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49 results (View BibTeX file of all listed publications)

2018

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Motion-based Object Segmentation based on Dense RGB-D Scene Flow

Shao, L., Shah, P., Dwaracherla, V., Bohg, J.

IEEE Robotics and Automation Letters, 3(4):3797-3804, IEEE, IEEE/RSJ International Conference on Intelligent Robots and Systems, October 2018 (conference)

Abstract
Given two consecutive RGB-D images, we propose a model that estimates a dense 3D motion field, also known as scene flow. We take advantage of the fact that in robot manipulation scenarios, scenes often consist of a set of rigidly moving objects. Our model jointly estimates (i) the segmentation of the scene into an unknown but finite number of objects, (ii) the motion trajectories of these objects and (iii) the object scene flow. We employ an hourglass, deep neural network architecture. In the encoding stage, the RGB and depth images undergo spatial compression and correlation. In the decoding stage, the model outputs three images containing a per-pixel estimate of the corresponding object center as well as object translation and rotation. This forms the basis for inferring the object segmentation and final object scene flow. To evaluate our model, we generated a new and challenging, large-scale, synthetic dataset that is specifically targeted at robotic manipulation: It contains a large number of scenes with a very diverse set of simultaneously moving 3D objects and is recorded with a commonly-used RGB-D camera. In quantitative experiments, we show that we significantly outperform state-of-the-art scene flow and motion-segmentation methods. In qualitative experiments, we show how our learned model transfers to challenging real-world scenes, visually generating significantly better results than existing methods.

Project Page arXiv DOI [BibTex]

2018

Shao, L., Shah, P., Dwaracherla, V., Bohg, J. Motion-based Object Segmentation based on Dense RGB-D Scene Flow IEEE Robotics and Automation Letters, 3(4):3797-3804, IEEE, IEEE/RSJ International Conference on Intelligent Robots and Systems, October 2018 (conference)

Project Page arXiv DOI [BibTex]

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Probabilistic Recurrent State-Space Models

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

In Proceedings of the International Conference on Machine Learning (ICML), International Conference on Machine Learning (ICML), July 2018 (inproceedings)

Abstract
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g., LSTMs) proved extremely successful in modeling complex time-series data. Fully probabilistic SSMs, however, unfortunately often prove hard to train, even for smaller problems. To overcome this limitation, we propose a scalable initialization and training algorithm based on doubly stochastic variational inference and Gaussian processes. In the variational approximation we propose in contrast to related approaches to fully capture the latent state temporal correlations to allow for robust training.

arXiv pdf Project Page [BibTex]

Doerr, A., Daniel, C., Schiegg, M., Nguyen-Tuong, D., Schaal, S., Toussaint, M., Trimpe, S. Probabilistic Recurrent State-Space Models In Proceedings of the International Conference on Machine Learning (ICML), International Conference on Machine Learning (ICML), July 2018 (inproceedings)

arXiv pdf Project Page [BibTex]

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Online Learning of a Memory for Learning Rates

(nominated for best paper award)

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

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, IEEE, International Conference on Robotics and Automation, May 2018, accepted (inproceedings)

Abstract
The promise of learning to learn for robotics rests on the hope that by extracting some information about the learning process itself we can speed up subsequent similar learning tasks. Here, we introduce a computationally efficient online meta-learning algorithm that builds and optimizes a memory model of the optimal learning rate landscape from previously observed gradient behaviors. While performing task specific optimization, this memory of learning rates predicts how to scale currently observed gradients. After applying the gradient scaling our meta-learner updates its internal memory based on the observed effect its prediction had. Our meta-learner can be combined with any gradient-based optimizer, learns on the fly and can be transferred to new optimization tasks. In our evaluations we show that our meta-learning algorithm speeds up learning of MNIST classification and a variety of learning control tasks, either in batch or online learning settings.

pdf video code [BibTex]

Meier, F., Kappler, D., Schaal, S. Online Learning of a Memory for Learning Rates In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, IEEE, International Conference on Robotics and Automation, May 2018, accepted (inproceedings)

pdf video code [BibTex]

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Learning Sensor Feedback Models from Demonstrations via Phase-Modulated Neural Networks

Sutanto, G., Su, Z., Schaal, S., Meier, F.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, IEEE, International Conference on Robotics and Automation, May 2018 (inproceedings)

pdf video [BibTex]

Sutanto, G., Su, Z., Schaal, S., Meier, F. Learning Sensor Feedback Models from Demonstrations via Phase-Modulated Neural Networks In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2018, IEEE, International Conference on Robotics and Automation, May 2018 (inproceedings)

pdf video [BibTex]

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On Time Optimization of Centroidal Momentum Dynamics

Ponton, B., Herzog, A., Del Prete, A., Schaal, S., Righetti, L.

In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 5776-5782, IEEE, Brisbane, Australia, 2018 (inproceedings)

Abstract
Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization approach difficult and timing is usually kept fixed in most trajectory optimization techniques to not introduce additional non convexities to the problem. But this can limit the versatility of the algorithms. In our previous work, we proposed a convex relaxation of the problem that allowed to efficiently compute momentum trajectories and contact forces. However, our approach could not minimize a desired angular momentum objective which seriously limited its applicability. Noticing that the non-convexity introduced by the time variables is of similar nature as the centroidal dynamics one, we propose two convex relaxations to the problem based on trust regions and soft constraints. The resulting approaches can compute time-optimized dynamically consistent trajectories sufficiently fast to make the approach realtime capable. The performance of the algorithm is demonstrated in several multi-contact scenarios for a humanoid robot. In particular, we show that the proposed convex relaxation of the original problem finds solutions that are consistent with the original non-convex problem and illustrate how timing optimization allows to find motion plans that would be difficult to plan with fixed timing † †Implementation details and demos can be found in the source code available at https://git-amd.tuebingen.mpg.de/bponton/timeoptimization.

link (url) DOI [BibTex]

Ponton, B., Herzog, A., Del Prete, A., Schaal, S., Righetti, L. On Time Optimization of Centroidal Momentum Dynamics In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 5776-5782, IEEE, Brisbane, Australia, 2018 (inproceedings)

link (url) DOI [BibTex]

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Unsupervised Contact Learning for Humanoid Estimation and Control

Rotella, N., Schaal, S., Righetti, L.

In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 411-417, IEEE, Brisbane, Australia, 2018 (inproceedings)

Abstract
This work presents a method for contact state estimation using fuzzy clustering to learn contact probability for full, six-dimensional humanoid contacts. The data required for training is solely from proprioceptive sensors - endeffector contact wrench sensors and inertial measurement units (IMUs) - and the method is completely unsupervised. The resulting cluster means are used to efficiently compute the probability of contact in each of the six endeffector degrees of freedom (DoFs) independently. This clustering-based contact probability estimator is validated in a kinematics-based base state estimator in a simulation environment with realistic added sensor noise for locomotion over rough, low-friction terrain on which the robot is subject to foot slip and rotation. The proposed base state estimator which utilizes these six DoF contact probability estimates is shown to perform considerably better than that which determines kinematic contact constraints purely based on measured normal force.

link (url) DOI [BibTex]

Rotella, N., Schaal, S., Righetti, L. Unsupervised Contact Learning for Humanoid Estimation and Control In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 411-417, IEEE, Brisbane, Australia, 2018 (inproceedings)

link (url) DOI [BibTex]

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Learning Task-Specific Dynamics to Improve Whole-Body Control

Gams, A., Mason, S., Ude, A., Schaal, S., Righetti, L.

In Hua, IEEE, Beijing, China, November 2018 (inproceedings)

Abstract
In task-based inverse dynamics control, reference accelerations used to follow a desired plan can be broken down into feedforward and feedback trajectories. The feedback term accounts for tracking errors that are caused from inaccurate dynamic models or external disturbances. On underactuated, free-floating robots, such as humanoids, high feedback terms can be used to improve tracking accuracy; however, this can lead to very stiff behavior or poor tracking accuracy due to limited control bandwidth. In this paper, we show how to reduce the required contribution of the feedback controller by incorporating learned task-space reference accelerations. Thus, we i) improve the execution of the given specific task, and ii) offer the means to reduce feedback gains, providing for greater compliance of the system. With a systematic approach we also reduce heuristic tuning of the model parameters and feedback gains, often present in real-world experiments. In contrast to learning task-specific joint-torques, which might produce a similar effect but can lead to poor generalization, our approach directly learns the task-space dynamics of the center of mass of a humanoid robot. Simulated and real-world results on the lower part of the Sarcos Hermes humanoid robot demonstrate the applicability of the approach.

link (url) [BibTex]

Gams, A., Mason, S., Ude, A., Schaal, S., Righetti, L. Learning Task-Specific Dynamics to Improve Whole-Body Control In Hua, IEEE, Beijing, China, November 2018 (inproceedings)

link (url) [BibTex]

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An MPC Walking Framework With External Contact Forces

Mason, S., Rotella, N., Schaal, S., Righetti, L.

In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 1785-1790, IEEE, Brisbane, Australia, May 2018 (inproceedings)

Abstract
In this work, we present an extension to a linear Model Predictive Control (MPC) scheme that plans external contact forces for the robot when given multiple contact locations and their corresponding friction cone. To this end, we set up a two-step optimization problem. In the first optimization, we compute the Center of Mass (CoM) trajectory, foot step locations, and introduce slack variables to account for violating the imposed constraints on the Zero Moment Point (ZMP). We then use the slack variables to trigger the second optimization, in which we calculate the optimal external force that compensates for the ZMP tracking error. This optimization considers multiple contacts positions within the environment by formulating the problem as a Mixed Integer Quadratic Program (MIQP) that can be solved at a speed between 100-300 Hz. Once contact is created, the MIQP reduces to a single Quadratic Program (QP) that can be solved in real-time ({\textless}; 1kHz). Simulations show that the presented walking control scheme can withstand disturbances 2-3× larger with the additional force provided by a hand contact.

link (url) DOI [BibTex]

Mason, S., Rotella, N., Schaal, S., Righetti, L. An MPC Walking Framework With External Contact Forces In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages: 1785-1790, IEEE, Brisbane, Australia, May 2018 (inproceedings)

link (url) DOI [BibTex]

2010

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Reinforcement learning of full-body humanoid motor skills

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

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

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

link (url) [BibTex]

2010

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

link (url) [BibTex]

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Enhanced Visual Scene Understanding through Human-Robot Dialog

Johnson-Roberson, M., Bohg, J., Kragic, D., Skantze, G., Gustafson, J., Carlson, R.

In Proceedings of AAAI 2010 Fall Symposium: Dialog with Robots, November 2010 (inproceedings)

pdf [BibTex]

Johnson-Roberson, M., Bohg, J., Kragic, D., Skantze, G., Gustafson, J., Carlson, R. Enhanced Visual Scene Understanding through Human-Robot Dialog In Proceedings of AAAI 2010 Fall Symposium: Dialog with Robots, November 2010 (inproceedings)

pdf [BibTex]

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Scene Representation and Object Grasping Using Active Vision

Gratal, X., Bohg, J., Björkman, M., Kragic, D.

In IROS’10 Workshop on Defining and Solving Realistic Perception Problems in Personal Robotics, October 2010 (inproceedings)

Abstract
Object grasping and manipulation pose major challenges for perception and control and require rich interaction between these two fields. In this paper, we concentrate on the plethora of perceptual problems that have to be solved before a robot can be moved in a controlled way to pick up an object. A vision system is presented that integrates a number of different computational processes, e.g. attention, segmentation, recognition or reconstruction to incrementally build up a representation of the scene suitable for grasping and manipulation of objects. Our vision system is equipped with an active robotic head and a robot arm. This embodiment enables the robot to perform a number of different actions like saccading, fixating, and grasping. By applying these actions, the robot can incrementally build a scene representation and use it for interaction. We demonstrate our system in a scenario for picking up known objects from a table top. We also show the system’s extendibility towards grasping of unknown and familiar objects.

video pdf slides [BibTex]

Gratal, X., Bohg, J., Björkman, M., Kragic, D. Scene Representation and Object Grasping Using Active Vision In IROS’10 Workshop on Defining and Solving Realistic Perception Problems in Personal Robotics, October 2010 (inproceedings)

video pdf slides [BibTex]

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Strategies for multi-modal scene exploration

Bohg, J., Johnson-Roberson, M., Björkman, M., Kragic, D.

In Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pages: 4509-4515, October 2010 (inproceedings)

Abstract
We propose a method for multi-modal scene exploration where initial object hypothesis formed by active visual segmentation are confirmed and augmented through haptic exploration with a robotic arm. We update the current belief about the state of the map with the detection results and predict yet unknown parts of the map with a Gaussian Process. We show that through the integration of different sensor modalities, we achieve a more complete scene model. We also show that the prediction of the scene structure leads to a valid scene representation even if the map is not fully traversed. Furthermore, we propose different exploration strategies and evaluate them both in simulation and on our robotic platform.

video pdf DOI Project Page [BibTex]

Bohg, J., Johnson-Roberson, M., Björkman, M., Kragic, D. Strategies for multi-modal scene exploration In Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pages: 4509-4515, October 2010 (inproceedings)

video pdf DOI Project Page [BibTex]

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Attention-based active 3D point cloud segmentation

Johnson-Roberson, M., Bohg, J., Björkman, M., Kragic, D.

In Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pages: 1165-1170, October 2010 (inproceedings)

Abstract
In this paper we present a framework for the segmentation of multiple objects from a 3D point cloud. We extend traditional image segmentation techniques into a full 3D representation. The proposed technique relies on a state-of-the-art min-cut framework to perform a fully 3D global multi-class labeling in a principled manner. Thereby, we extend our previous work in which a single object was actively segmented from the background. We also examine several seeding methods to bootstrap the graphical model-based energy minimization and these methods are compared over challenging scenes. All results are generated on real-world data gathered with an active vision robotic head. We present quantitive results over aggregate sets as well as visual results on specific examples.

pdf DOI [BibTex]

Johnson-Roberson, M., Bohg, J., Björkman, M., Kragic, D. Attention-based active 3D point cloud segmentation In Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pages: 1165-1170, October 2010 (inproceedings)

pdf DOI [BibTex]

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Relative Entropy Policy Search

Peters, J., Mülling, K., Altun, Y.

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

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

PDF Web [BibTex]

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

PDF Web [BibTex]

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

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

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

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

link (url) [BibTex]

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

link (url) [BibTex]

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Inverse dynamics control of floating base systems using orthogonal decomposition

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

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

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

link (url) [BibTex]

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

link (url) [BibTex]

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Fast, robust quadruped locomotion over challenging terrain

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

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

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

link (url) [BibTex]

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

link (url) [BibTex]

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Accelerometer-based Tilt Estimation of a Rigid Body with only Rotational Degrees of Freedom

Trimpe, S., D’Andrea, R.

In Proceedings of the IEEE International Conference on Robotics and Automation, 2010 (inproceedings)

PDF DOI [BibTex]

Trimpe, S., D’Andrea, R. Accelerometer-based Tilt Estimation of a Rigid Body with only Rotational Degrees of Freedom In Proceedings of the IEEE International Conference on Robotics and Automation, 2010 (inproceedings)

PDF DOI [BibTex]

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Locally weighted regression for control

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

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

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

link (url) [BibTex]

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

link (url) [BibTex]

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Are reaching movements planned in kinematic or dynamic coordinates?

Ellmer, A., Schaal, S.

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

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

[BibTex]

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

[BibTex]

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Optimality in Neuromuscular Systems

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

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

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

PDF [BibTex]

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

PDF [BibTex]

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Learning Policy Improvements with Path Integrals

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

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

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

PDF [BibTex]

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

PDF [BibTex]

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Learning optimal control solutions: a path integral approach

Theodorou, E., Schaal, S.

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

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

[BibTex]

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

[BibTex]

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

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

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

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

link (url) DOI [BibTex]

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

link (url) DOI [BibTex]

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Variable impedance control - a reinforcement learning approach

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

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

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

link (url) [BibTex]

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

link (url) [BibTex]

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

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

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

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

DOI [BibTex]

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

DOI [BibTex]

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

Peters, J., Schaal, S. Learning operational space control 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)

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]

Peters, J., Schaal, S. Reinforcement Learning for Parameterized Motor Primitives In Proceedings of the 2006 International Joint Conference on Neural Networks, pages: 73-80, IJCNN, 2006, clmc (inproceedings)

link (url) DOI [BibTex]

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Policy gradient methods for robotics

Peters, J., Schaal, S.

In Proceedings of the IEEE International Conference on Intelligent Robotics Systems, pages: 2219-2225, IROS, 2006, clmc (inproceedings)

Abstract
The aquisition and improvement of motor skills and control policies for robotics from trial and error is of essential importance if robots should ever leave precisely pre-structured environments. However, to date only few existing reinforcement learning methods have been scaled into the domains of highdimensional robots such as manipulator, legged or humanoid robots. Policy gradient methods remain one of the few exceptions and have found a variety of applications. Nevertheless, the application of such methods is not without peril if done in an uninformed manner. In this paper, we give an overview on learning with policy gradient methods for robotics with a strong focus on recent advances in the field. We outline previous applications to robotics and show how the most recently developed methods can significantly improve learning performance. Finally, we evaluate our most promising algorithm in the application of hitting a baseball with an anthropomorphic arm.

link (url) DOI [BibTex]

Peters, J., Schaal, S. Policy gradient methods for robotics In Proceedings of the IEEE International Conference on Intelligent Robotics Systems, pages: 2219-2225, IROS, 2006, clmc (inproceedings)

link (url) DOI [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]

Vijayakumar, S., DSouza, A., Schaal, S. Approximate nearest neighbor regression in very high dimensions 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]

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

Schaal, S., Sternad, D., Dean, W., Kotoska, S., Osu, R., Kawato, M. Reciprocal excitation between biological and robotic research 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)

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]

Schaal, S., Kotosaka, S., Sternad, D. Nonlinear dynamical systems as movement primitives In Humanoids2000, First IEEE-RAS International Conference on Humanoid Robots, CD-Proceedings, Cambridge, MA, September 2000, clmc (inproceedings)

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]

Vijayakumar, S., Schaal, S. Real Time Learning in Humanoids: A challenge for scalability of Online Algorithms In Humanoids2000, First IEEE-RAS International Conference on Humanoid Robots, CD-Proceedings, Cambridge, MA, September 2000, clmc (inproceedings)

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]

Kotosaka, S., Schaal, S. Synchronized robot drumming by neural oscillator In The International Symposium on Adaptive Motion of Animals and Machines, Montreal, Canada, August 2000, clmc (inproceedings)

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]

Schaal, S., Atkeson, C. G., Vijayakumar, S. Real-time robot learning with locally weighted statistical learning In International Conference on Robotics and Automation (ICRA2000), San Francisco, April 2000, 2000, clmc (inproceedings)

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]

Shibata, T., Schaal, S. Biomimetic gaze stabilization In Robot learning: an Interdisciplinary approach, pages: 31-52, (Editors: Demiris, J.;Birk, A.), World Scientific, 2000, clmc (inbook)

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]

Shibata, T., Schaal, S. Fast learning of biomimetic oculomotor control with nonparametric regression networks In International Conference on Robotics and Automation (ICRA2000), pages: 3847-3854, San Francisco, April 2000, 2000, clmc (inproceedings)

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]

Vijayakumar, S., Schaal, S. Locally weighted projection regression: An O(n) algorithm for incremental real time learning in high dimensional spaces In Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000), 1, pages: 288-293, Stanford, CA, 2000, clmc (inproceedings)

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]

Tevatia, G., Schaal, S. Inverse kinematics for humanoid robots In International Conference on Robotics and Automation (ICRA2000), pages: 294-299, San Fransisco, April 24-28, 2000, 2000, clmc (inproceedings)

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]

Vijayakumar, S., Schaal, S. Fast and efficient incremental learning for high-dimensional movement systems In International Conference on Robotics and Automation (ICRA2000), San Francisco, April 2000, 2000, clmc (inproceedings)

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]

Conradt, J., Tevatia, G., Vijayakumar, S., Schaal, S. On-line learning for humanoid robot systems In Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000), 1, pages: 191-198, Stanford, CA, 2000, clmc (inproceedings)

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]

Kotosaka, S., Shibata, T., Schaal, S. Humanoid Robot DB In Proceedings of the International Conference on Machine Automation (ICMA2000), pages: 21-26, 2000, clmc (inproceedings)

[BibTex]

1994

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Robot learning by nonparametric regression

Schaal, S., Atkeson, C. G.

In Proceedings of the International Conference on Intelligent Robots and Systems (IROS’94), pages: 478-485, Munich Germany, 1994, clmc (inproceedings)

Abstract
We present an approach to robot learning grounded on a nonparametric regression technique, locally weighted regression. The model of the task to be performed is represented by infinitely many local linear models, i.e., the (hyper-) tangent planes at every query point. Such a model, however, is only generated when a query is performed and is not retained. This is in contrast to other methods using a finite set of linear models to accomplish a piecewise linear model. Architectural parameters of our approach, such as distance metrics, are also a function of the current query point instead of being global. Statistical tests are presented for when a local model is good enough such that it can be reliably used to build a local controller. These statistical measures also direct the exploration of the robot. We explicitly deal with the case where prediction accuracy requirements exist during exploration: By gradually shifting a center of exploration and controlling the speed of the shift with local prediction accuracy, a goal-directed exploration of state space takes place along the fringes of the current data support until the task goal is achieved. We illustrate this approach by describing how it has been used to enable a robot to learn a challenging juggling task: Within 40 to 100 trials the robot accomplished the task goal starting out with no initial experiences.

[BibTex]

1994

Schaal, S., Atkeson, C. G. Robot learning by nonparametric regression In Proceedings of the International Conference on Intelligent Robots and Systems (IROS’94), pages: 478-485, Munich Germany, 1994, clmc (inproceedings)

[BibTex]

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Assessing the quality of learned local models

Schaal, S., Atkeson, C. G.

In Advances in Neural Information Processing Systems 6, pages: 160-167, (Editors: Cowan, J.;Tesauro, G.;Alspector, J.), Morgan Kaufmann, San Mateo, CA, 1994, clmc (inproceedings)

Abstract
An approach is presented to learning high dimensional functions in the case where the learning algorithm can affect the generation of new data. A local modeling algorithm, locally weighted regression, is used to represent the learned function. Architectural parameters of the approach, such as distance metrics, are also localized and become a function of the query point instead of being global. Statistical tests are given for when a local model is good enough and sampling should be moved to a new area. Our methods explicitly deal with the case where prediction accuracy requirements exist during exploration: By gradually shifting a "center of exploration" and controlling the speed of the shift with local prediction accuracy, a goal-directed exploration of state space takes place along the fringes of the current data support until the task goal is achieved. We illustrate this approach with simulation results and results from a real robot learning a complex juggling task.

link (url) [BibTex]

Schaal, S., Atkeson, C. G. Assessing the quality of learned local models In Advances in Neural Information Processing Systems 6, pages: 160-167, (Editors: Cowan, J.;Tesauro, G.;Alspector, J.), Morgan Kaufmann, San Mateo, CA, 1994, clmc (inproceedings)

link (url) [BibTex]

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Memory-based robot learning

Schaal, S., Atkeson, C. G.

In IEEE International Conference on Robotics and Automation, 3, pages: 2928-2933, San Diego, CA, 1994, clmc (inproceedings)

Abstract
We present a memory-based local modeling approach to robot learning using a nonparametric regression technique, locally weighted regression. The model of the task to be performed is represented by infinitely many local linear models, the (hyper-) tangent planes at every query point. This is in contrast to other methods using a finite set of linear models to accomplish a piece-wise linear model. Architectural parameters of our approach, such as distance metrics, are a function of the current query point instead of being global. Statistical tests are presented for when a local model is good enough such that it can be reliably used to build a local controller. These statistical measures also direct the exploration of the robot. We explicitly deal with the case where prediction accuracy requirements exist during exploration: By gradually shifting a center of exploration and controlling the speed of the shift with local prediction accuracy, a goal-directed exploration of state space takes place along the fringes of the current data support until the task goal is achieved. We illustrate this approach by describing how it has been used to enable a robot to learn a challenging juggling task: within 40 to 100 trials the robot accomplished the task goal starting out with no initial experiences.

[BibTex]

Schaal, S., Atkeson, C. G. Memory-based robot learning In IEEE International Conference on Robotics and Automation, 3, pages: 2928-2933, San Diego, CA, 1994, clmc (inproceedings)

[BibTex]

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Nonparametric regression for learning

Schaal, S.

In Conference on Adaptive Behavior and Learning, Center of Interdisciplinary Research (ZIF) Bielefeld Germany, also technical report TR-H-098 of the ATR Human Information Processing Research Laboratories, 1994, clmc (inproceedings)

Abstract
In recent years, learning theory has been increasingly influenced by the fact that many learning algorithms have at least in part a comprehensive interpretation in terms of well established statistical theories. Furthermore, with little modification, several statistical methods can be directly cast into learning algorithms. One family of such methods stems from nonparametric regression. This paper compares nonparametric learning with the more widely used parametric counterparts and investigates how these two families differ in their properties and their applicability. 

link (url) [BibTex]

Schaal, S. Nonparametric regression for learning In Conference on Adaptive Behavior and Learning, Center of Interdisciplinary Research (ZIF) Bielefeld Germany, also technical report TR-H-098 of the ATR Human Information Processing Research Laboratories, 1994, clmc (inproceedings)

link (url) [BibTex]

1992

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Informationssysteme mit CAD (Information systems within CAD)

Schaal, S.

In CAD/CAM Grundlagen, pages: 199-204, (Editors: Milberg, J.), Springer, Buchreihe CIM-TT. Berlin, 1992, clmc (inbook)

[BibTex]

1992

Schaal, S. Informationssysteme mit CAD (Information systems within CAD) In CAD/CAM Grundlagen, pages: 199-204, (Editors: Milberg, J.), Springer, Buchreihe CIM-TT. Berlin, 1992, clmc (inbook)

[BibTex]

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What should be learned?

Schaal, S., Atkeson, C. G., Botros, S.

In Proceedings of Seventh Yale Workshop on Adaptive and Learning Systems, pages: 199-204, New Haven, CT, May 20-22, 1992, clmc (inproceedings)

[BibTex]

Schaal, S., Atkeson, C. G., Botros, S. What should be learned? In Proceedings of Seventh Yale Workshop on Adaptive and Learning Systems, pages: 199-204, New Haven, CT, May 20-22, 1992, clmc (inproceedings)

[BibTex]

1991

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Ways to smarter CAD-systems

Ehrlenspiel, K., Schaal, S.

In Proceedings of ICED’91Heurista, pages: 10-16, (Editors: Hubka), Edition, Schriftenreihe WDK 21. Zürich, 1991, clmc (inbook)

[BibTex]

1991

Ehrlenspiel, K., Schaal, S. Ways to smarter CAD-systems In Proceedings of ICED’91Heurista, pages: 10-16, (Editors: Hubka), Edition, Schriftenreihe WDK 21. Zürich, 1991, clmc (inbook)

[BibTex]