-Tuong, D., Marco, A., Schaal, S., Trimpe, S. Model-Based Policy Search for Automatic Tuning of Multivariate PID Controllers In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 5295-5301, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

PDF arXiv DOI Project Page [BibTex]

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Learning Feedback Terms for Reactive Planning and Control

Rai, A., Sutanto, G., Schaal, S., Meier, F.

Proceedings 2017 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (conference)

pdf video [BibTex]

Rai, A., Sutanto, G., Schaal, S., Meier, F. Learning Feedback Terms for Reactive Planning and Control Proceedings 2017 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (conference)

pdf video [BibTex]

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Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization

Marco, A., Berkenkamp, F., Hennig, P., Schoellig, A. P., Krause, A., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 1557-1563, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]

Marco, A., Berkenkamp, F., Hennig, P., Schoellig, A. P., Krause, A., Schaal, S., Trimpe, S. Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 1557-1563, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]

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Probabilistic Articulated Real-Time Tracking for Robot Manipulation

(Best Paper of RA-L 2017, Finalist of Best Robotic Vision Paper Award of ICRA 2017)

Garcia Cifuentes, C., Issac, J., Wüthrich, M., Schaal, S., Bohg, J.

IEEE Robotics and Automation Letters (RA-L), 2(2):577-584, April 2017 (article)

Abstract
We propose a probabilistic filtering method which fuses joint measurements with depth images to yield a precise, real-time estimate of the end-effector pose in the camera frame. This avoids the need for frame transformations when using it in combination with visual object tracking methods. Precision is achieved by modeling and correcting biases in the joint measurements as well as inaccuracies in the robot model, such as poor extrinsic camera calibration. We make our method computationally efficient through a principled combination of Kalman filtering of the joint measurements and asynchronous depth-image updates based on the Coordinate Particle Filter. We quantitatively evaluate our approach on a dataset recorded from a real robotic platform, annotated with ground truth from a motion capture system. We show that our approach is robust and accurate even under challenging conditions such as fast motion, significant and long-term occlusions, and time-varying biases. We release the dataset along with open-source code of our approach to allow for quantitative comparison with alternative approaches.

arXiv video code and dataset video PDF DOI Project Page [BibTex]

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Anticipatory Action Selection for Human-Robot Table Tennis

Wang, Z., Boularias, A., Mülling, K., Schölkopf, B., Peters, J.

Artificial Intelligence, 247, pages: 399-414, 2017, Special Issue on AI and Robotics (article)

Abstract
Abstract Anticipation can enhance the capability of a robot in its interaction with humans, where the robot predicts the humans' intention for selecting its own action. We present a novel framework of anticipatory action selection for human-robot interaction, which is capable to handle nonlinear and stochastic human behaviors such as table tennis strokes and allows the robot to choose the optimal action based on prediction of the human partner's intention with uncertainty. The presented framework is generic and can be used in many human-robot interaction scenarios, for example, in navigation and human-robot co-manipulation. In this article, we conduct a case study on human-robot table tennis. Due to the limited amount of time for executing hitting movements, a robot usually needs to initiate its hitting movement before the opponent hits the ball, which requires the robot to be anticipatory based on visual observation of the opponent's movement. Previous work on Intention-Driven Dynamics Models (IDDM) allowed the robot to predict the intended target of the opponent. In this article, we address the problem of action selection and optimal timing for initiating a chosen action by formulating the anticipatory action selection as a Partially Observable Markov Decision Process (POMDP), where the transition and observation are modeled by the \{IDDM\} framework. We present two approaches to anticipatory action selection based on the \{POMDP\} formulation, i.e., a model-free policy learning method based on Least-Squares Policy Iteration (LSPI) that employs the \{IDDM\} for belief updates, and a model-based Monte-Carlo Planning (MCP) method, which benefits from the transition and observation model by the IDDM. Experimental results using real data in a simulated environment show the importance of anticipatory action selection, and that \{POMDPs\} are suitable to formulate the anticipatory action selection problem by taking into account the uncertainties in prediction. We also show that existing algorithms for POMDPs, such as \{LSPI\} and MCP, can be applied to substantially improve the robot's performance in its interaction with humans.

DOI Project Page [BibTex]

Wang, Z., Boularias, A., Mülling, K., Schölkopf, B., Peters, J. Anticipatory Action Selection for Human-Robot Table Tennis Artificial Intelligence, 247, pages: 399-414, 2017, Special Issue on AI and Robotics (article)

DOI Project Page [BibTex]

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Robot Learning

Peters, J., Lee, D., Kober, J., Nguyen-Tuong, D., Bagnell, J., Schaal, S.

In Springer Handbook of Robotics, pages: 357-394, 15, 2nd, (Editors: Siciliano, Bruno and Khatib, Oussama), Springer International Publishing, 2017 (inbook)

Project Page [BibTex]

Peters, J., Lee, D., Kober, J., Nguyen-Tuong, D., Bagnell, J., Schaal, S. Robot Learning In Springer Handbook of Robotics, pages: 357-394, 15, 2nd, (Editors: Siciliano, Bruno and Khatib, Oussama), Springer International Publishing, 2017 (inbook)

Project Page [BibTex]

2013

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Probabilistic Object Tracking Using a Range Camera

Wüthrich, M., Pastor, P., Kalakrishnan, M., Bohg, J., Schaal, S.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3195-3202, IEEE, November 2013 (inproceedings)

Abstract
We address the problem of tracking the 6-DoF pose of an object while it is being manipulated by a human or a robot. We use a dynamic Bayesian network to perform inference and compute a posterior distribution over the current object pose. Depending on whether a robot or a human manipulates the object, we employ a process model with or without knowledge of control inputs. Observations are obtained from a range camera. As opposed to previous object tracking methods, we explicitly model self-occlusions and occlusions from the environment, e.g, the human or robotic hand. This leads to a strongly non-linear observation model and additional dependencies in the Bayesian network. We employ a Rao-Blackwellised particle filter to compute an estimate of the object pose at every time step. In a set of experiments, we demonstrate the ability of our method to accurately and robustly track the object pose in real-time while it is being manipulated by a human or a robot.

arXiv Video Code Video DOI Project Page [BibTex]

2013

Wüthrich, M., Pastor, P., Kalakrishnan, M., Bohg, J., Schaal, S. Probabilistic Object Tracking Using a Range Camera In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3195-3202, IEEE, November 2013 (inproceedings)

arXiv Video Code Video DOI Project Page [BibTex]

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3-D Object Reconstruction of Symmetric Objects by Fusing Visual and Tactile Sensing

Illonen, J., Bohg, J., Kyrki, V.

The International Journal of Robotics Research, 33(2):321-341, Sage, October 2013 (article)

Abstract
In this work, we propose to reconstruct a complete 3-D model of an unknown object by fusion of visual and tactile information while the object is grasped. Assuming the object is symmetric, a first hypothesis of its complete 3-D shape is generated. A grasp is executed on the object with a robotic manipulator equipped with tactile sensors. Given the detected contacts between the fingers and the object, the initial full object model including the symmetry parameters can be refined. This refined model will then allow the planning of more complex manipulation tasks. The main contribution of this work is an optimal estimation approach for the fusion of visual and tactile data applying the constraint of object symmetry. The fusion is formulated as a state estimation problem and solved with an iterative extended Kalman filter. The approach is validated experimentally using both artificial and real data from two different robotic platforms.

Web DOI Project Page [BibTex]

Illonen, J., Bohg, J., Kyrki, V. 3-D Object Reconstruction of Symmetric Objects by Fusing Visual and Tactile Sensing The International Journal of Robotics Research, 33(2):321-341, Sage, October 2013 (article)

Web DOI Project Page [BibTex]

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Learning and Optimization with Submodular Functions

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L.

ArXiv, May 2013 (techreport)

Abstract
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

arxiv link (url) [BibTex]

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L. Learning and Optimization with Submodular Functions ArXiv, May 2013 (techreport)

arxiv link (url) [BibTex]

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Hypothesis Testing Framework for Active Object Detection

Sankaran, B., Atanasov, N., Le Ny, J., Koletschka, T., Pappas, G., Daniilidis, K.

In IEEE International Conference on Robotics and Automation (ICRA), May 2013, clmc (inproceedings)

Abstract
One of the central problems in computer vision is the detection of semantically important objects and the estimation of their pose. Most of the work in object detection has been based on single image processing and its performance is limited by occlusions and ambiguity in appearance and geometry. This paper proposes an active approach to object detection by controlling the point of view of a mobile depth camera. When an initial static detection phase identifies an object of interest, several hypotheses are made about its class and orientation. The sensor then plans a sequence of view-points, which balances the amount of energy used to move with the chance of identifying the correct hypothesis. We formulate an active M-ary hypothesis testing problem, which includes sensor mobility, and solve it using a point-based approximate POMDP algorithm. The validity of our approach is verified through simulation and experiments with real scenes captured by a kinect sensor. The results suggest a significant improvement over static object detection.

pdf [BibTex]

Sankaran, B., Atanasov, N., Le Ny, J., Koletschka, T., Pappas, G., Daniilidis, K. Hypothesis Testing Framework for Active Object Detection In IEEE International Conference on Robotics and Automation (ICRA), May 2013, clmc (inproceedings)

pdf [BibTex]

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Action and Goal Related Decision Variables Modulate the Competition Between Multiple Potential Targets

Enachescu, V, Christopoulos, Vassilios N, Schrater, P. R., Schaal, S.

In Abstracts of Neural Control of Movement Conference (NCM 2013), February 2013 (inproceedings)

[BibTex]

Enachescu, V, Christopoulos, Vassilios N, Schrater, P. R., Schaal, S. Action and Goal Related Decision Variables Modulate the Competition Between Multiple Potential Targets In Abstracts of Neural Control of Movement Conference (NCM 2013), February 2013 (inproceedings)

[BibTex]

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Optimal control of reaching includes kinematic constraints

Mistry, M., Theodorou, E., Schaal, S., Kawato, M.

Journal of Neurophysiology, 2013, clmc (article)

Abstract
We investigate adaptation under a reaching task with an acceleration-based force field perturbation designed to alter the nominal straight hand trajectory in a potentially benign manner:pushing the hand of course in one direction before subsequently restoring towards the target. In this particular task, an explicit strategy to reduce motor effort requires a distinct deviation from the nominal rectilinear hand trajectory. Rather, our results display a clear directional preference during learning, as subjects adapted perturbed curved trajectories towards their initial baselines. We model this behavior using the framework of stochastic optimal control theory and an objective function that trades-of the discordant requirements of 1) target accuracy, 2) motor effort, and 3) desired trajectory. Our work addresses the underlying objective of a reaching movement, and we suggest that robustness, particularly against internal model uncertainly, is as essential to the reaching task as terminal accuracy and energy effciency.

PDF [BibTex]

Mistry, M., Theodorou, E., Schaal, S., Kawato, M. Optimal control of reaching includes kinematic constraints Journal of Neurophysiology, 2013, clmc (article)

PDF [BibTex]

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Fusing visual and tactile sensing for 3-D object reconstruction while grasping

Ilonen, J., Bohg, J., Kyrki, V.

In IEEE International Conference on Robotics and Automation (ICRA), pages: 3547-3554, 2013 (inproceedings)

Abstract
In this work, we propose to reconstruct a complete 3-D model of an unknown object by fusion of visual and tactile information while the object is grasped. Assuming the object is symmetric, a first hypothesis of its complete 3-D shape is generated from a single view. This initial model is used to plan a grasp on the object which is then executed with a robotic manipulator equipped with tactile sensors. Given the detected contacts between the fingers and the object, the full object model including the symmetry parameters can be refined. This refined model will then allow the planning of more complex manipulation tasks. The main contribution of this work is an optimal estimation approach for the fusion of visual and tactile data applying the constraint of object symmetry. The fusion is formulated as a state estimation problem and solved with an iterative extended Kalman filter. The approach is validated experimentally using both artificial and real data from two different robotic platforms.

DOI Project Page [BibTex]

Ilonen, J., Bohg, J., Kyrki, V. Fusing visual and tactile sensing for 3-D object reconstruction while grasping In IEEE International Conference on Robotics and Automation (ICRA), pages: 3547-3554, 2013 (inproceedings)

DOI Project Page [BibTex]

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Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors

Ijspeert, A., Nakanishi, J., Pastor, P., Hoffmann, H., Schaal, S.

Neural Computation, (25):328-373, 2013, clmc (article)

Abstract
Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by meansof a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

link (url) [BibTex]

Ijspeert, A., Nakanishi, J., Pastor, P., Hoffmann, H., Schaal, S. Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors Neural Computation, (25):328-373, 2013, clmc (article)

link (url) [BibTex]

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Learning Objective Functions for Manipulation

Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In 2013 IEEE International Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
We present an approach to learning objective functions for robotic manipulation based on inverse reinforcement learning. Our path integral inverse reinforcement learning algorithm can deal with high-dimensional continuous state-action spaces, and only requires local optimality of demonstrated trajectories. We use L 1 regularization in order to achieve feature selection, and propose an efficient algorithm to minimize the resulting convex objective function. We demonstrate our approach by applying it to two core problems in robotic manipulation. First, we learn a cost function for redundancy resolution in inverse kinematics. Second, we use our method to learn a cost function over trajectories, which is then used in optimization-based motion planning for grasping and manipulation tasks. Experimental results show that our method outperforms previous algorithms in high-dimensional settings.

link (url) DOI [BibTex]

Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S. Learning Objective Functions for Manipulation In 2013 IEEE International Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

link (url) DOI [BibTex]

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Using Torque Redundancy to Optimize Contact Forces in Legged Robots

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

In Redundancy in Robot Manipulators and Multi-Robot Systems, 57, pages: 35-51, Lecture Notes in Electrical Engineering, Springer Berlin Heidelberg, 2013 (incollection)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In the following, we present an inverse dynamics controller that exploits torque redundancy to directly and explicitly minimize any combination of linear and quadratic costs in the contact constraints and in the commands. Such a result is particularly relevant for legged robots as it allows to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, it can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The proposed controller is very simple and computationally efficient, and most importantly it can greatly improve the performance of legged locomotion on difficult terrains as can be seen in the experimental results.

link (url) [BibTex]

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S. Using Torque Redundancy to Optimize Contact Forces in Legged Robots In Redundancy in Robot Manipulators and Multi-Robot Systems, 57, pages: 35-51, Lecture Notes in Electrical Engineering, Springer Berlin Heidelberg, 2013 (incollection)

link (url) [BibTex]

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Optimal distribution of contact forces with inverse-dynamics control

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

The International Journal of Robotics Research, 32(3):280-298, March 2013 (article)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of the contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In this contribution we develop an inverse-dynamics controller for floating-base robots under contact constraints that can minimize any combination of linear and quadratic costs in the contact constraints and the commands. Our main result is the exact analytical derivation of the controller. Such a result is particularly relevant for legged robots as it allows us to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, we can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The main advantages of the controller are its simplicity, computational efficiency and robustness to model inaccuracies. We present detailed experimental results on simulated humanoid and quadruped robots as well as a real quadruped robot. The experiments demonstrate that the controller can greatly improve the robustness of locomotion of the robots.1

link (url) DOI [BibTex]

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S. Optimal distribution of contact forces with inverse-dynamics control The International Journal of Robotics Research, 32(3):280-298, March 2013 (article)

link (url) DOI [BibTex]

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Learning Task Error Models for Manipulation

Pastor, P., Kalakrishnan, M., Binney, J., Kelly, J., Righetti, L., Sukhatme, G. S., Schaal, S.

In 2013 IEEE Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
Precise kinematic forward models are important for robots to successfully perform dexterous grasping and manipulation tasks, especially when visual servoing is rendered infeasible due to occlusions. A lot of research has been conducted to estimate geometric and non-geometric parameters of kinematic chains to minimize reconstruction errors. However, kinematic chains can include non-linearities, e.g. due to cable stretch and motor-side encoders, that result in significantly different errors for different parts of the state space. Previous work either does not consider such non-linearities or proposes to estimate non-geometric parameters of carefully engineered models that are robot specific. We propose a data-driven approach that learns task error models that account for such unmodeled non-linearities. We argue that in the context of grasping and manipulation, it is sufficient to achieve high accuracy in the task relevant state space. We identify this relevant state space using previously executed joint configurations and learn error corrections for those. Therefore, our system is developed to generate subsequent executions that are similar to previous ones. The experiments show that our method successfully captures the non-linearities in the head kinematic chain (due to a counterbalancing spring) and the arm kinematic chains (due to cable stretch) of the considered experimental platform, see Fig. 1. The feasibility of the presented error learning approach has also been evaluated in independent DARPA ARM-S testing contributing to successfully complete 67 out of 72 grasping and manipulation tasks.

link (url) DOI [BibTex]

Pastor, P., Kalakrishnan, M., Binney, J., Kelly, J., Righetti, L., Sukhatme, G. S., Schaal, S. Learning Task Error Models for Manipulation In 2013 IEEE Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

link (url) DOI [BibTex]

2010

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Reinforcement learning of full-body humanoid motor skills

Stulp, F., Buchli, J., Theodorou, E., Schaal, S.

In Humanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on, pages: 405-410, December 2010, clmc (inproceedings)

Abstract
Applying reinforcement learning to humanoid robots is challenging because humanoids have a large number of degrees of freedom and state and action spaces are continuous. Thus, most reinforcement learning algorithms would become computationally infeasible and require a prohibitive amount of trials to explore such high-dimensional spaces. In this paper, we present a probabilistic reinforcement learning approach, which is derived from the framework of stochastic optimal control and path integrals. The algorithm, called Policy Improvement with Path Integrals (PI2), has a surprisingly simple form, has no open tuning parameters besides the exploration noise, is model-free, and performs numerically robustly in high dimensional learning problems. We demonstrate how PI2 is able to learn full-body motor skills on a 34-DOF humanoid robot. To demonstrate the generality of our approach, we also apply PI2 in the context of variable impedance control, where both planned trajectories and gain schedules for each joint are optimized simultaneously.

link (url) [BibTex]

2010

Stulp, F., Buchli, J., Theodorou, E., Schaal, S. Reinforcement learning of full-body humanoid motor skills In Humanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on, pages: 405-410, December 2010, clmc (inproceedings)

link (url) [BibTex]

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Relative Entropy Policy Search

Peters, J., Mülling, K., Altun, Y.

In Proceedings of the Twenty-Fourth National Conference on Artificial Intelligence, pages: 1607-1612, (Editors: Fox, M. , D. Poole), AAAI Press, Menlo Park, CA, USA, Twenty-Fourth National Conference on Artificial Intelligence (AAAI-10), July 2010 (inproceedings)

Abstract
Policy search is a successful approach to reinforcement learning. However, policy improvements often result in the loss of information. Hence, it has been marred by premature convergence and implausible solutions. As first suggested in the context of covariant policy gradients (Bagnell and Schneider 2003), many of these problems may be addressed by constraining the information loss. In this paper, we continue this path of reasoning and suggest the Relative Entropy Policy Search (REPS) method. The resulting method differs significantly from previous policy gradient approaches and yields an exact update step. It works well on typical reinforcement learning benchmark problems.

PDF Web [BibTex]

Peters, J., Mülling, K., Altun, Y. Relative Entropy Policy Search In Proceedings of the Twenty-Fourth National Conference on Artificial Intelligence, pages: 1607-1612, (Editors: Fox, M. , D. Poole), AAAI Press, Menlo Park, CA, USA, Twenty-Fourth National Conference on Artificial Intelligence (AAAI-10), July 2010 (inproceedings)

PDF Web [BibTex]

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Reinforcement learning of motor skills in high dimensions: A path integral approach

Theodorou, E., Buchli, J., Schaal, S.

In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 2397-2403, May 2010, clmc (inproceedings)

Abstract
Reinforcement learning (RL) is one of the most general approaches to learning control. Its applicability to complex motor systems, however, has been largely impossible so far due to the computational difficulties that reinforcement learning encounters in high dimensional continuous state-action spaces. In this paper, we derive a novel approach to RL for parameterized control policies based on the framework of stochastic optimal control with path integrals. While solidly grounded in optimal control theory and estimation theory, the update equations for learning are surprisingly simple and have no danger of numerical instabilities as neither matrix inversions nor gradient learning rates are required. Empirical evaluations demonstrate significant performance improvements over gradient-based policy learning and scalability to high-dimensional control problems. Finally, a learning experiment on a robot dog illustrates the functionality of our algorithm in a real-world scenario. We believe that our new algorithm, Policy Improvement with Path Integrals (PI2), offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL in robotics.

link (url) [BibTex]

Theodorou, E., Buchli, J., Schaal, S. Reinforcement learning of motor skills in high dimensions: A path integral approach In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 2397-2403, May 2010, clmc (inproceedings)

link (url) [BibTex]

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Inverse dynamics control of floating base systems using orthogonal decomposition

Mistry, M., Buchli, J., Schaal, S.

In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 3406-3412, May 2010, clmc (inproceedings)

Abstract
Model-based control methods can be used to enable fast, dexterous, and compliant motion of robots without sacrificing control accuracy. However, implementing such techniques on floating base robots, e.g., humanoids and legged systems, is non-trivial due to under-actuation, dynamically changing constraints from the environment, and potentially closed loop kinematics. In this paper, we show how to compute the analytically correct inverse dynamics torques for model-based control of sufficiently constrained floating base rigid-body systems, such as humanoid robots with one or two feet in contact with the environment. While our previous inverse dynamics approach relied on an estimation of contact forces to compute an approximate inverse dynamics solution, here we present an analytically correct solution by using an orthogonal decomposition to project the robot dynamics onto a reduced dimensional space, independent of contact forces. We demonstrate the feasibility and robustness of our approach on a simulated floating base bipedal humanoid robot and an actual robot dog locomoting over rough terrain.

link (url) [BibTex]

Mistry, M., Buchli, J., Schaal, S. Inverse dynamics control of floating base systems using orthogonal decomposition In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 3406-3412, May 2010, clmc (inproceedings)

link (url) [BibTex]

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Fast, robust quadruped locomotion over challenging terrain

Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S.

In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 2665-2670, May 2010, clmc (inproceedings)

Abstract
We present a control architecture for fast quadruped locomotion over rough terrain. We approach the problem by decomposing it into many sub-systems, in which we apply state-of-the-art learning, planning, optimization and control techniques to achieve robust, fast locomotion. Unique features of our control strategy include: (1) a system that learns optimal foothold choices from expert demonstration using terrain templates, (2) a body trajectory optimizer based on the Zero-Moment Point (ZMP) stability criterion, and (3) a floating-base inverse dynamics controller that, in conjunction with force control, allows for robust, compliant locomotion over unperceived obstacles. We evaluate the performance of our controller by testing it on the LittleDog quadruped robot, over a wide variety of rough terrain of varying difficulty levels. We demonstrate the generalization ability of this controller by presenting test results from an independent external test team on terrains that have never been shown to us.

link (url) [BibTex]

Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S. Fast, robust quadruped locomotion over challenging terrain In Robotics and Automation (ICRA), 2010 IEEE International Conference on, pages: 2665-2670, May 2010, clmc (inproceedings)

link (url) [BibTex]

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Policy learning algorithmis for motor learning (Algorithmen zum automatischen Erlernen von Motorfähigkigkeiten)

Peters, J., Kober, J., Schaal, S.

Automatisierungstechnik, 58(12):688-694, 2010, clmc (article)

Abstract
Robot learning methods which allow au- tonomous robots to adapt to novel situations have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. However, to date, learning techniques have yet to ful- fill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics. If possible, scaling was usually only achieved in precisely pre-structured domains. In this paper, we investigate the ingredients for a general ap- proach policy learning with the goal of an application to motor skill refinement in order to get one step closer towards human- like performance. For doing so, we study two major components for such an approach, i. e., firstly, we study policy learning algo- rithms which can be applied in the general setting of motor skill learning, and, secondly, we study a theoretically well-founded general approach to representing the required control structu- res for task representation and execution.

link (url) [BibTex]

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A Bayesian approach to nonlinear parameter identification for rigid-body dynamics

Ting, J., DSouza, A., Schaal, S.

Neural Networks, 2010, clmc (article)

Abstract
For complex robots such as humanoids, model-based control is highly beneficial for accurate tracking while keeping negative feedback gains low for compliance. However, in such multi degree-of-freedom lightweight systems, conventional identification of rigid body dynamics models using CAD data and actuator models is inaccurate due to unknown nonlinear robot dynamic effects. An alternative method is data-driven parameter estimation, but significant noise in measured and inferred variables affects it adversely. Moreover, standard estimation procedures may give physically inconsistent results due to unmodeled nonlinearities or insufficiently rich data. This paper addresses these problems, proposing a Bayesian system identification technique for linear or piecewise linear systems. Inspired by Factor Analysis regression, we develop a computationally efficient variational Bayesian regression algorithm that is robust to ill-conditioned data, automatically detects relevant features, and identifies input and output noise. We evaluate our approach on rigid body parameter estimation for various robotic systems, achieving an error of up to three times lower than other state-of-the-art machine learning methods.

link (url) [BibTex]

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A first optimal control solution for a complex, nonlinear, tendon driven neuromuscular finger model

Theodorou, E. A., Todorov, E., Valero-Cuevas, F.

Proceedings of the ASME 2010 Summer Bioengineering Conference August 30-September 2, 2010, Naples, Florida, USA, 2010, clmc (article)

Abstract
In this work we present the first constrained stochastic op- timal feedback controller applied to a fully nonlinear, tendon driven index finger model. Our model also takes into account an extensor mechanism, and muscle force-length and force-velocity properties. We show this feedback controller is robust to noise and perturbations to the dynamics, while successfully handling the nonlinearities and high dimensionality of the system. By ex- tending prior methods, we are able to approximate physiological realism by ensuring positivity of neural commands and tendon tensions at all timesthus can, for the first time, use the optimal control framework to predict biologically plausible tendon tensions for a nonlinear neuromuscular finger model. METHODS 1 Muscle Model The rigid-body triple pendulum finger model with slightly viscous joints is actuated by Hill-type muscle models. Joint torques are generated by the seven muscles of the index fin-

PDF [BibTex]

Theodorou, E. A., Todorov, E., Valero-Cuevas, F. A first optimal control solution for a complex, nonlinear, tendon driven neuromuscular finger model Proceedings of the ASME 2010 Summer Bioengineering Conference August 30-September 2, 2010, Naples, Florida, USA, 2010, clmc (article)

PDF [BibTex]

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Locally weighted regression for control

Ting, J., Vijayakumar, S., Schaal, S.

In Encyclopedia of Machine Learning, pages: 613-624, (Editors: Sammut, C.;Webb, G. I.), Springer, 2010, clmc (inbook)

Abstract
This is article addresses two topics: learning control and locally weighted regression.

link (url) [BibTex]

Ting, J., Vijayakumar, S., Schaal, S. Locally weighted regression for control In Encyclopedia of Machine Learning, pages: 613-624, (Editors: Sammut, C.;Webb, G. I.), Springer, 2010, clmc (inbook)

link (url) [BibTex]

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Are reaching movements planned in kinematic or dynamic coordinates?

Ellmer, A., Schaal, S.

In Abstracts of Neural Control of Movement Conference (NCM 2010), Naples, Florida, 2010, 2010, clmc (inproceedings)

Abstract
Whether human reaching movements are planned and optimized in kinematic (task space) or dynamic (joint or muscle space) coordinates is still an issue of debate. The first hypothesis implies that a planner produces a desired end-effector position at each point in time during the reaching movement, whereas the latter hypothesis includes the dynamics of the muscular-skeletal control system to produce a continuous end-effector trajectory. Previous work by Wolpert et al (1995) showed that when subjects were led to believe that their straight reaching paths corresponded to curved paths as shown on a computer screen, participants adapted the true path of their hand such that they would visually perceive a straight line in visual space, despite that they actually produced a curved path. These results were interpreted as supporting the stance that reaching trajectories are planned in kinematic coordinates. However, this experiment could only demonstrate that adaptation to altered paths, i.e. the position of the end-effector, did occur, but not that the precise timing of end-effector position was equally planned, i.e., the trajectory. Our current experiment aims at filling this gap by explicitly testing whether position over time, i.e. velocity, is a property of reaching movements that is planned in kinematic coordinates. In the current experiment, the velocity profiles of cursor movements corresponding to the participant's hand motions were skewed either to the left or to the right; the path itself was left unaltered. We developed an adaptation paradigm, where the skew of the velocity profile was introduced gradually and participants reported no awareness of any manipulation. Preliminary results indicate that the true hand motion of participants did not alter, i.e. there was no adaptation so as to counterbalance the introduced skew. However, for some participants, peak hand velocities were lowered for higher skews, which suggests that participants interpreted the manipulation as mere noise due to variance in their own movement. In summary, for a visuomotor transformation task, the hypothesis of a planned continuous end-effector trajectory predicts adaptation to a modified velocity profile. The current experiment found no systematic adaptation under such transformation, but did demonstrate an effect that is more in accordance that subjects could not perceive the manipulation and rather interpreted as an increase of noise.

[BibTex]

Ellmer, A., Schaal, S. Are reaching movements planned in kinematic or dynamic coordinates? In Abstracts of Neural Control of Movement Conference (NCM 2010), Naples, Florida, 2010, 2010, clmc (inproceedings)

[BibTex]

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Optimality in Neuromuscular Systems

Theodorou, E. A., Valero-Cuevas, F.

In 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2010, clmc (inproceedings)

Abstract
Abstract? We provide an overview of optimal control meth- ods to nonlinear neuromuscular systems and discuss their lim- itations. Moreover we extend current optimal control methods to their application to neuromuscular models with realistically numerous musculotendons; as most prior work is limited to torque-driven systems. Recent work on computational motor control has explored the used of control theory and esti- mation as a conceptual tool to understand the underlying computational principles of neuromuscular systems. After all, successful biological systems regularly meet conditions for stability, robustness and performance for multiple classes of complex tasks. Among a variety of proposed control theory frameworks to explain this, stochastic optimal control has become a dominant framework to the point of being a standard computational technique to reproduce kinematic trajectories of reaching movements (see [12]) In particular, we demonstrate the application of optimal control to a neuromuscular model of the index finger with all seven musculotendons producing a tapping task. Our simu- lations include 1) a muscle model that includes force- length and force-velocity characteristics; 2) an anatomically plausible biomechanical model of the index finger that includes a tendi- nous network for the extensor mechanism and 3) a contact model that is based on a nonlinear spring-damper attached at the end effector of the index finger. We demonstrate that it is feasible to apply optimal control to systems with realistically large state vectors and conclude that, while optimal control is an adequate formalism to create computational models of neuro- musculoskeletal systems, there remain important challenges and limitations that need to be considered and overcome such as contact transitions, curse of dimensionality, and constraints on states and controls.

PDF [BibTex]

Theodorou, E. A., Valero-Cuevas, F. Optimality in Neuromuscular Systems In 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2010, clmc (inproceedings)

PDF [BibTex]

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Efficient learning and feature detection in high dimensional regression

Ting, J., D’Souza, A., Vijayakumar, S., Schaal, S.

Neural Computation, 22, pages: 831-886, 2010, clmc (article)

Abstract
We present a novel algorithm for efficient learning and feature selection in high- dimensional regression problems. We arrive at this model through a modification of the standard regression model, enabling us to derive a probabilistic version of the well-known statistical regression technique of backfitting. Using the Expectation- Maximization algorithm, along with variational approximation methods to overcome intractability, we extend our algorithm to include automatic relevance detection of the input features. This Variational Bayesian Least Squares (VBLS) approach retains its simplicity as a linear model, but offers a novel statistically robust â??black- boxâ? approach to generalized linear regression with high-dimensional inputs. It can be easily extended to nonlinear regression and classification problems. In particular, we derive the framework of sparse Bayesian learning, e.g., the Relevance Vector Machine, with VBLS at its core, offering significant computational and robustness advantages for this class of methods. We evaluate our algorithm on synthetic and neurophysiological data sets, as well as on standard regression and classification benchmark data sets, comparing it with other competitive statistical approaches and demonstrating its suitability as a drop-in replacement for other generalized linear regression techniques.

link (url) [BibTex]

Ting, J., D’Souza, A., Vijayakumar, S., Schaal, S. Efficient learning and feature detection in high dimensional regression Neural Computation, 22, pages: 831-886, 2010, clmc (article)

link (url) [BibTex]

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Stochastic Differential Dynamic Programming

Theodorou, E., Tassa, Y., Todorov, E.

In the proceedings of American Control Conference (ACC 2010) , 2010, clmc (article)

Abstract
We present a generalization of the classic Differential Dynamic Programming algorithm. We assume the existence of state- and control-dependent process noise, and proceed to derive the second-order expansion of the cost-to-go. Despite having quartic and cubic terms in the initial expression, we show that these vanish, leaving us with the same quadratic structure as standard DDP.

PDF [BibTex]

Theodorou, E., Tassa, Y., Todorov, E. Stochastic Differential Dynamic Programming In the proceedings of American Control Conference (ACC 2010) , 2010, clmc (article)

PDF [BibTex]

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Learning Policy Improvements with Path Integrals

Theodorou, E. A., Buchli, J., Schaal, S.

In International Conference on Artificial Intelligence and Statistics (AISTATS 2010), 2010, clmc (inproceedings)

Abstract
With the goal to generate more scalable algo- rithms with higher efficiency and fewer open parameters, reinforcement learning (RL) has recently moved towards combining classi- cal techniques from optimal control and dy- namic programming with modern learning techniques from statistical estimation the- ory. In this vein, this paper suggests the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parametrized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton-Jacobi-Bellman (HJB) equations, policy improvements can be transformed into an approximation problem of a path inte- gral which has no open parameters other than the exploration noise. The resulting algorithm can be conceived of as model- based, semi-model-based, or even model free, depending on how the learning problem is structured. Our new algorithm demon- strates interesting similarities with previous RL research in the framework of proba- bility matching and provides intuition why the slightly heuristically motivated proba- bility matching approach can actually per- form well. Empirical evaluations demon- strate significant performance improvements over gradient-based policy learning and scal- ability to high-dimensional control problems. We believe that Policy Improvement with Path Integrals (PI2) offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL based on trajectory roll-outs.

PDF [BibTex]

Theodorou, E. A., Buchli, J., Schaal, S. Learning Policy Improvements with Path Integrals In International Conference on Artificial Intelligence and Statistics (AISTATS 2010), 2010, clmc (inproceedings)

PDF [BibTex]

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Learning optimal control solutions: a path integral approach

Theodorou, E., Schaal, S.

In Abstracts of Neural Control of Movement Conference (NCM 2010), Naples, Florida, 2010, 2010, clmc (inproceedings)

Abstract
Investigating principles of human motor control in the framework of optimal control has had a long tradition in neural control of movement, and has recently experienced a new surge of investigations. Ideally, optimal control problems are addresses as a reinforcement learning (RL) problem, which would allow to investigate both the process of acquiring an optimal control solution as well as the solution itself. Unfortunately, the applicability of RL to complex neural and biomechanics systems has been largely impossible so far due to the computational difficulties that arise in high dimensional continuous state-action spaces. As a way out, research has focussed on computing optimal control solutions based on iterative optimal control methods that are based on linear and quadratic approximations of dynamical models and cost functions. These methods require perfect knowledge of the dynamics and cost functions while they are based on gradient and Newton optimization schemes. Their applicability is also restricted to low dimensional problems due to problematic convergence in high dimensions. Moreover, the process of computing the optimal solution is removed from the learning process that might be plausible in biology. In this work, we present a new reinforcement learning method for learning optimal control solutions or motor control. This method, based on the framework of stochastic optimal control with path integrals, has a very solid theoretical foundation, while resulting in surprisingly simple learning algorithms. It is also possible to apply this approach without knowledge of the system model, and to use a wide variety of complex nonlinear cost functions for optimization. We illustrate the theoretical properties of this approach and its applicability to learning motor control tasks for reaching movements and locomotion studies. We discuss its applicability to learning desired trajectories, variable stiffness control (co-contraction), and parameterized control policies. We also investigate the applicability to signal dependent noise control systems. We believe that the suggested method offers one of the easiest to use approaches to learning optimal control suggested in the literature so far, which makes it ideally suited for computational investigations of biological motor control.

[BibTex]

Theodorou, E., Schaal, S. Learning optimal control solutions: a path integral approach In Abstracts of Neural Control of Movement Conference (NCM 2010), Naples, Florida, 2010, 2010, clmc (inproceedings)

[BibTex]

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Learning control in robotics – trajectory-based opitimal control techniques

Schaal, S., Atkeson, C. G.

Robotics and Automation Magazine, 17(2):20-29, 2010, clmc (article)

Abstract
In a not too distant future, robots will be a natural part of daily life in human society, providing assistance in many areas ranging from clinical applications, education and care giving, to normal household environments [1]. It is hard to imagine that all possible tasks can be preprogrammed in such robots. Robots need to be able to learn, either by themselves or with the help of human supervision. Additionally, wear and tear on robots in daily use needs to be automatically compensated for, which requires a form of continuous self-calibration, another form of learning. Finally, robots need to react to stochastic and dynamic environments, i.e., they need to learn how to optimally adapt to uncertainty and unforeseen changes. Robot learning is going to be a key ingredient for the future of autonomous robots. While robot learning covers a rather large field, from learning to perceive, to plan, to make decisions, etc., we will focus this review on topics of learning control, in particular, as it is concerned with learning control in simulated or actual physical robots. In general, learning control refers to the process of acquiring a control strategy for a particular control system and a particular task by trial and error. Learning control is usually distinguished from adaptive control [2] in that the learning system can have rather general optimization objectivesâ??not just, e.g., minimal tracking errorâ??and is permitted to fail during the process of learning, while adaptive control emphasizes fast convergence without failure. Thus, learning control resembles the way that humans and animals acquire new movement strategies, while adaptive control is a special case of learning control that fulfills stringent performance constraints, e.g., as needed in life-critical systems like airplanes. Learning control has been an active topic of research for at least three decades. However, given the lack of working robots that actually use learning components, more work needs to be done before robot learning will make it beyond the laboratory environment. This article will survey some ongoing and past activities in robot learning to assess where the field stands and where it is going. We will largely focus on nonwheeled robots and less on topics of state estimation, as typically explored in wheeled robots [3]â??6], and we emphasize learning in continuous state-action spaces rather than discrete state-action spaces [7], [8]. We will illustrate the different topics of robot learning with examples from our own research with anthropomorphic and humanoid robots.

link (url) [BibTex]

Schaal, S., Atkeson, C. G. Learning control in robotics – trajectory-based opitimal control techniques Robotics and Automation Magazine, 17(2):20-29, 2010, clmc (article)

link (url) [BibTex]

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Learning, planning, and control for quadruped locomotion over challenging terrain

Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S.

International Journal of Robotics Research, 30(2):236-258, 2010, clmc (article)

Abstract
We present a control architecture for fast quadruped locomotion over rough terrain. We approach the problem by decomposing it into many sub-systems, in which we apply state-of-the-art learning, planning, optimization, and control techniques to achieve robust, fast locomotion. Unique features of our control strategy include: (1) a system that learns optimal foothold choices from expert demonstration using terrain templates, (2) a body trajectory optimizer based on the Zero- Moment Point (ZMP) stability criterion, and (3) a floating-base inverse dynamics controller that, in conjunction with force control, allows for robust, compliant locomotion over unperceived obstacles. We evaluate the performance of our controller by testing it on the LittleDog quadruped robot, over a wide variety of rough terrains of varying difficulty levels. The terrain that the robot was tested on includes rocks, logs, steps, barriers, and gaps, with obstacle sizes up to the leg length of the robot. We demonstrate the generalization ability of this controller by presenting results from testing performed by an independent external test team on terrain that has never been shown to us.

link (url) Project Page [BibTex]

Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S. Learning, planning, and control for quadruped locomotion over challenging terrain International Journal of Robotics Research, 30(2):236-258, 2010, clmc (article)

link (url) Project Page [BibTex]

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Constrained Accelerations for Controlled Geometric Reduction: Sagittal-Plane Decoupling for Bipedal Locomotion

Gregg, R., Righetti, L., Buchli, J., Schaal, S.

In 2010 10th IEEE-RAS International Conference on Humanoid Robots, pages: 1-7, IEEE, Nashville, USA, 2010 (inproceedings)

Abstract
Energy-shaping control methods have produced strong theoretical results for asymptotically stable 3D bipedal dynamic walking in the literature. In particular, geometric controlled reduction exploits robot symmetries to control momentum conservation laws that decouple the sagittal-plane dynamics, which are easier to stabilize. However, the associated control laws require high-dimensional matrix inverses multiplied with complicated energy-shaping terms, often making these control theories difficult to apply to highly-redundant humanoid robots. This paper presents a first step towards the application of energy-shaping methods on real robots by casting controlled reduction into a framework of constrained accelerations for inverse dynamics control. By representing momentum conservation laws as constraints in acceleration space, we construct a general expression for desired joint accelerations that render the constraint surface invariant. By appropriately choosing an orthogonal projection, we show that the unconstrained (reduced) dynamics are decoupled from the constrained dynamics. Any acceleration-based controller can then be used to stabilize this planar subsystem, including passivity-based methods. The resulting control law is surprisingly simple and represents a practical way to employ control theoretic stability results in robotic platforms. Simulated walking of a 3D compass-gait biped show correspondence between the new and original controllers, and simulated motions of a 16-DOF humanoid demonstrate the applicability of this method.

link (url) DOI [BibTex]

Gregg, R., Righetti, L., Buchli, J., Schaal, S. Constrained Accelerations for Controlled Geometric Reduction: Sagittal-Plane Decoupling for Bipedal Locomotion In 2010 10th IEEE-RAS International Conference on Humanoid Robots, pages: 1-7, IEEE, Nashville, USA, 2010 (inproceedings)

link (url) DOI [BibTex]

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Variable impedance control - a reinforcement learning approach

Buchli, J., Theodorou, E., Stulp, F., Schaal, S.

In Robotics Science and Systems (2010), Zaragoza, Spain, June 27-30, 2010, clmc (inproceedings)

Abstract
One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high DOF robotic tasks. In this contribution, we accomplish such gain scheduling with a reinforcement learning approach algorithm, PI2 (Policy Improvement with Path Integrals). PI2 is a model-free, sampling based learning method derived from first principles of optimal control. The PI2 algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PI2 is that it can scale to problems of many DOFs, so that RL on real robotic systems becomes feasible. We sketch the PI2 algorithm and its theoretical properties, and how it is applied to gain scheduling. We evaluate our approach by presenting results on two different simulated robotic systems, a 3-DOF Phantom Premium Robot and a 6-DOF Kuka Lightweight Robot. We investigate tasks where the optimal strategy requires both tuning of the impedance of the end-effector, and tuning of a reference trajectory. The results show that we can use path integral based RL not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications.

link (url) [BibTex]

Buchli, J., Theodorou, E., Stulp, F., Schaal, S. Variable impedance control - a reinforcement learning approach In Robotics Science and Systems (2010), Zaragoza, Spain, June 27-30, 2010, clmc (inproceedings)

link (url) [BibTex]

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Inverse dynamics with optimal distribution of ground reaction forces for legged robot

Righetti, L., Buchli, J., Mistry, M., Schaal, S.

In Proceedings of the 13th International Conference on Climbing and Walking Robots (CLAWAR), pages: 580-587, Nagoya, Japan, sep 2010 (inproceedings)

Abstract
Contact interaction with the environment is crucial in the design of locomotion controllers for legged robots, to prevent slipping for example. Therefore, it is of great importance to be able to control the effects of the robots movements on the contact reaction forces. In this contribution, we extend a recent inverse dynamics algorithm for floating base robots to optimize the distribution of contact forces while achieving precise trajectory tracking. The resulting controller is algorithmically simple as compared to other approaches. Numerical simulations show that this result significantly increases the range of possible movements of a humanoid robot as compared to the previous inverse dynamics algorithm. We also present a simplification of the result where no inversion of the inertia matrix is needed which is particularly relevant for practical use on a real robot. Such an algorithm becomes interesting for agile locomotion of robots on difficult terrains where the contacts with the environment are critical, such as walking over rough or slippery terrain.

DOI [BibTex]

Righetti, L., Buchli, J., Mistry, M., Schaal, S. Inverse dynamics with optimal distribution of ground reaction forces for legged robot In Proceedings of the 13th International Conference on Climbing and Walking Robots (CLAWAR), pages: 580-587, Nagoya, Japan, sep 2010 (inproceedings)

DOI [BibTex]