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2017


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

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

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

pdf video [BibTex]

2017

pdf video [BibTex]


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On the Design of LQR Kernels for Efficient Controller Learning

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

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

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

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

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


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Optimizing Long-term Predictions for Model-based Policy Search

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

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

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

PDF Project Page [BibTex]

PDF Project Page [BibTex]


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A New Data Source for Inverse Dynamics Learning

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

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

[BibTex]

[BibTex]


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Bayesian Regression for Artifact Correction in Electroencephalography

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

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

DOI [BibTex]

DOI [BibTex]


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

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

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

DOI [BibTex]

DOI [BibTex]


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On the relevance of grasp metrics for predicting grasp success

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

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

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

Project Page [BibTex]

Project Page [BibTex]


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Local Bayesian Optimization of Motor Skills

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

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

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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

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

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

pdf video [BibTex]

pdf video [BibTex]


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

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

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

PDF arXiv DOI Project Page [BibTex]

PDF arXiv DOI Project Page [BibTex]


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Learning Feedback Terms for Reactive Planning and Control

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

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

pdf video [BibTex]

pdf video [BibTex]


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

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

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

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

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

2011


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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]

2011

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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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]

2007


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Towards Machine Learning of Motor Skills

Peters, J., Schaal, S., Schölkopf, B.

In Proceedings of Autonome Mobile Systeme (AMS), pages: 138-144, (Editors: K Berns and T Luksch), 2007, clmc (inproceedings)

Abstract
Autonomous robots that can adapt to novel situations has been a long standing vision of robotics, artificial intelligence, and cognitive sciences. Early approaches to this goal during the heydays of artificial intelligence research in the late 1980s, however, made it clear that an approach purely based on reasoning or human insights would not be able to model all the perceptuomotor tasks that a robot should fulfill. Instead, new hope was put in the growing wake of machine learning that promised fully adaptive control algorithms which learn both by observation and trial-and-error. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics, and usually scaling was only achieved in precisely pre-structured domains. In this paper, we investigate the ingredients for a general approach to motor skill learning in order to get one step closer towards human-like performance. For doing so, we study two ma jor components for such an approach, i.e., firstly, a theoretically well-founded general approach to representing the required control structures for task representation and execution and, secondly, appropriate learning algorithms which can be applied in this setting.

PDF DOI [BibTex]

2007

PDF DOI [BibTex]


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Reinforcement Learning for Optimal Control of Arm Movements

Theodorou, E., Peters, J., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience., Neuroscience, 2007, clmc (inproceedings)

Abstract
Every day motor behavior consists of a plethora of challenging motor skills from discrete movements such as reaching and throwing to rhythmic movements such as walking, drumming and running. How this plethora of motor skills can be learned remains an open question. In particular, is there any unifying computa-tional framework that could model the learning process of this variety of motor behaviors and at the same time be biologically plausible? In this work we aim to give an answer to these questions by providing a computational framework that unifies the learning mechanism of both rhythmic and discrete movements under optimization criteria, i.e., in a non-supervised trial-and-error fashion. Our suggested framework is based on Reinforcement Learning, which is mostly considered as too costly to be a plausible mechanism for learning com-plex limb movement. However, recent work on reinforcement learning with pol-icy gradients combined with parameterized movement primitives allows novel and more efficient algorithms. By using the representational power of such mo-tor primitives we show how rhythmic motor behaviors such as walking, squash-ing and drumming as well as discrete behaviors like reaching and grasping can be learned with biologically plausible algorithms. Using extensive simulations and by using different reward functions we provide results that support the hy-pothesis that Reinforcement Learning could be a viable candidate for motor learning of human motor behavior when other learning methods like supervised learning are not feasible.

[BibTex]

[BibTex]


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Reinforcement learning by reward-weighted regression for operational space control

Peters, J., Schaal, S.

In Proceedings of the 24th Annual International Conference on Machine Learning, pages: 745-750, ICML, 2007, clmc (inproceedings)

Abstract
Many robot control problems of practical importance, including operational space control, can be reformulated as immediate reward reinforcement learning problems. However, few of the known optimization or reinforcement learning algorithms can be used in online learning control for robots, as they are either prohibitively slow, do not scale to interesting domains of complex robots, or require trying out policies generated by random search, which are infeasible for a physical system. Using a generalization of the EM-base reinforcement learning framework suggested by Dayan & Hinton, we reduce the problem of learning with immediate rewards to a reward-weighted regression problem with an adaptive, integrated reward transformation for faster convergence. The resulting algorithm is efficient, learns smoothly without dangerous jumps in solution space, and works well in applications of complex high degree-of-freedom robots.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Policy gradient methods for machine learning

Peters, J., Theodorou, E., Schaal, S.

In Proceedings of the 14th INFORMS Conference of the Applied Probability Society, pages: 97-98, Eindhoven, Netherlands, July 9-11, 2007, 2007, clmc (inproceedings)

Abstract
We present an in-depth survey of policy gradient methods as they are used in the machine learning community for optimizing parameterized, stochastic control policies in Markovian systems with respect to the expected reward. Despite having been developed separately in the reinforcement learning literature, policy gradient methods employ likelihood ratio gradient estimators as also suggested in the stochastic simulation optimization community. It is well-known that this approach to policy gradient estimation traditionally suffers from three drawbacks, i.e., large variance, a strong dependence on baseline functions and a inefficient gradient descent. In this talk, we will present a series of recent results which tackles each of these problems. The variance of the gradient estimation can be reduced significantly through recently introduced techniques such as optimal baselines, compatible function approximations and all-action gradients. However, as even the analytically obtainable policy gradients perform unnaturally slow, it required the step from ÔvanillaÕ policy gradient methods towards natural policy gradients in order to overcome the inefficiency of the gradient descent. This development resulted into the Natural Actor-Critic architecture which can be shown to be very efficient in application to motor primitive learning for robotics.

[BibTex]

[BibTex]


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Policy Learning for Motor Skills

Peters, J., Schaal, S.

In Proceedings of 14th International Conference on Neural Information Processing (ICONIP), pages: 233-242, (Editors: Ishikawa, M. , K. Doya, H. Miyamoto, T. Yamakawa), 2007, clmc (inproceedings)

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

PDF DOI [BibTex]

PDF DOI [BibTex]


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Reinforcement learning for operational space control

Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Conference on Robotics and Automation, pages: 2111-2116, IEEE Computer Society, ICRA, 2007, 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 supervised 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-convexity of the solution space, i.e., the learning system could generate motor commands that try to steer the robot into physically impossible configurations. The important insight that many operational space control algorithms can be reformulated as optimal control problems, however, allows addressing this inverse learning problem in the framework of reinforcement learning. However, few of the known optimization or reinforcement learning algorithms can be used in online learning control for robots, as they are either prohibitively slow, do not scale to interesting domains of complex robots, or require trying out policies generated by random search, which are infeasible for a physical system. Using a generalization of the EM-based reinforcement learning framework suggested by Dayan & Hinton, we reduce the problem of learning with immediate rewards to a reward-weighted regression problem with an adaptive, integrated reward transformation for faster convergence. The resulting algorithm is efficient, learns smoothly without dangerous jumps in solution space, and works well in applications of complex high degree-of-freedom robots.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Using reward-weighted regression for reinforcement learning of task space control

Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, pages: 262-267, Honolulu, Hawaii, April 1-5, 2007, 2007, clmc (inproceedings)

Abstract
In this paper, we evaluate different versions from the three main kinds of model-free policy gradient methods, i.e., finite difference gradients, `vanilla' policy gradients and natural policy gradients. Each of these methods is first presented in its simple form and subsequently refined and optimized. By carrying out numerous experiments on the cart pole regulator benchmark we aim to provide a useful baseline for future research on parameterized policy search algorithms. Portable C++ code is provided for both plant and algorithms; thus, the results in this paper can be reevaluated, reused and new algorithms can be inserted with ease.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Evaluation of Policy Gradient Methods and Variants on the Cart-Pole Benchmark

Riedmiller, M., Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, pages: 254-261, ADPRL, 2007, clmc (inproceedings)

Abstract
In this paper, we evaluate different versions from the three main kinds of model-free policy gradient methods, i.e., finite difference gradients, `vanilla' policy gradients and natural policy gradients. Each of these methods is first presented in its simple form and subsequently refined and optimized. By carrying out numerous experiments on the cart pole regulator benchmark we aim to provide a useful baseline for future research on parameterized policy search algorithms. Portable C++ code is provided for both plant and algorithms; thus, the results in this paper can be reevaluated, reused and new algorithms can be inserted with ease.

PDF [BibTex]

PDF [BibTex]


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Uncertain 3D Force Fields in Reaching Movements: Do Humans Favor Robust or Average Performance?

Mistry, M., Theodorou, E., Hoffmann, H., Schaal, S.

In Abstracts of the 37th Meeting of the Society of Neuroscience, 2007, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Applying the episodic natural actor-critic architecture to motor primitive learning

Peters, J., Schaal, S.

In Proceedings of the 2007 European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium, April 25-27, 2007, clmc (inproceedings)

Abstract
In this paper, we investigate motor primitive learning with the Natural Actor-Critic approach. The Natural Actor-Critic consists out of actor updates which are achieved using natural stochastic policy gradients while the critic obtains the natural policy gradient by linear regression. We show that this architecture can be used to learn the Òbuilding blocks of movement generationÓ, called motor primitives. Motor primitives are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. We 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) [BibTex]

link (url) [BibTex]


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A computational model of human trajectory planning based on convergent flow fields

Hoffman, H., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov. 3-7, 2007, clmc (inproceedings)

Abstract
A popular computational model suggests that smooth reaching movements are generated in humans by minimizing a difference vector between hand and target in visual coordinates (Shadmehr and Wise, 2005). To achieve such a task, the optimal joint accelerations may be pre-computed. However, this pre-planning is inflexible towards perturbations of the limb, and there is strong evidence that reaching movements can be modified on-line at any moment during the movement. Thus, next-state planning models (Bullock and Grossberg, 1988) have been suggested that compute the current control command from a function of the goal state such that the overall movement smoothly converges to the goal (see Shadmehr and Wise (2005) for an overview). So far, these models have been restricted to simple point-to-point reaching movements with (approximately) straight trajectories. Here, we present a computational model for learning and executing arbitrary trajectories that combines ideas from pattern generation with dynamic systems and the observation of convergent force fields, which control a frog leg after spinal stimulation (Giszter et al., 1993). In our model, we incorporate the following two observations: first, the orientation of vectors in a force field is invariant over time, but their amplitude is modulated by a time-varying function, and second, two force fields add up when stimulated simultaneously (Giszter et al., 1993). This addition of convergent force fields varying over time results in a virtual trajectory (a moving equilibrium point) that correlates with the actual leg movement (Giszter et al., 1993). Our next-state planner is a set of differential equations that provide the desired end-effector or joint accelerations using feedback of the current state of the limb. These accelerations can be interpreted as resulting from a damped spring that links the current limb position with a virtual trajectory. This virtual trajectory can be learned to realize any desired limb trajectory and velocity profile, and learning is efficient since the time-modulated sum of convergent force fields equals a sum of weighted basis functions (Gaussian time pulses). Thus, linear algebra is sufficient to compute these weights, which correspond to points on the virtual trajectory. During movement execution, the differential equation corrects automatically for perturbations and brings back smoothly the limb towards the goal. Virtual trajectories can be rescaled and added allowing to build a set of movement primitives to describe movements more complex than previously learned. We demonstrate the potential of the suggested model by learning and generating a wide variety of movements.

[BibTex]

[BibTex]


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A Computational Model of Arm Trajectory Modification Using Dynamic Movement Primitives

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

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov 3-7, 2007, clmc (inproceedings)

Abstract
Several scientists used a double-step target-displacement protocol to investigate how an unexpected upcoming new target modifies ongoing discrete movements. Interesting observations are the initial direction of the movement, the spatial path of the movement to the second target, and the amplification of the speed in the second movement. Experimental data show that the above properties are influenced by the movement reaction time and the interstimulus interval between the onset of the first and second target. Hypotheses in the literature concerning the interpretation of the observed data include a) the second movement is superimposed on the first movement (Henis and Flash, 1995), b) the first movement is aborted and the second movement is planned to smoothly connect the current state of the arm with the new target (Hoff and Arbib, 1992), c) the second movement is initiated by a new control signal that replaces the first movement's control signal, but does not take the state of the system into account (Flanagan et al., 1993), and (d) the second movement is initiated by a new goal command, but the control structure stays unchanged, and feed-back from the current state is taken into account (Hoff and Arbib, 1993). We investigate target switching from the viewpoint of Dynamic Movement Primitives (DMPs). DMPs are trajectory planning units that are formalized as stable nonlinear attractor systems (Ijspeert et al., 2002). They are a useful framework for biological motor control as they are highly flexible in creating complex rhythmic and discrete behaviors that can quickly adapt to the inevitable perturbations of dynamically changing, stochastic environments. In this model, target switching is accomplished simply by updating the target input to the discrete movement primitive for reaching. The reaching trajectory in this model can be straight or take any other route; in contrast, the Hoff and Arbib (1993) model is restricted to straight reaching movement plans. In the present study, we use DMPs to reproduce in simulation a large number of target-switching experimental data from the literature and to show that online correction and the observed target switching phenomena can be accomplished by changing the goal state of an on-going DMP, without the need to switch to different movement primitives or to re-plan the movement. :

PDF [BibTex]

PDF [BibTex]


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Inverse dynamics control with floating base and constraints

Nakanishi, J., Mistry, M., Schaal, S.

In International Conference on Robotics and Automation (ICRA2007), pages: 1942-1947, Rome, Italy, April 10-14, 2007, clmc (inproceedings)

Abstract
In this paper, we address the issues of compliant control of a robot under contact constraints with a goal of using joint space based pattern generators as movement primitives, as often considered in the studies of legged locomotion and biological motor control. For this purpose, we explore inverse dynamics control of constrained dynamical systems. When the system is overconstrained, it is not straightforward to formulate an inverse dynamics control law since the problem becomes an ill-posed one, where infinitely many combinations of joint torques are possible to achieve the desired joint accelerations. The goal of this paper is to develop a general and computationally efficient inverse dynamics algorithm for a robot with a free floating base and constraints. We suggest an approximate way of computing inverse dynamics algorithm by treating constraint forces computed with a Lagrange multiplier method as simply external forces based on FeatherstoneÕs floating base formulation of inverse dynamics. We present how all the necessary quantities to compute our controller can be efficiently extracted from FeatherstoneÕs spatial notation of robot dynamics. We evaluate the effectiveness of the suggested approach on a simulated biped robot model.

link (url) [BibTex]

link (url) [BibTex]


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Kernel carpentry for onlne regression using randomly varying coefficient model

Edakunni, N. U., Schaal, S., Vijayakumar, S.

In Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India: Jan. 6-12, 2007, clmc (inproceedings)

Abstract
We present a Bayesian formulation of locally weighted learning (LWL) using the novel concept of a randomly varying coefficient model. Based on this, we propose a mechanism for multivariate non-linear regression using spatially localised linear models that learns completely independent of each other, uses only local information and adapts the local model complexity in a data driven fashion. We derive online updates for the model parameters based on variational Bayesian EM. The evaluation of the proposed algorithm against other state-of-the-art methods reveal the excellent, robust generalization performance beside surprisingly efficient time and space complexity properties. This paper, for the first time, brings together the computational efficiency and the adaptability of Õnon-competitiveÕ locally weighted learning schemes and the modeling guarantees of the Bayesian formulation.

link (url) [BibTex]

link (url) [BibTex]


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A robust quadruped walking gait for traversing rough terrain

Pongas, D., Mistry, M., Schaal, S.

In International Conference on Robotics and Automation (ICRA2007), pages: 1474-1479, Rome, April 10-14, 2007, 2007, clmc (inproceedings)

Abstract
Legged locomotion excels when terrains become too rough for wheeled systems or open-loop walking pattern generators to succeed, i.e., when accurate foot placement is of primary importance in successfully reaching the task goal. In this paper we address the scenario where the rough terrain is traversed with a static walking gait, and where for every foot placement of a leg, the location of the foot placement was selected irregularly by a planning algorithm. Our goal is to adjust a smooth walking pattern generator with the selection of every foot placement such that the COG of the robot follows a stable trajectory characterized by a stability margin relative to the current support triangle. We propose a novel parameterization of the COG trajectory based on the current position, velocity, and acceleration of the four legs of the robot. This COG trajectory has guaranteed continuous velocity and acceleration profiles, which leads to continuous velocity and acceleration profiles of the leg movement, which is ideally suited for advanced model-based controllers. Pitch, yaw, and ground clearance of the robot are easily adjusted automatically under any terrain situation. We evaluate our gait generation technique on the Little-Dog quadruped robot when traversing complex rocky and sloped terrains.

link (url) [BibTex]

link (url) [BibTex]


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Bayesian Nonparametric Regression with Local Models

Ting, J., Schaal, S.

In Workshop on Robotic Challenges for Machine Learning, NIPS 2007, 2007, clmc (inproceedings)

[BibTex]

[BibTex]


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Task space control with prioritization for balance and locomotion

Mistry, M., Nakanishi, J., Schaal, S.

In IEEE International Conference on Intelligent Robotics Systems (IROS 2007), San Diego, CA: Oct. 29 Ð Nov. 2, 2007, clmc (inproceedings)

Abstract
This paper addresses locomotion with active balancing, via task space control with prioritization. The center of gravity (COG) and foot of the swing leg are treated as task space control points. Floating base inverse kinematics with constraints is employed, thereby allowing for a mobile platform suitable for locomotion. Different techniques of task prioritization are discussed and we clarify differences and similarities of previous suggested work. Varying levels of prioritization for control are examined with emphasis on singularity robustness and the negative effects of constraint switching. A novel controller for task space control of balance and locomotion is developed which attempts to address singularity robustness, while minimizing discontinuities created by constraint switching. Controllers are evaluated using a quadruped robot simulator engaging in a locomotion task.

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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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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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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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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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]