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56 results (View BibTeX file of all listed publications)

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]

2011

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

Kalakrishnan, Mrinal, Buchli, Jonas, Pastor, Peter, Mistry, Michael, Schaal, S.

International Journal of Robotics Research, 30(2):236-258, February 2011 (article)

[BibTex]

2011

Kalakrishnan, Mrinal, Buchli, Jonas, Pastor, Peter, Mistry, Michael, Schaal, S. Learning, planning, and control for quadruped locomotion over challenging terrain International Journal of Robotics Research, 30(2):236-258, February 2011 (article)

[BibTex]

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STOMP: Stochastic trajectory optimization for motion planning

Kalakrishnan, M., Chitta, S., Theodorou, E., Pastor, P., Schaal, S.

In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9-13, 2011, clmc (inproceedings)

Abstract
We present a new approach to motion planning using a stochastic trajectory optimization framework. The approach relies on generating noisy trajectories to explore the space around an initial (possibly infeasible) trajectory, which are then combined to produced an updated trajectory with lower cost. A cost function based on a combination of obstacle and smoothness cost is optimized in each iteration. No gradient information is required for the particular optimization algorithm that we use and so general costs for which derivatives may not be available (e.g. costs corresponding to constraints and motor torques) can be included in the cost function. We demonstrate the approach both in simulation and on a dual-arm mobile manipulation system for unconstrained and constrained tasks. We experimentally show that the stochastic nature of STOMP allows it to overcome local minima that gradient-based optimizers like CHOMP can get stuck in.

link (url) Project Page [BibTex]

Kalakrishnan, M., Chitta, S., Theodorou, E., Pastor, P., Schaal, S. STOMP: Stochastic trajectory optimization for motion planning In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9-13, 2011, clmc (inproceedings)

link (url) Project Page [BibTex]

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Path Integral Control and Bounded Rationality

Braun, D. A., Ortega, P. A., Theodorou, E., Schaal, S.

In IEEE Symposium on Adaptive Dynamic Programming And Reinforcement Learning (ADPRL), 2011, clmc (inproceedings)

Abstract
Path integral methods [7], [15],[1] have recently been shown to be applicable to a very general class of optimal control problems. Here we examine the path integral formalism from a decision-theoretic point of view, since an optimal controller can always be regarded as an instance of a perfectly rational decision-maker that chooses its actions so as to maximize its expected utility [8]. The problem with perfect rationality is, however, that finding optimal actions is often very difficult due to prohibitive computational resource costs that are not taken into account. In contrast, a bounded rational decision-maker has only limited resources and therefore needs to strike some compromise between the desired utility and the required resource costs [14]. In particular, we suggest an information-theoretic measure of resource costs that can be derived axiomatically [11]. As a consequence we obtain a variational principle for choice probabilities that trades off maximizing a given utility criterion and avoiding resource costs that arise due to deviating from initially given default choice probabilities. The resulting bounded rational policies are in general probabilistic. We show that the solutions found by the path integral formalism are such bounded rational policies. Furthermore, we show that the same formalism generalizes to discrete control problems, leading to linearly solvable bounded rational control policies in the case of Markov systems. Importantly, Bellman?s optimality principle is not presupposed by this variational principle, but it can be derived as a limit case. This suggests that the information- theoretic formalization of bounded rationality might serve as a general principle in control design that unifies a number of recently reported approximate optimal control methods both in the continuous and discrete domain.

PDF [BibTex]

Braun, D. A., Ortega, P. A., Theodorou, E., Schaal, S. Path Integral Control and Bounded Rationality In IEEE Symposium on Adaptive Dynamic Programming And Reinforcement Learning (ADPRL), 2011, clmc (inproceedings)

PDF [BibTex]

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Skill learning and task outcome prediction for manipulation

Pastor, P., Kalakrishnan, M., Chitta, S., Theodorou, E., Schaal, S.

In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9-13, 2011, clmc (inproceedings)

Abstract
Learning complex motor skills for real world tasks is a hard problem in robotic manipulation that often requires painstaking manual tuning and design by a human expert. In this work, we present a Reinforcement Learning based approach to acquiring new motor skills from demonstration. Our approach allows the robot to learn fine manipulation skills and significantly improve its success rate and skill level starting from a possibly coarse demonstration. Our approach aims to incorporate task domain knowledge, where appropriate, by working in a space consistent with the constraints of a specific task. In addition, we also present an approach to using sensor feedback to learn a predictive model of the task outcome. This allows our system to learn the proprioceptive sensor feedback needed to monitor subsequent executions of the task online and abort execution in the event of predicted failure. We illustrate our approach using two example tasks executed with the PR2 dual-arm robot: a straight and accurate pool stroke and a box flipping task using two chopsticks as tools.

link (url) Project Page Project Page [BibTex]

Pastor, P., Kalakrishnan, M., Chitta, S., Theodorou, E., Schaal, S. Skill learning and task outcome prediction for manipulation In IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9-13, 2011, clmc (inproceedings)

link (url) Project Page Project Page [BibTex]

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An Iterative Path Integral Stochastic Optimal Control Approach for Learning Robotic Tasks

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

In Proceedings of the 18th World Congress of the International Federation of Automatic Control, 2011, clmc (inproceedings)

Abstract
Recent work on path integral stochastic optimal control theory Theodorou et al. (2010a); Theodorou (2011) has shown promising results in planning and control of nonlinear systems in high dimensional state spaces. The path integral control framework relies on the transformation of the nonlinear Hamilton Jacobi Bellman (HJB) partial differential equation (PDE) into a linear PDE and the approximation of its solution via the use of the Feynman Kac lemma. In this work, we are reviewing the generalized version of path integral stochastic optimal control formalism Theodorou et al. (2010a), used for optimal control and planing of stochastic dynamical systems with state dependent control and diffusion matrices. Moreover we present the iterative path integral control approach, the so called Policy Improvement with Path Integrals or (PI2 ) which is capable of scaling in high dimensional robotic control problems. Furthermore we present a convergence analysis of the proposed algorithm and we apply the proposed framework to a variety of robotic tasks. Finally with the goal to perform locomotion the iterative path integral control is applied for learning nonlinear limit cycle attractors with adjustable land scape.

PDF [BibTex]

Theodorou, E., Stulp, F., Buchli, J., Schaal, S. An Iterative Path Integral Stochastic Optimal Control Approach for Learning Robotic Tasks In Proceedings of the 18th World Congress of the International Federation of Automatic Control, 2011, clmc (inproceedings)

PDF [BibTex]

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Bayesian robot system identification with input and output noise

Ting, J., D’Souza, A., Schaal, S.

Neural Networks, 24(1):99-108, 2011, 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]

Ting, J., D’Souza, A., Schaal, S. Bayesian robot system identification with input and output noise Neural Networks, 24(1):99-108, 2011, clmc (article)

link (url) [BibTex]

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Learning variable impedance control

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

International Journal of Robotics Research, 2011, clmc (article)

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 degree-of-freedom (DOF) robotic tasks. In this contribution, we accomplish such variable impedance control with the reinforcement learning (RL) algorithm PISq ({f P}olicy {f I}mprovement with {f P}ath {f I}ntegrals). PISq is a model-free, sampling based learning method derived from first principles of stochastic optimal control. The PISq 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 PISq is that it can scale to problems of many DOFs, so that reinforcement learning on real robotic systems becomes feasible. We sketch the PISq algorithm and its theoretical properties, and how it is applied to gain scheduling for variable impedance control. We evaluate our approach by presenting results on several simulated and real robots. We consider tasks involving accurate tracking through via-points, and manipulation tasks requiring physical contact with the environment. In these tasks, the optimal strategy requires both tuning of a reference trajectory emph{and} the impedance of the end-effector. The results show that we can use path integral based reinforcement learning 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., Stulp, F., Theodorou, E., Schaal, S. Learning variable impedance control International Journal of Robotics Research, 2011, clmc (article)

link (url) [BibTex]

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Iterative path integral stochastic optimal control: Theory and applications to motor control

Theodorou, E. A.

University of Southern California, University of Southern California, Los Angeles, CA, 2011 (phdthesis)

PDF [BibTex]

Theodorou, E. A. Iterative path integral stochastic optimal control: Theory and applications to motor control University of Southern California, University of Southern California, Los Angeles, CA, 2011 (phdthesis)

PDF [BibTex]

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Learning of grasp selection based on shape-templates

Herzog, A.

Karlsruhe Institute of Technology, 2011 (mastersthesis)

[BibTex]

Herzog, A. Learning of grasp selection based on shape-templates Karlsruhe Institute of Technology, 2011 (mastersthesis)

[BibTex]

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Understanding haptics by evolving mechatronic systems

Loeb, G. E., Tsianos, G.A., Fishel, J.A., Wettels, N., Schaal, S.

Progress in Brain Research, 192, pages: 129, 2011 (article)

[BibTex]

Loeb, G. E., Tsianos, G.A., Fishel, J.A., Wettels, N., Schaal, S. Understanding haptics by evolving mechatronic systems Progress in Brain Research, 192, pages: 129, 2011 (article)

[BibTex]

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Movement segmentation using a primitive library

Meier, F., Theodorou, E., Stulp, F., Schaal, S.

In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011), Sept. 25-30, San Francisco, CA, 2011, clmc (inproceedings)

Abstract
Segmenting complex movements into a sequence of primitives remains a difficult problem with many applications in the robotics and vision communities. In this work, we show how the movement segmentation problem can be reduced to a sequential movement recognition problem. To this end, we reformulate the orig-inal Dynamic Movement Primitive (DMP) formulation as a linear dynamical sys-tem with control inputs. Based on this new formulation, we develop an Expecta-tion-Maximization algorithm to estimate the duration and goal position of a par-tially observed trajectory. With the help of this algorithm and the assumption that a library of movement primitives is present, we present a movement seg-mentation framework. We illustrate the usefulness of the new DMP formulation on the two applications of online movement recognition and movement segmen-tation.

link (url) [BibTex]

Meier, F., Theodorou, E., Stulp, F., Schaal, S. Movement segmentation using a primitive library In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011), Sept. 25-30, San Francisco, CA, 2011, clmc (inproceedings)

link (url) [BibTex]

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Learning Force Control Policies for Compliant Manipulation

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

In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 4639-4644, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Developing robots capable of fine manipulation skills is of major importance in order to build truly assistive robots. These robots need to be compliant in their actuation and control in order to operate safely in human environments. Manipulation tasks imply complex contact interactions with the external world, and involve reasoning about the forces and torques to be applied. Planning under contact conditions is usually impractical due to computational complexity, and a lack of precise dynamics models of the environment. We present an approach to acquiring manipulation skills on compliant robots through reinforcement learning. The initial position control policy for manipulation is initialized through kinesthetic demonstration. We augment this policy with a force/torque profile to be controlled in combination with the position trajectories. We use the Policy Improvement with Path Integrals (PI2) algorithm to learn these force/torque profiles by optimizing a cost function that measures task success. We demonstrate our approach on the Barrett WAM robot arm equipped with a 6-DOF force/torque sensor on two different manipulation tasks: opening a door with a lever door handle, and picking up a pen off the table. We show that the learnt force control policies allow successful, robust execution of the tasks.

link (url) DOI [BibTex]

Kalakrishnan, M., Righetti, L., Pastor, P., Schaal, S. Learning Force Control Policies for Compliant Manipulation In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 4639-4644, IEEE, San Francisco, USA, sep 2011 (inproceedings)

link (url) DOI [BibTex]

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Control of legged robots with optimal distribution of contact forces

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

In 2011 11th IEEE-RAS International Conference on Humanoid Robots, pages: 318-324, IEEE, Bled, Slovenia, 2011 (inproceedings)

Abstract
The development of agile and safe humanoid robots require controllers that guarantee both high tracking performance and compliance with the environment. More specifically, the control of contact interaction is of crucial importance for robots that will actively interact with their environment. Model-based controllers such as inverse dynamics or operational space control are very appealing as they offer both high tracking performance and compliance. However, while widely used for fully actuated systems such as manipulators, they are not yet standard controllers for legged robots such as humanoids. Indeed such robots are fundamentally different from manipulators as they are underactuated due to their floating-base and subject to switching contact constraints. In this paper we present an inverse dynamics controller for legged robots that use torque redundancy to create an optimal distribution of contact constraints. The resulting controller is able to minimize, given a desired motion, any quadratic cost of the contact constraints at each instant of time. In particular we show how this can be used to minimize tangential forces during locomotion, therefore significantly improving the locomotion of legged robots on difficult terrains. In addition to the theoretical result, we present simulations of a humanoid and a quadruped robot, as well as experiments on a real quadruped robot that demonstrate the advantages of the controller.

link (url) DOI [BibTex]

Righetti, L., Buchli, J., Mistry, M., Schaal, S. Control of legged robots with optimal distribution of contact forces In 2011 11th IEEE-RAS International Conference on Humanoid Robots, pages: 318-324, IEEE, Bled, Slovenia, 2011 (inproceedings)

link (url) DOI [BibTex]

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Learning Motion Primitive Goals for Robust Manipulation

Stulp, F., Theodorou, E., Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 325-331, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Applying model-free reinforcement learning to manipulation remains challenging for several reasons. First, manipulation involves physical contact, which causes discontinuous cost functions. Second, in manipulation, the end-point of the movement must be chosen carefully, as it represents a grasp which must be adapted to the pose and shape of the object. Finally, there is uncertainty in the object pose, and even the most carefully planned movement may fail if the object is not at the expected position. To address these challenges we 1) present a simplified, computationally more efficient version of our model-free reinforcement learning algorithm PI2; 2) extend PI2 so that it simultaneously learns shape parameters and goal parameters of motion primitives; 3) use shape and goal learning to acquire motion primitives that are robust to object pose uncertainty. We evaluate these contributions on a manipulation platform consisting of a 7-DOF arm with a 4-DOF hand.

link (url) DOI [BibTex]

Stulp, F., Theodorou, E., Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S. Learning Motion Primitive Goals for Robust Manipulation In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 325-331, IEEE, San Francisco, USA, sep 2011 (inproceedings)

link (url) DOI [BibTex]

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Inverse Dynamics Control of Floating-Base Robots with External Constraints: a Unified View

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

In 2011 IEEE International Conference on Robotics and Automation, pages: 1085-1090, IEEE, Shanghai, China, 2011 (inproceedings)

Abstract
Inverse dynamics controllers and operational space controllers have proved to be very efficient for compliant control of fully actuated robots such as fixed base manipulators. However legged robots such as humanoids are inherently different as they are underactuated and subject to switching external contact constraints. Recently several methods have been proposed to create inverse dynamics controllers and operational space controllers for these robots. In an attempt to compare these different approaches, we develop a general framework for inverse dynamics control and show that these methods lead to very similar controllers. We are then able to greatly simplify recent whole-body controllers based on operational space approaches using kinematic projections, bringing them closer to efficient practical implementations. We also generalize these controllers such that they can be optimal under an arbitrary quadratic cost in the commands.

link (url) DOI [BibTex]

Righetti, L., Buchli, J., Mistry, M., Schaal, S. Inverse Dynamics Control of Floating-Base Robots with External Constraints: a Unified View In 2011 IEEE International Conference on Robotics and Automation, pages: 1085-1090, IEEE, Shanghai, China, 2011 (inproceedings)

link (url) DOI [BibTex]

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Online movement adaptation based on previous sensor experiences

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

In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 365-371, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Personal robots can only become widespread if they are capable of safely operating among humans. In uncertain and highly dynamic environments such as human households, robots need to be able to instantly adapt their behavior to unforseen events. In this paper, we propose a general framework to achieve very contact-reactive motions for robotic grasping and manipulation. Associating stereotypical movements to particular tasks enables our system to use previous sensor experiences as a predictive model for subsequent task executions. We use dynamical systems, named Dynamic Movement Primitives (DMPs), to learn goal-directed behaviors from demonstration. We exploit their dynamic properties by coupling them with the measured and predicted sensor traces. This feedback loop allows for online adaptation of the movement plan. Our system can create a rich set of possible motions that account for external perturbations and perception uncertainty to generate truly robust behaviors. As an example, we present an application to grasping with the WAM robot arm.

link (url) DOI [BibTex]

Pastor, P., Righetti, L., Kalakrishnan, M., Schaal, S. Online movement adaptation based on previous sensor experiences In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 365-371, IEEE, San Francisco, USA, sep 2011 (inproceedings)

link (url) DOI [BibTex]

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Learning to grasp under uncertainty

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

In Robotics and Automation (ICRA), 2011 IEEE International Conference on, Shanghai, China, May 9-13, 2011, clmc (inproceedings)

Abstract
We present an approach that enables robots to learn motion primitives that are robust towards state estimation uncertainties. During reaching and preshaping, the robot learns to use fine manipulation strategies to maneuver the object into a pose at which closing the hand to perform the grasp is more likely to succeed. In contrast, common assumptions in grasp planning and motion planning for reaching are that these tasks can be performed independently, and that the robot has perfect knowledge of the pose of the objects in the environment. We implement our approach using Dynamic Movement Primitives and the probabilistic model-free reinforcement learning algorithm Policy Improvement with Path Integrals (PI2 ). The cost function that PI2 optimizes is a simple boolean that penalizes failed grasps. The key to acquiring robust motion primitives is to sample the actual pose of the object from a distribution that represents the state estimation uncertainty. During learning, the robot will thus optimize the chance of grasping an object from this distribution, rather than at one specific pose. In our empirical evaluation, we demonstrate how the motion primitives become more robust when grasping simple cylindrical objects, as well as more complex, non-convex objects. We also investigate how well the learned motion primitives generalize towards new object positions and other state estimation uncertainty distributions.

link (url) [BibTex]

Stulp, F., Theodorou, E., Buchli, J., Schaal, S. Learning to grasp under uncertainty In Robotics and Automation (ICRA), 2011 IEEE International Conference on, Shanghai, China, May 9-13, 2011, clmc (inproceedings)

link (url) [BibTex]

2005

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Composite adaptive control with locally weighted statistical learning

Nakanishi, J., Farrell, J. A., Schaal, S.

Neural Networks, 18(1):71-90, January 2005, clmc (article)

Abstract
This paper introduces a provably stable learning adaptive control framework with statistical learning. The proposed algorithm employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and the working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using a nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized on-line. Inspired by composite adaptive control methods, the proposed learning adaptive control algorithm uses both the tracking error and the estimation error to update the parameters. We first discuss statistical learning of nonlinear functions, and motivate our choice of the locally weighted learning framework. Second, we begin with a class of first order SISO systems for theoretical development of our learning adaptive control framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Then, we generalize our adaptive controller to higher order SISO systems, and discuss further extension to MIMO problems. Finally, we evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control.

link (url) [BibTex]

2005

Nakanishi, J., Farrell, J. A., Schaal, S. Composite adaptive control with locally weighted statistical learning Neural Networks, 18(1):71-90, January 2005, clmc (article)

link (url) [BibTex]

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Natural Actor-Critic

Peters, J., Vijayakumar, S., Schaal, S.

In Proceedings of the 16th European Conference on Machine Learning, 3720, pages: 280-291, (Editors: Gama, J.;Camacho, R.;Brazdil, P.;Jorge, A.;Torgo, L.), Springer, ECML, 2005, clmc (inproceedings)

Abstract
This paper investigates a novel model-free reinforcement learning architecture, the Natural Actor-Critic. The actor updates are based on stochastic policy gradients employing AmariÕs natural gradient approach, while the critic obtains both the natural policy gradient and additional parameters of a value function simultaneously by linear regres- sion. We show that actor improvements with natural policy gradients are particularly appealing as these are independent of coordinate frame of the chosen policy representation, and can be estimated more efficiently than regular policy gradients. The critic makes use of a special basis function parameterization motivated by the policy-gradient compatible function approximation. We show that several well-known reinforcement learning methods such as the original Actor-Critic and BradtkeÕs Linear Quadratic Q-Learning are in fact Natural Actor-Critic algorithms. Em- pirical evaluations illustrate the effectiveness of our techniques in com- parison to previous methods, and also demonstrate their applicability for learning control on an anthropomorphic robot arm.

link (url) DOI [BibTex]

Peters, J., Vijayakumar, S., Schaal, S. Natural Actor-Critic In Proceedings of the 16th European Conference on Machine Learning, 3720, pages: 280-291, (Editors: Gama, J.;Camacho, R.;Brazdil, P.;Jorge, A.;Torgo, L.), Springer, ECML, 2005, clmc (inproceedings)

link (url) DOI [BibTex]

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Comparative experiments on task space control with redundancy resolution

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S.

In Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3901-3908, Edmonton, Alberta, Canada, Aug. 2-6, IROS, 2005, clmc (inproceedings)

Abstract
Understanding the principles of motor coordination with redundant degrees of freedom still remains a challenging problem, particularly for new research in highly redundant robots like humanoids. Even after more than a decade of research, task space control with redundacy resolution still remains an incompletely understood theoretical topic, and also lacks a larger body of thorough experimental investigation on complex robotic systems. This paper presents our first steps towards the development of a working redundancy resolution algorithm which is robust against modeling errors and unforeseen disturbances arising from contact forces. To gain a better understanding of the pros and cons of different approaches to redundancy resolution, we focus on a comparative empirical evaluation. First, we review several redundancy resolution schemes at the velocity, acceleration and torque levels presented in the literature in a common notational framework and also introduce some new variants of these previous approaches. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm. Surprisingly, one of our simplest algorithms empirically demonstrates the best performance, despite, from a theoretical point, the algorithm does not share the same beauty as some of the other methods. Finally, we discuss practical properties of these control algorithms, particularly in light of inevitable modeling errors of the robot dynamics.

link (url) DOI [BibTex]

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S. Comparative experiments on task space control with redundancy resolution In Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3901-3908, Edmonton, Alberta, Canada, Aug. 2-6, IROS, 2005, clmc (inproceedings)

link (url) DOI [BibTex]

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A model of smooth pursuit based on learning of the target dynamics using only retinal signals

Shibata, T., Tabata, H., Schaal, S., Kawato, M.

Neural Networks, 18, pages: 213-225, 2005, clmc (article)

Abstract
While the predictive nature of the primate smooth pursuit system has been evident through several behavioural and neurophysiological experiments, few models have attempted to explain these results comprehensively. The model we propose in this paper in line with previous models employing optimal control theory; however, we hypothesize two new issues: (1) the medical superior temporal (MST) area in the cerebral cortex implements a recurrent neural network (RNN) in order to predict the current or future target velocity, and (2) a forward model of the target motion is acquired by on-line learning. We use stimulation studies to demonstrate how our new model supports these hypotheses.

link (url) [BibTex]

Shibata, T., Tabata, H., Schaal, S., Kawato, M. A model of smooth pursuit based on learning of the target dynamics using only retinal signals Neural Networks, 18, pages: 213-225, 2005, clmc (article)

link (url) [BibTex]

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Linear and Nonlinear Estimation models applied to Hemodynamic Model

Theodorou, E.

Technical Report-2005-1, Computational Action and Vision Lab University of Minnesota, 2005, clmc (techreport)

Abstract
The relation between BOLD signal and neural activity is still poorly understood. The Gaussian Linear Model known as GLM is broadly used in many fMRI data analysis for recovering the underlying neural activity. Although GLM has been proved to be a really useful tool for analyzing fMRI data it can not be used for describing the complex biophysical process of neural metabolism. In this technical report we make use of a system of Stochastic Differential Equations that is based on Buxton model [1] for describing the underlying computational principles of hemodynamic process. Based on this SDE we built a Kalman Filter estimator so as to estimate the induced neural signal as well as the blood inflow under physiologic and sensor noise. The performance of Kalman Filter estimator is investigated under different physiologic noise characteristics and measurement frequencies.

PDF [BibTex]

Theodorou, E. Linear and Nonlinear Estimation models applied to Hemodynamic Model Technical Report-2005-1, Computational Action and Vision Lab University of Minnesota, 2005, clmc (techreport)

PDF [BibTex]

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Predicting EMG Data from M1 Neurons with Variational Bayesian Least Squares

Ting, J., D’Souza, A., Yamamoto, K., Yoshioka, T., Hoffman, D., Kakei, S., Sergio, L., Kalaska, J., Kawato, M., Strick, P., Schaal, S.

In Advances in Neural Information Processing Systems 18 (NIPS 2005), (Editors: Weiss, Y.;Schölkopf, B.;Platt, J.), Cambridge, MA: MIT Press, Vancouver, BC, Dec. 6-11, 2005, clmc (inproceedings)

Abstract
An increasing number of projects in neuroscience requires the statistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing, or in operating artificial devices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classi-cal linear regression approaches are often numercially too fragile in high dimen-sions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faithfully reconstructed with linear ap-proaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that automatically detects and excludes irrelevant features in the data, and regular-izes against overfitting. In comparison with ordinary least squares, stepwise re-gression, partial least squares, and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of regularization against overfitting, computational efficiency, and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques. As neuroscientific results, our analyses demonstrate that EMG data can be well pre-dicted from M1 neurons, further opening the path for possible real-time inter-faces between brains and machines.

link (url) [BibTex]

Ting, J., D’Souza, A., Yamamoto, K., Yoshioka, T., Hoffman, D., Kakei, S., Sergio, L., Kalaska, J., Kawato, M., Strick, P., Schaal, S. Predicting EMG Data from M1 Neurons with Variational Bayesian Least Squares In Advances in Neural Information Processing Systems 18 (NIPS 2005), (Editors: Weiss, Y.;Schölkopf, B.;Platt, J.), Cambridge, MA: MIT Press, Vancouver, BC, Dec. 6-11, 2005, clmc (inproceedings)

link (url) [BibTex]

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Rapbid synchronization and accurate phase-locking of rhythmic motor primitives

Pongas, D., Billard, A., Schaal, S.

In IEEE International Conference on Intelligent Robots and Systems (IROS 2005), pages: 2911-2916, Edmonton, Alberta, Canada, Aug. 2-6, 2005, clmc (inproceedings)

Abstract
Rhythmic movement is ubiquitous in human and animal behavior, e.g., as in locomotion, dancing, swimming, chewing, scratching, music playing, etc. A particular feature of rhythmic movement in biology is the rapid synchronization and phase locking with other rhythmic events in the environment, for instance music or visual stimuli as in ball juggling. In traditional oscillator theories to rhythmic movement generation, synchronization with another signal is relatively slow, and it is not easy to achieve accurate phase locking with a particular feature of the driving stimulus. Using a recently developed framework of dynamic motor primitives, we demonstrate a novel algorithm for very rapid synchronizaton of a rhythmic movement pattern, which can phase lock any feature of the movement to any particulur event in the driving stimulus. As an example application, we demonstrate how an anthropomorphic robot can use imitation learning to acquire a complex rumming pattern and keep it synchronized with an external rhythm generator that changes its frequency over time.

link (url) [BibTex]

Pongas, D., Billard, A., Schaal, S. Rapbid synchronization and accurate phase-locking of rhythmic motor primitives In IEEE International Conference on Intelligent Robots and Systems (IROS 2005), pages: 2911-2916, Edmonton, Alberta, Canada, Aug. 2-6, 2005, clmc (inproceedings)

link (url) [BibTex]

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Parametric and Non-Parametric approaches for nonlinear tracking of moving objects

Hidaka, Y, Theodorou, E.

Technical Report-2005-1, 2005, clmc (article)

PDF [BibTex]

Hidaka, Y, Theodorou, E. Parametric and Non-Parametric approaches for nonlinear tracking of moving objects Technical Report-2005-1, 2005, clmc (article)

PDF [BibTex]

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A new methodology for robot control design

Peters, J., Mistry, M., Udwadia, F. E., Schaal, S.

In The 5th ASME International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC 2005), Long Beach, CA, Sept. 24-28, 2005, clmc (inproceedings)

Abstract
Gauss principle of least constraint and its generalizations have provided a useful insights for the development of tracking controllers for mechanical systems (Udwadia,2003). Using this concept, we present a novel methodology for the design of a specific class of robot controllers. With our new framework, we demonstrate that well-known and also several novel nonlinear robot control laws can be derived from this generic framework, and show experimental verifications on a Sarcos Master Arm robot for some of these controllers. We believe that the suggested approach unifies and simplifies the design of optimal nonlinear control laws for robots obeying rigid body dynamics equations, both with or without external constraints, holonomic or nonholonomic constraints, with over-actuation or underactuation, as well as open-chain and closed-chain kinematics.

link (url) [BibTex]

Peters, J., Mistry, M., Udwadia, F. E., Schaal, S. A new methodology for robot control design In The 5th ASME International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC 2005), Long Beach, CA, Sept. 24-28, 2005, clmc (inproceedings)

link (url) [BibTex]

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Arm movement experiments with joint space force fields using an exoskeleton robot

Mistry, M., Mohajerian, P., Schaal, S.

In IEEE Ninth International Conference on Rehabilitation Robotics, pages: 408-413, Chicago, Illinois, June 28-July 1, 2005, clmc (inproceedings)

Abstract
A new experimental platform permits us to study a novel variety of issues of human motor control, particularly full 3-D movements involving the major seven degrees-of-freedom (DOF) of the human arm. We incorporate a seven DOF robot exoskeleton, and can minimize weight and inertia through gravity, Coriolis, and inertia compensation, such that subjects' arm movements are largely unaffected by the manipulandum. Torque perturbations can be individually applied to any or all seven joints of the human arm, thus creating novel dynamic environments, or force fields, for subjects to respond and adapt to. Our first study investigates a joint space force field where the shoulder velocity drives a disturbing force in the elbow joint. Results demonstrate that subjects learn to compensate for the force field within about 100 trials, and from the strong presence of aftereffects when removing the field in some randomized catch trials, that an inverse dynamics, or internal model, of the force field is formed by the nervous system. Interestingly, while post-learning hand trajectories return to baseline, joint space trajectories remained changed in response to the field, indicating that besides learning a model of the force field, the nervous system also chose to exploit the space to minimize the effects of the force field on the realization of the endpoint trajectory plan. Further applications for our apparatus include studies in motor system redundancy resolution and inverse kinematics, as well as rehabilitation.

link (url) [BibTex]

Mistry, M., Mohajerian, P., Schaal, S. Arm movement experiments with joint space force fields using an exoskeleton robot In IEEE Ninth International Conference on Rehabilitation Robotics, pages: 408-413, Chicago, Illinois, June 28-July 1, 2005, clmc (inproceedings)

link (url) [BibTex]

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A unifying framework for the control of robotics systems

Peters, J., Mistry, M., Udwadia, F. E., Cory, R., Nakanishi, J., Schaal, S.

In IEEE International Conference on Intelligent Robots and Systems (IROS 2005), pages: 1824-1831, Edmonton, Alberta, Canada, Aug. 2-6, 2005, clmc (inproceedings)

Abstract
Recently, [1] suggested to derive tracking controllers for mechanical systems using a generalization of GaussÕ principle of least constraint. This method al-lows us to reformulate control problems as a special class of optimal control. We take this line of reasoning one step further and demonstrate that well-known and also several novel nonlinear robot control laws can be derived from this generic methodology. We show experimental verifications on a Sar-cos Master Arm robot for some of the the derived controllers.We believe that the suggested approach offers a promising unification and simplification of nonlinear control law design for robots obeying rigid body dynamics equa-tions, both with or without external constraints, with over-actuation or under-actuation, as well as open-chain and closed-chain kinematics.

link (url) [BibTex]

Peters, J., Mistry, M., Udwadia, F. E., Cory, R., Nakanishi, J., Schaal, S. A unifying framework for the control of robotics systems In IEEE International Conference on Intelligent Robots and Systems (IROS 2005), pages: 1824-1831, Edmonton, Alberta, Canada, Aug. 2-6, 2005, clmc (inproceedings)

link (url) [BibTex]

1999

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Is imitation learning the route to humanoid robots?

Schaal, S.

Trends in Cognitive Sciences, 3(6):233-242, 1999, clmc (article)

Abstract
This review will focus on two recent developments in artificial intelligence and neural computation: learning from imitation and the development of humanoid robots. It will be postulated that the study of imitation learning offers a promising route to gain new insights into mechanisms of perceptual motor control that could ultimately lead to the creation of autonomous humanoid robots. This hope is justified because imitation learning channels research efforts towards three important issues: efficient motor learning, the connection between action and perception, and modular motor control in form of movement primitives. In order to make these points, first, a brief review of imitation learning will be given from the view of psychology and neuroscience. In these fields, representations and functional connections between action and perception have been explored that contribute to the understanding of motor acts of other beings. The recent discovery that some areas in the primate brain are active during both movement perception and execution provided a first idea of the possible neural basis of imitation. Secondly, computational approaches to imitation learning will be described, initially from the perspective of traditional AI and robotics, and then with a focus on neural network models and statistical learning research. Parallels and differences between biological and computational approaches to imitation will be highlighted. The review will end with an overview of current projects that actually employ imitation learning for humanoid robots.

link (url) [BibTex]

1999

Schaal, S. Is imitation learning the route to humanoid robots? Trends in Cognitive Sciences, 3(6):233-242, 1999, clmc (article)

link (url) [BibTex]

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Nonparametric regression for learning nonlinear transformations

Schaal, S.

In Prerational Intelligence in Strategies, High-Level Processes and Collective Behavior, 2, pages: 595-621, (Editors: Ritter, H.;Cruse, H.;Dean, J.), Kluwer Academic Publishers, 1999, clmc (inbook)

Abstract
Information processing in animals and artificial movement systems consists of a series of transformations that map sensory signals to intermediate representations, and finally to motor commands. Given the physical and neuroanatomical differences between individuals and the need for plasticity during development, it is highly likely that such transformations are learned rather than pre-programmed by evolution. Such self-organizing processes, capable of discovering nonlinear dependencies between different groups of signals, are one essential part of prerational intelligence. While neural network algorithms seem to be the natural choice when searching for solutions for learning transformations, this paper will take a more careful look at which types of neural networks are actually suited for the requirements of an autonomous learning system. The approach that we will pursue is guided by recent developments in learning theory that have linked neural network learning to well established statistical theories. In particular, this new statistical understanding has given rise to the development of neural network systems that are directly based on statistical methods. One family of such methods stems from nonparametric regression. This paper will compare nonparametric learning with the more widely used parametric counterparts in a non technical fashion, and investigate how these two families differ in their properties and their applicabilities. We will argue that nonparametric neural networks offer a set of characteristics that make them a very promising candidate for on-line learning in autonomous system.

link (url) [BibTex]

Schaal, S. Nonparametric regression for learning nonlinear transformations In Prerational Intelligence in Strategies, High-Level Processes and Collective Behavior, 2, pages: 595-621, (Editors: Ritter, H.;Cruse, H.;Dean, J.), Kluwer Academic Publishers, 1999, clmc (inbook)

link (url) [BibTex]

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Segmentation of endpoint trajectories does not imply segmented control

Sternad, D., Schaal, D.

Experimental Brain Research, 124(1):118-136, 1999, clmc (article)

Abstract
While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, still remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in 3D human drawing movements are re-examined: (1) the stroke-based segmentation hypothesis based on the results that the proportionality coefficient of the 2/3 power law changes discontinuously with each new â??strokeâ?, and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of 3D drawing movements. In two experiments human subjects performed a set of elliptical and figure-8 patterns of different sizes and orientations using their whole arm in 3D. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features as reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.

link (url) [BibTex]

Sternad, D., Schaal, D. Segmentation of endpoint trajectories does not imply segmented control Experimental Brain Research, 124(1):118-136, 1999, clmc (article)

link (url) [BibTex]

1998

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Programmable pattern generators

Schaal, S., Sternad, D.

In 3rd International Conference on Computational Intelligence in Neuroscience, pages: 48-51, Research Triangle Park, NC, Oct. 24-28, October 1998, clmc (inproceedings)

Abstract
This paper explores the idea to create complex human-like arm movements from movement primitives based on nonlinear attractor dynamics. Each degree-of-freedom of an arm is assumed to have two independent abilities to create movement, one through a discrete dynamic system, and one through a rhythmic system. The discrete system creates point-to-point movements based on internal or external target specifications. The rhythmic system can add an additional oscillatory movement relative to the current position of the discrete system. In the present study, we develop appropriate dynamic systems that can realize the above model, motivate the particular choice of the systems from a biological and engineering point of view, and present simulation results of the performance of such movement primitives. Implementation results on a Sarcos Dexterous Arm are discussed.

link (url) [BibTex]

1998

Schaal, S., Sternad, D. Programmable pattern generators In 3rd International Conference on Computational Intelligence in Neuroscience, pages: 48-51, Research Triangle Park, NC, Oct. 24-28, October 1998, clmc (inproceedings)

link (url) [BibTex]

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Robust local learning in high dimensional spaces

Vijayakumar, S., Schaal, S.

In 5th Joint Symposium on Neural Computation, pages: 186-193, Institute for Neural Computation, University of California, San Diego, San Diego, CA, 1998, clmc (inproceedings)

Abstract
Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings requires a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper, we suggest a partial revision of this view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm.

[BibTex]

Vijayakumar, S., Schaal, S. Robust local learning in high dimensional spaces In 5th Joint Symposium on Neural Computation, pages: 186-193, Institute for Neural Computation, University of California, San Diego, San Diego, CA, 1998, clmc (inproceedings)

[BibTex]

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Local dimensionality reduction

Schaal, S., Vijayakumar, S., Atkeson, C. G.

In Advances in Neural Information Processing Systems 10, pages: 633-639, (Editors: Jordan, M. I.;Kearns, M. J.;Solla, S. A.), MIT Press, Cambridge, MA, 1998, clmc (inproceedings)

Abstract
If globally high dimensional data has locally only low dimensional distributions, it is advantageous to perform a local dimensionality reduction before further processing the data. In this paper we examine several techniques for local dimensionality reduction in the context of locally weighted linear regression. As possible candidates, we derive local versions of factor analysis regression, principle component regression, principle component regression on joint distributions, and partial least squares regression. After outlining the statistical bases of these methods, we perform Monte Carlo simulations to evaluate their robustness with respect to violations of their statistical assumptions. One surprising outcome is that locally weighted partial least squares regression offers the best average results, thus outperforming even factor analysis, the theoretically most appealing of our candidate techniques.

link (url) [BibTex]

Schaal, S., Vijayakumar, S., Atkeson, C. G. Local dimensionality reduction In Advances in Neural Information Processing Systems 10, pages: 633-639, (Editors: Jordan, M. I.;Kearns, M. J.;Solla, S. A.), MIT Press, Cambridge, MA, 1998, clmc (inproceedings)

link (url) [BibTex]

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Constructive incremental learning from only local information

Schaal, S., Atkeson, C. G.

Neural Computation, 10(8):2047-2084, 1998, clmc (article)

Abstract
We introduce a constructive, incremental learning system for regression problems that models data by means of spatially localized linear models. In contrast to other approaches, the size and shape of the receptive field of each locally linear model as well as the parameters of the locally linear model itself are learned independently, i.e., without the need for competition or any other kind of communication. Independent learning is accomplished by incrementally minimizing a weighted local cross validation error. As a result, we obtain a learning system that can allocate resources as needed while dealing with the bias-variance dilemma in a principled way. The spatial localization of the linear models increases robustness towards negative interference. Our learning system can be interpreted as a nonparametric adaptive bandwidth smoother, as a mixture of experts where the experts are trained in isolation, and as a learning system which profits from combining independent expert knowledge on the same problem. This paper illustrates the potential learning capabilities of purely local learning and offers an interesting and powerful approach to learning with receptive fields. 

link (url) [BibTex]

Schaal, S., Atkeson, C. G. Constructive incremental learning from only local information Neural Computation, 10(8):2047-2084, 1998, clmc (article)

link (url) [BibTex]

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Biomimetic gaze stabilization based on a study of the vestibulocerebellum

Shibata, T., Schaal, S.

In European Workshop on Learning Robots, pages: 84-94, Edinburgh, UK, 1998, clmc (inproceedings)

Abstract
Accurate oculomotor control is one of the essential pre-requisites for successful visuomotor coordination. In this paper, we suggest a biologically inspired control system for learning gaze stabilization with a biomimetic robotic oculomotor system. In a stepwise fashion, we develop a control circuit for the vestibulo-ocular reflex (VOR) and the opto-kinetic response (OKR), and add a nonlinear learning network to allow adaptivity. We discuss the parallels and differences of our system with biological oculomotor control and suggest solutions how to deal with nonlinearities and time delays in the control system. In simulation and actual robot studies, we demonstrate that our system can learn gaze stabilization in real time in only a few seconds with high final accuracy.

link (url) [BibTex]

Shibata, T., Schaal, S. Biomimetic gaze stabilization based on a study of the vestibulocerebellum In European Workshop on Learning Robots, pages: 84-94, Edinburgh, UK, 1998, clmc (inproceedings)

link (url) [BibTex]

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Towards biomimetic vision

Shibata, T., Schaal, S.

In International Conference on Intelligence Robots and Systems, pages: 872-879, Victoria, Canada, 1998, clmc (inproceedings)

Abstract
Oculomotor control is the foundation of most biological visual systems, as well as an important component in the entire perceptual-motor system. We review some of the most basic principles of biological oculomotor systems, and explore their usefulness from both the biological and computational point of view. As an example of biomimetic oculomotor control, we present the state of our implementations and experimental results using the vestibulo-ocular-reflex and opto-kinetic-reflex paradigm

link (url) [BibTex]

Shibata, T., Schaal, S. Towards biomimetic vision In International Conference on Intelligence Robots and Systems, pages: 872-879, Victoria, Canada, 1998, clmc (inproceedings)

link (url) [BibTex]