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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

[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]

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]

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]

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]

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]

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]

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]

PDF [BibTex]


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Learning of grasp selection based on shape-templates

Herzog, A.

Karlsruhe Institute of Technology, 2011 (mastersthesis)

[BibTex]

[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]

[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]

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]

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]

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]

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]

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]

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]

link (url) [BibTex]

2006


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Learning operational space control

Peters, J., Schaal, S.

In Robotics: Science and Systems II (RSS 2006), pages: 255-262, (Editors: Gaurav S. Sukhatme and Stefan Schaal and Wolfram Burgard and Dieter Fox), Cambridge, MA: MIT Press, RSS , 2006, clmc (inproceedings)

Abstract
While operational space control is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in complex robots, e.g., humanoid robots. In such cases, learning control methods can offer an interesting alternative to analytical control algorithms. However, the resulting learning problem is ill-defined as it requires to learn an inverse mapping of a usually redundant system, which is well known to suffer from the property of non-covexity of the solution space, i.e., the learning system could generate motor commands that try to steer the robot into physically impossible configurations. A first important insight for this paper is that, nevertheless, a physically correct solution to the inverse problem does exits when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on a recent insight that many operational space controllers can be understood in terms of a constraint optimal control problem. The cost function associated with this optimal control problem allows us to formulate a learning algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the view of machine learning, the learning problem corresponds to a reinforcement learning problem that maximizes an immediate reward and that employs an expectation-maximization policy search algorithm. Evaluations on a three degrees of freedom robot arm illustrate the feasability of our suggested approach.

link (url) [BibTex]

2006

link (url) [BibTex]


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Reinforcement Learning for Parameterized Motor Primitives

Peters, J., Schaal, S.

In Proceedings of the 2006 International Joint Conference on Neural Networks, pages: 73-80, IJCNN, 2006, clmc (inproceedings)

Abstract
One of the major challenges in both action generation for robotics and in the understanding of human motor control is to learn the "building blocks of movement generation", called motor primitives. Motor primitives, as used in this paper, are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. While a lot of progress has been made in teaching parameterized motor primitives using supervised or imitation learning, the self-improvement by interaction of the system with the environment remains a challenging problem. In this paper, we evaluate different reinforcement learning approaches for improving the performance of parameterized motor primitives. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and outline both established and novel algorithms for the gradient-based improvement of parameterized policies. We compare these algorithms in the context of motor primitive learning, and show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Statistical Learning of LQG controllers

Theodorou, E.

Technical Report-2006-1, Computational Action and Vision Lab University of Minnesota, 2006, clmc (techreport)

PDF [BibTex]

PDF [BibTex]


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Approximate nearest neighbor regression in very high dimensions

Vijayakumar, S., DSouza, A., Schaal, S.

In Nearest-Neighbor Methods in Learning and Vision, pages: 103-142, (Editors: Shakhnarovich, G.;Darrell, T.;Indyk, P.), Cambridge, MA: MIT Press, 2006, clmc (inbook)

link (url) [BibTex]

link (url) [BibTex]

2004


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Discovering optimal imitation strategies

Billard, A., Epars, Y., Calinon, S., Cheng, G., Schaal, S.

Robotics and Autonomous Systems, 47(2-3):68-77, 2004, clmc (article)

Abstract
This paper develops a general policy for learning relevant features of an imitation task. We restrict our study to imitation of manipulative tasks or of gestures. The imitation process is modeled as a hierarchical optimization system, which minimizes the discrepancy between two multi-dimensional datasets. To classify across manipulation strategies, we apply a probabilistic analysis to data in Cartesian and joint spaces. We determine a general metric that optimizes the policy of task reproduction, following strategy determination. The model successfully discovers strategies in six different imitative tasks and controls task reproduction by a full body humanoid robot.

[BibTex]

2004

[BibTex]


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Learning Composite Adaptive Control for a Class of Nonlinear Systems

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

In IEEE International Conference on Robotics and Automation, pages: 2647-2652, New Orleans, LA, USA, April 2004, 2004, clmc (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Rhythmic movement is not discrete

Schaal, S., Sternad, D., Osu, R., Kawato, M.

Nature Neuroscience, 7(10):1137-1144, 2004, clmc (article)

Abstract
Rhythmic movements, like walking, chewing, or scratching, are phylogenetically old mo-tor behaviors found in many organisms, ranging from insects to primates. In contrast, discrete movements, like reaching, grasping, or kicking, are behaviors that have reached sophistication primarily in younger species, particularly in primates. Neurophysiological and computational research on arm motor control has focused almost exclusively on dis-crete movements, essentially assuming similar neural circuitry for rhythmic tasks. In con-trast, many behavioral studies focused on rhythmic models, subsuming discrete move-ment as a special case. Here, using a human functional neuroimaging experiment, we show that in addition to areas activated in rhythmic movement, discrete movement in-volves several higher cortical planning areas, despite both movement conditions were confined to the same single wrist joint. These results provide the first neuroscientific evi-dence that rhythmic arm movement cannot be part of a more general discrete movement system, and may require separate neurophysiological and theoretical treatment.

link (url) [BibTex]

link (url) [BibTex]


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Learning from demonstration and adaptation of biped locomotion

Nakanishi, J., Morimoto, J., Endo, G., Cheng, G., Schaal, S., Kawato, M.

Robotics and Autonomous Systems, 47(2-3):79-91, 2004, clmc (article)

Abstract
In this paper, we introduce a framework for learning biped locomotion using dynamical movement primitives based on non-linear oscillators. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like locomotion. We suggest dynamical movement primitives as a central pattern generator (CPG) of a biped robot, an approach we have previously proposed for learning and encoding complex human movements. Demonstrated trajectories are learned through movement primitives by locally weighted regression, and the frequency of the learned trajectories is adjusted automatically by a novel frequency adaptation algorithmbased on phase resetting and entrainment of coupled oscillators. Numerical simulations and experimental implementation on a physical robot demonstrate the effectiveness of the proposed locomotioncontroller.

link (url) [BibTex]

link (url) [BibTex]


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Towards Tractable Parameter-Free Statistical Learning (Phd Thesis)

D’Souza, A

Department of Computer Science, University of Southern California, Los Angeles, 2004, clmc (phdthesis)

link (url) [BibTex]

link (url) [BibTex]


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A framework for learning biped locomotion with dynamic movement primitives

Nakanishi, J., Morimoto, J., Endo, G., Cheng, G., Schaal, S., Kawato, M.

In IEEE-RAS/RSJ International Conference on Humanoid Robots (Humanoids 2004), IEEE, Los Angeles, CA: Nov.10-12, Santa Monica, CA, 2004, clmc (inproceedings)

Abstract
This article summarizes our framework for learning biped locomotion using dynamical movement primitives based on nonlinear oscillators. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like locomotion. We suggest dynamical movement primitives as a central pattern generator (CPG) of a biped robot, an approach we have previously proposed for learning and encoding complex human movements. Demonstrated trajectories are learned through movement primitives by locally weighted regression, and the frequency of the learned trajectories is adjusted automatically by a frequency adaptation algorithm based on phase resetting and entrainment of coupled oscillators. Numerical simulations and experimental implementation on a physical robot demonstrate the effectiveness of the proposed locomotion controller. Furthermore, we demonstrate that phase resetting contributes to robustness against external perturbations and environmental changes by numerical simulations and experiments.

link (url) [BibTex]

link (url) [BibTex]


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Learning Motor Primitives with Reinforcement Learning

Peters, J., Schaal, S.

In Proceedings of the 11th Joint Symposium on Neural Computation, http://resolver.caltech.edu/CaltechJSNC:2004.poster020, 2004, clmc (inproceedings)

Abstract
One of the major challenges in action generation for robotics and in the understanding of human motor control is to learn the "building blocks of move- ment generation," or more precisely, motor primitives. Recently, Ijspeert et al. [1, 2] suggested a novel framework how to use nonlinear dynamical systems as motor primitives. While a lot of progress has been made in teaching these mo- tor primitives using supervised or imitation learning, the self-improvement by interaction of the system with the environment remains a challenging problem. In this poster, we evaluate different reinforcement learning approaches can be used in order to improve the performance of motor primitives. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and line out how these lead to a novel algorithm which is based on natural policy gradients [3]. We compare this algorithm to previous reinforcement learning algorithms in the context of dynamic motor primitive learning, and show that it outperforms these by at least an order of magnitude. We demonstrate the efficiency of the resulting reinforcement learning method for creating complex behaviors for automous robotics. The studied behaviors will include both discrete, finite tasks such as baseball swings, as well as complex rhythmic patterns as they occur in biped locomotion

[BibTex]

[BibTex]


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Feedback error learning and nonlinear adaptive control

Nakanishi, J., Schaal, S.

Neural Networks, 17(10):1453-1465, 2004, clmc (article)

Abstract
In this paper, we present our theoretical investigations of the technique of feedback error learning (FEL) from the viewpoint of adaptive control. We first discuss the relationship between FEL and nonlinear adaptive control with adaptive feedback linearization, and show that FEL can be interpreted as a form of nonlinear adaptive control. Second, we present a Lyapunov analysis suggesting that the condition of strictly positive realness (SPR) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Specifically, for a class of second order SISO systems, we show that this condition reduces to KD^2 > KP; where KP and KD are positive position and velocity feedback gains, respectively. Moreover, we provide a ÔpassivityÕ-based stability analysis which suggests that SPR of the tracking error dynamics is a necessary and sufficient condition for asymptotic hyperstability. Thus, the condition KD^2>KP mentioned above is not only a sufficient but also necessary condition to guarantee asymptotic hyperstability of FEL, i.e. the tracking error is bounded and asymptotically converges to zero. As a further point, we explore the adaptive control and FEL framework for feedforward control formulations, and derive an additional sufficient condition for asymptotic stability in the sense of Lyapunov. Finally, we present numerical simulations to illustrate the stability properties of FEL obtained from our mathematical analysis.

link (url) [BibTex]

link (url) [BibTex]


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Computational approaches to motor learning by imitation

Schaal, S., Ijspeert, A., Billard, A.

In The Neuroscience of Social Interaction, (1431):199-218, (Editors: Frith, C. D.;Wolpert, D.), Oxford University Press, Oxford, 2004, clmc (inbook)

Abstract
Movement imitation requires a complex set of mechanisms that map an observed movement of a teacher onto one's own movement apparatus. Relevant problems include movement recognition, pose estimation, pose tracking, body correspondence, coordinate transformation from external to egocentric space, matching of observed against previously learned movement, resolution of redundant degrees-of-freedom that are unconstrained by the observation, suitable movement representations for imitation, modularization of motor control, etc. All of these topics by themselves are active research problems in computational and neurobiological sciences, such that their combination into a complete imitation system remains a daunting undertaking - indeed, one could argue that we need to understand the complete perception-action loop. As a strategy to untangle the complexity of imitation, this paper will examine imitation purely from a computational point of view, i.e. we will review statistical and mathematical approaches that have been suggested for tackling parts of the imitation problem, and discuss their merits, disadvantages and underlying principles. Given the focus on action recognition of other contributions in this special issue, this paper will primarily emphasize the motor side of imitation, assuming that a perceptual system has already identified important features of a demonstrated movement and created their corresponding spatial information. Based on the formalization of motor control in terms of control policies and their associated performance criteria, useful taxonomies of imitation learning can be generated that clarify different approaches and future research directions.

link (url) [BibTex]

link (url) [BibTex]

2000


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Reciprocal excitation between biological and robotic research

Schaal, S., Sternad, D., Dean, W., Kotoska, S., Osu, R., Kawato, M.

In Sensor Fusion and Decentralized Control in Robotic Systems III, Proceedings of SPIE, 4196, pages: 30-40, Boston, MA, Nov.5-8, 2000, November 2000, clmc (inproceedings)

Abstract
While biological principles have inspired researchers in computational and engineering research for a long time, there is still rather limited knowledge flow back from computational to biological domains. This paper presents examples of our work where research on anthropomorphic robots lead us to new insights into explaining biological movement phenomena, starting from behavioral studies up to brain imaging studies. Our research over the past years has focused on principles of trajectory formation with nonlinear dynamical systems, on learning internal models for nonlinear control, and on advanced topics like imitation learning. The formal and empirical analyses of the kinematics and dynamics of movements systems and the tasks that they need to perform lead us to suggest principles of motor control that later on we found surprisingly related to human behavior and even brain activity.

link (url) [BibTex]

2000

link (url) [BibTex]


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Nonlinear dynamical systems as movement primitives

Schaal, S., Kotosaka, S., Sternad, D.

In Humanoids2000, First IEEE-RAS International Conference on Humanoid Robots, CD-Proceedings, Cambridge, MA, September 2000, clmc (inproceedings)

Abstract
This paper explores the idea to create complex human-like movements from movement primitives based on nonlinear attractor dynamics. Each degree-of-freedom of a limb 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. The model was implemented for a drumming task on a humanoid robot

link (url) [BibTex]

link (url) [BibTex]


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Real Time Learning in Humanoids: A challenge for scalability of Online Algorithms

Vijayakumar, S., Schaal, S.

In Humanoids2000, First IEEE-RAS International Conference on Humanoid Robots, CD-Proceedings, Cambridge, MA, September 2000, clmc (inproceedings)

Abstract
While recent research in neural networks and statistical learning has focused mostly on learning from finite data sets without stringent constraints on computational efficiency, there is an increasing number of learning problems that require real-time performance from an essentially infinite stream of incrementally arriving data. This paper demonstrates how even high-dimensional learning problems of this kind can successfully be dealt with by techniques from nonparametric regression and locally weighted learning. As an example, we describe the application of one of the most advanced of such algorithms, Locally Weighted Projection Regression (LWPR), to the on-line learning of the inverse dynamics model of an actual seven degree-of-freedom anthropomorphic robot arm. LWPR's linear computational complexity in the number of input dimensions, its inherent mechanisms of local dimensionality reduction, and its sound learning rule based on incremental stochastic leave-one-out cross validation allows -- to our knowledge for the first time -- implementing inverse dynamics learning for such a complex robot with real-time performance. In our sample task, the robot acquires the local inverse dynamics model needed to trace a figure-8 in only 60 seconds of training.

link (url) [BibTex]

link (url) [BibTex]


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Synchronized robot drumming by neural oscillator

Kotosaka, S., Schaal, S.

In The International Symposium on Adaptive Motion of Animals and Machines, Montreal, Canada, August 2000, clmc (inproceedings)

Abstract
Sensory-motor integration is one of the key issues in robotics. In this paper, we propose an approach to rhythmic arm movement control that is synchronized with an external signal based on exploiting a simple neural oscillator network. Trajectory generation by the neural oscillator is a biologically inspired method that can allow us to generate a smooth and continuous trajectory. The parameter tuning of the oscillators is used to generate a synchronized movement with wide intervals. We adopted the method for the drumming task as an example task. By using this method, the robot can realize synchronized drumming with wide drumming intervals in real time. The paper also shows the experimental results of drumming by a humanoid robot.

link (url) [BibTex]

link (url) [BibTex]


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A brachiating robot controller

Nakanishi, J., Fukuda, T., Koditschek, D. E.

IEEE Transactions on Robotics and Automation, 16(2):109-123, 2000, clmc (article)

Abstract
We report on our empirical studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an apeâ??s brachiation, we encode this task as the output of a â??target dynamical system.â? Numerical simulations indicate that the resulting controller solves a number of brachiation problems that we term the â??ladder,â? â??swing-up,â? and â??ropeâ? problems. Preliminary analysis provides some explanation for this success. The proposed controller is implemented on a physical system in our laboratory. The robot achieves behaviors including â??swing locomotionâ? and â??swing upâ? and is capable of continuous locomotion over several rungs of a ladder. We discuss a number of formal questions whose answers will be required to gain a full understanding of the strengths and weaknesses of this approach.

link (url) [BibTex]

link (url) [BibTex]


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Real-time robot learning with locally weighted statistical learning

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

In International Conference on Robotics and Automation (ICRA2000), San Francisco, April 2000, 2000, clmc (inproceedings)

Abstract
Locally weighted learning (LWL) is a class of statistical learning techniques that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional beliefs that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested in up to 50 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing of a humanoid robot arm, and inverse-dynamics learning for a seven degree-of-freedom robot.

link (url) [BibTex]

link (url) [BibTex]


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Biomimetic gaze stabilization

Shibata, T., Schaal, S.

In Robot learning: an Interdisciplinary approach, pages: 31-52, (Editors: Demiris, J.;Birk, A.), World Scientific, 2000, clmc (inbook)

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]

link (url) [BibTex]


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Fast learning of biomimetic oculomotor control with nonparametric regression networks

Shibata, T., Schaal, S.

In International Conference on Robotics and Automation (ICRA2000), pages: 3847-3854, San Francisco, April 2000, 2000, clmc (inproceedings)

Abstract
Accurate oculomotor control is one of the essential pre-requisites of successful visuomotor coordination. Given the variable nonlinearities of the geometry of binocular vision as well as the possible nonlinearities of the oculomotor plant, it is desirable to accomplish accurate oculomotor control through learning approaches. In this paper, we investigate learning control for a biomimetic active vision system mounted on a humanoid robot. By combining a biologically inspired cerebellar learning scheme with a state-of-the-art statistical learning network, our robot system is able to acquire high performance visual stabilization reflexes after about 40 seconds of learning despite significant nonlinearities and processing delays in the system.

link (url) [BibTex]

link (url) [BibTex]


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Interaction of rhythmic and discrete pattern generators in single joint movements

Sternad, D., Dean, W. J., Schaal, S.

Human Movement Science, 19(4):627-665, 2000, clmc (article)

Abstract
The study investigates a single-joint movement task that combines a translatory and cyclic component with the objective to investigate the interaction of discrete and rhythmic movement elements. Participants performed an elbow movement in the horizontal plane, oscillating at a prescribed frequency around one target and shifting to a second target upon a trigger signal, without stopping the oscillation. Analyses focused on extracting the mutual influences of the rhythmic and the discrete component of the task. Major findings are: (1) The onset of the discrete movement was confined to a limited phase window in the rhythmic cycle. (2) Its duration was influenced by the period of oscillation. (3) The rhythmic oscillation was "perturbed" by the discrete movement as indicated by phase resetting. On the basis of these results we propose a model for the coordination of discrete and rhythmic actions (K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptations, Biological Cybernetics 52 (1985) 367-376; Mechanisms of frequency and pattern control in the neural rhythm generators, Biological Cybernetics 56 (1987) 345-353). For rhythmic movements an oscillatory pattern generator is developed following models of half-center oscillations (D. Bullock, S. Grossberg, The VITE model: a neural command circuit for generating arm and articulated trajectories, in: J.A.S. Kelso, A.J. Mandel, M. F. Shlesinger (Eds.), Dynamic Patterns in Complex Systems. World Scientific. Singapore. 1988. pp. 305-326). For discrete movements a point attractor dynamics is developed close to the VITE model For each joint degree of freedom both pattern generators co-exist but exert mutual inhibition onto each other. The suggested modeling framework provides a unified account for both discrete and rhythmic movements on the basis of neuronal circuitry. Simulation results demonstrated that the effects observed in human performance can be replicated using the two pattern generators with a mutually inhibiting coupling.

link (url) [BibTex]


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Locally weighted projection regression: An O(n) algorithm for incremental real time learning in high dimensional spaces

Vijayakumar, S., Schaal, S.

In Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000), 1, pages: 288-293, Stanford, CA, 2000, clmc (inproceedings)

Abstract
Locally weighted projection regression is a new algorithm that achieves nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it uses locally linear models, spanned by a small number of univariate regressions in selected directions in input space. This paper evaluates different methods of projection regression and derives a nonlinear function approximator based on them. This nonparametric local learning system i) learns rapidly with second order learning methods based on incremental training, ii) uses statistically sound stochastic cross validation to learn iii) adjusts its weighting kernels based on local information only, iv) has a computational complexity that is linear in the number of inputs, and v) can deal with a large number of - possibly redundant - inputs, as shown in evaluations with up to 50 dimensional data sets. To our knowledge, this is the first truly incremental spatially localized learning method to combine all these properties.

link (url) [BibTex]

link (url) [BibTex]


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Dynamics of a bouncing ball in human performance

Sternad, D., Duarte, M., Katsumata, H., Schaal, S.

Physical Review E, 63(011902):1-8, 2000, clmc (article)

Abstract
On the basis of a modified bouncing-ball model, we investigated whether human movements utilize principles of dynamic stability in their performance of a similar movement task. Stability analyses of the model provided predictions about conditions indicative of a dynamically stable period-one regime. In a series of experiments, human subjects bounced a ball rhythmically on a racket and displayed these conditions supporting that they attuned to and exploited the dynamic stability properties of the task.

link (url) [BibTex]

link (url) [BibTex]


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Inverse kinematics for humanoid robots

Tevatia, G., Schaal, S.

In International Conference on Robotics and Automation (ICRA2000), pages: 294-299, San Fransisco, April 24-28, 2000, 2000, clmc (inproceedings)

Abstract
Real-time control of the endeffector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates methods of resolved motion rate control (RMRC) that employ optimization criteria to resolve kinematic redundancies. In particular we focus on two established techniques, the pseudo inverse with explicit optimization and the extended Jacobian method. We prove that the extended Jacobian method includes pseudo-inverse methods as a special solution. In terms of computational complexity, however, pseudo-inverse and extended Jacobian differ significantly in favor of pseudo-inverse methods. Employing numerical estimation techniques, we introduce a computationally efficient version of the extended Jacobian with performance comparable to the original version . Our results are illustrated in simulation studies with a multiple degree-of-freedom robot, and were tested on a 30 degree-of-freedom robot. 

link (url) [BibTex]

link (url) [BibTex]


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Fast and efficient incremental learning for high-dimensional movement systems

Vijayakumar, S., Schaal, S.

In International Conference on Robotics and Automation (ICRA2000), San Francisco, April 2000, 2000, clmc (inproceedings)

Abstract
We introduce a new algorithm, Locally Weighted Projection Regression (LWPR), for incremental real-time learning of nonlinear functions, as particularly useful for problems of autonomous real-time robot control that re-quires internal models of dynamics, kinematics, or other functions. At its core, LWPR uses locally linear models, spanned by a small number of univariate regressions in selected directions in input space, to achieve piecewise linear function approximation. The most outstanding properties of LWPR are that it i) learns rapidly with second order learning methods based on incremental training, ii) uses statistically sound stochastic cross validation to learn iii) adjusts its local weighting kernels based on only local information to avoid interference problems, iv) has a computational complexity that is linear in the number of inputs, and v) can deal with a large number ofâ??possibly redundant and/or irrelevantâ??inputs, as shown in evaluations with up to 50 dimensional data sets for learning the inverse dynamics of an anthropomorphic robot arm. To our knowledge, this is the first incremental neural network learning method to combine all these properties and that is well suited for complex on-line learning problems in robotics.

link (url) [BibTex]

link (url) [BibTex]


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On-line learning for humanoid robot systems

Conradt, J., Tevatia, G., Vijayakumar, S., Schaal, S.

In Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000), 1, pages: 191-198, Stanford, CA, 2000, clmc (inproceedings)

Abstract
Humanoid robots are high-dimensional movement systems for which analytical system identification and control methods are insufficient due to unknown nonlinearities in the system structure. As a way out, supervised learning methods can be employed to create model-based nonlinear controllers which use functions in the control loop that are estimated by learning algorithms. However, internal models for humanoid systems are rather high-dimensional such that conventional learning algorithms would suffer from slow learning speed, catastrophic interference, and the curse of dimensionality. In this paper we explore a new statistical learning algorithm, locally weighted projection regression (LWPR), for learning internal models in real-time. LWPR is a nonparametric spatially localized learning system that employs the less familiar technique of partial least squares regression to represent functional relationships in a piecewise linear fashion. The algorithm can work successfully in very high dimensional spaces and detect irrelevant and redundant inputs while only requiring a computational complexity that is linear in the number of input dimensions. We demonstrate the application of the algorithm in learning two classical internal models of robot control, the inverse kinematics and the inverse dynamics of an actual seven degree-of-freedom anthropomorphic robot arm. For both examples, LWPR can achieve excellent real-time learning results from less than one hour of actual training data.

link (url) [BibTex]

link (url) [BibTex]


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Humanoid Robot DB

Kotosaka, S., Shibata, T., Schaal, S.

In Proceedings of the International Conference on Machine Automation (ICMA2000), pages: 21-26, 2000, clmc (inproceedings)

[BibTex]

[BibTex]