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2015


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Data-Driven Online Decision Making for Autonomous Manipulation

Kappler, D., Pastor, P., Kalakrishnan, M., Wuthrich, M., Schaal, S.

In Proceedings of Robotics: Science and Systems, Rome, Italy, 2015 (inproceedings)

Project Page [BibTex]

2015

Project Page [BibTex]


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Predicting Human Reaching Motion in Collaborative Tasks Using Inverse Optimal Control and Iterative Re-planning

Mainprice, J., Hayne, R., Berenson, D.

In Proceedings of the IEEE International Conference on Robotics and Automation, 2015 (inproceedings)

Project Page [BibTex]

Project Page [BibTex]


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Semi-Autonomous 3rd-Hand Robot

Lopes, M., Peters, J., Piater, J., Toussaint, M., Baisero, A., Busch, B., Erkent, O., Kroemer, O., Lioutikov, R., Maeda, G., Mollard, Y., Munzer, T., Shukla, D.

In Workshop on Cognitive Robotics in Future Manufacturing Scenarios, European Robotics Forum, 2015 (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Sensory synergy as environmental input integration

Alnajjar, F., Itkonen, M., Berenz, V., Tournier, M., Nagai, C., Shimoda, S.

Frontiers in Neuroscience, 8, pages: 436, 2015 (article)

Abstract
The development of a method to feed proper environmental inputs back to the central nervous system (CNS) remains one of the challenges in achieving natural movement when part of the body is replaced with an artificial device. Muscle synergies are widely accepted as a biologically plausible interpretation of the neural dynamics between the CNS and the muscular system. Yet the sensorineural dynamics of environmental feedback to the CNS has not been investigated in detail. In this study, we address this issue by exploring the concept of sensory synergy. In contrast to muscle synergy, we hypothesize that sensory synergy plays an essential role in integrating the overall environmental inputs to provide low-dimensional information to the CNS. We assume that sensor synergy and muscle synergy communicate using these low-dimensional signals. To examine our hypothesis, we conducted posture control experiments involving lateral disturbance with 9 healthy participants. Proprioceptive information represented by the changes on muscle lengths were estimated by using the musculoskeletal model analysis software SIMM. Changes on muscles lengths were then used to compute sensory synergies. The experimental results indicate that the environmental inputs were translated into the two dimensional signals and used to move the upper limb to the desired position immediately after the lateral disturbance. Participants who showed high skill in posture control were found to be likely to have a strong correlation between sensory and muscle signaling as well as high coordination between the utilized sensory synergies. These results suggest the importance of integrating environmental inputs into suitable low-dimensional signals before providing them to the CNS. This mechanism should be essential when designing the prosthesis’ sensory system to make the controller simpler

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Active Reward Learning with a Novel Acquisition Function

Daniel, C., Kroemer, O., Viering, M., Metz, J., Peters, J.

Autonomous Robots, 39(3):389-405, 2015 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Inverse Dynamics Models with Contacts

Calandra, R., Ivaldi, S., Deisenroth, M., Rückert, E., Peters, J.

In IEEE International Conference on Robotics and Automation, pages: 3186-3191, ICRA, 2015 (inproceedings)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A Probabilistic Framework for Semi-Autonomous Robots Based on Interaction Primitives with Phase Estimation

Maeda, G., Neumann, G., Ewerton, M., Lioutikov, R., Peters, J.

In Proceedings of the International Symposium of Robotics Research, ISRR, 2015 (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Learning Movement Primitive Attractor Goals and Sequential Skills from Kinesthetic Demonstrations

Manschitz, S., Kober, J., Gienger, M., Peters, J.

Robotics and Autonomous Systems, 74, Part A, pages: 97-107, 2015 (article)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Bayesian Optimization for Learning Gaits under Uncertainty

Calandra, R., Seyfarth, A., Peters, J., Deisenroth, M.

Annals of Mathematics and Artificial Intelligence, pages: 1-19, 2015 (article)

DOI [BibTex]

DOI [BibTex]


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Towards Learning Hierarchical Skills for Multi-Phase Manipulation Tasks

Kroemer, O., Daniel, C., Neumann, G., van Hoof, H., Peters, J.

In IEEE International Conference on Robotics and Automation, pages: 1503 - 1510, ICRA, 2015 (inproceedings)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Force estimation and slip detection/classification for grip control using a biomimetic tactile sensor

Su, Z., Hausman, K., Chebotar, Y., Molchanov, A., Loeb, G. E., Sukhatme, G. S., Schaal, S.

In IEEE-RAS International Conference on Humanoid Robots (Humanoids), pages: 297-303, 2015 (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Policy Learning with Hypothesis Based Local Action Selection

Sankaran, B., Bohg, J., Ratliff, N., Schaal, S.

In Reinforcement Learning and Decision Making, 2015 (inproceedings)

Abstract
For robots to be able to manipulate in unknown and unstructured environments the robot should be capable of operating under partial observability of the environment. Object occlusions and unmodeled environments are some of the factors that result in partial observability. A common scenario where this is encountered is manipulation in clutter. In the case that the robot needs to locate an object of interest and manipulate it, it needs to perform a series of decluttering actions to accurately detect the object of interest. To perform such a series of actions, the robot also needs to account for the dynamics of objects in the environment and how they react to contact. This is a non trivial problem since one needs to reason not only about robot-object interactions but also object-object interactions in the presence of contact. In the example scenario of manipulation in clutter, the state vector would have to account for the pose of the object of interest and the structure of the surrounding environment. The process model would have to account for all the aforementioned robot-object, object-object interactions. The complexity of the process model grows exponentially as the number of objects in the scene increases. This is commonly the case in unstructured environments. Hence it is not reasonable to attempt to model all object-object and robot-object interactions explicitly. Under this setting we propose a hypothesis based action selection algorithm where we construct a hypothesis set of the possible poses of an object of interest given the current evidence in the scene and select actions based on our current set of hypothesis. This hypothesis set tends to represent the belief about the structure of the environment and the number of poses the object of interest can take. The agent's only stopping criterion is when the uncertainty regarding the pose of the object is fully resolved.

Web Project Page [BibTex]


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Learning Optimal Striking Points for A Ping-Pong Playing Robot

Huang, Y., Schölkopf, B., Peters, J.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 4587-4592, IROS, 2015 (inproceedings)

PDF DOI [BibTex]

PDF DOI [BibTex]


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Model-Based Relative Entropy Stochastic Search

Abdolmaleki, A., Peters, J., Neumann, G.

In Advances in Neural Information Processing Systems 28, pages: 3523-3531, (Editors: C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama and R. Garnett), Curran Associates, Inc., 29th Annual Conference on Neural Information Processing Systems (NIPS), 2015 (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Modeling Spatio-Temporal Variability in Human-Robot Interaction with Probabilistic Movement Primitives

Ewerton, M., Neumann, G., Lioutikov, R., Ben Amor, H., Peters, J., Maeda, G.

In Workshop on Machine Learning for Social Robotics, ICRA, 2015 (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Extracting Low-Dimensional Control Variables for Movement Primitives

Rueckert, E., Mundo, J., Paraschos, A., Peters, J., Neumann, G.

In IEEE International Conference on Robotics and Automation, pages: 1511-1518, ICRA, 2015 (inproceedings)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A New Perspective and Extension of the Gaussian Filter

Wüthrich, M., Trimpe, S., Kappler, D., Schaal, S.

In Robotics: Science and Systems, 2015 (inproceedings)

Abstract
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependencies in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end we view the GF from a variational-inference perspective, and analyze how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.

Web PDF Project Page [BibTex]


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Learning multiple collaborative tasks with a mixture of Interaction Primitives

Ewerton, M., Neumann, G., Lioutikov, R., Ben Amor, H., Peters, J., Maeda, G.

In IEEE International Conference on Robotics and Automation, pages: 1535-1542, ICRA, 2015 (inproceedings)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Tacit Learning for Emergence of Task-Related Behaviour through Signal Accumulation

Berenz, V., Alnajjar, F., Hayashibe, M., Shimoda, S.

In Emergent Trends in Robotics and Intelligent Systems: Where is the Role of Intelligent Technologies in the Next Generation of Robots?, pages: 31-38, Springer International Publishing, Cham, 2015 (inbook)

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Whole-body motor strategies for balancing on a beam when changing the number of available degrees of freedom

Chiovetto, E, Huber, M, Righetti, L., Schaal, S., Sternad, D, Giese, M.

In Progress in Motor Control X, Budapest, Hungry, 2015 (inproceedings)

[BibTex]

[BibTex]


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From Humans to Robots and Back: Role of Arm Movement in Medio-lateral Balance Control

Huber, M, Chiovetto, E, Schaal, S., Giese, M., Sternad, D

In Annual Meeting of Neural Control of Movement, Charleston, NC, 2015 (inproceedings)

[BibTex]

[BibTex]


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Trajectory generation for multi-contact momentum control

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

In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pages: 874-880, IEEE, Seoul, South Korea, 2015 (inproceedings)

Abstract
Simplified models of the dynamics such as the linear inverted pendulum model (LIPM) have proven to perform well for biped walking on flat ground. However, for more complex tasks the assumptions of these models can become limiting. For example, the LIPM does not allow for the control of contact forces independently, is limited to co-planar contacts and assumes that the angular momentum is zero. In this paper, we propose to use the full momentum equations of a humanoid robot in a trajectory optimization framework to plan its center of mass, linear and angular momentum trajectories. The model also allows for planning desired contact forces for each end-effector in arbitrary contact locations. We extend our previous results on linear quadratic regulator (LQR) design for momentum control by computing the (linearized) optimal momentum feedback law in a receding horizon fashion. The resulting desired momentum and the associated feedback law are then used in a hierarchical whole body control approach. Simulation experiments show that the approach is computationally fast and is able to generate plans for locomotion on complex terrains while demonstrating good tracking performance for the full humanoid control.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Humanoid Momentum Estimation Using Sensed Contact Wrenches

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

In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pages: 556-563, IEEE, Seoul, South Korea, 2015 (inproceedings)

Abstract
This work presents approaches for the estimation of quantities important for the control of the momentum of a humanoid robot. In contrast to previous approaches which use simplified models such as the Linear Inverted Pendulum Model, we present estimators based on the momentum dynamics of the robot. By using this simple yet dynamically-consistent model, we avoid the issues of using simplified models for estimation. We develop an estimator for the center of mass and full momentum which can be reformulated to estimate center of mass offsets as well as external wrenches applied to the robot. The observability of these estimators is investigated and their performance is evaluated in comparison to previous approaches.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Robot Learning

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

In Springer Handbook of Robotics 2nd Edition, pages: 1371-1394, Springer Berlin Heidelberg, Berlin, Heidelberg, 2015 (incollection)

[BibTex]

[BibTex]

2008


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Learning to control in operational space

Peters, J., Schaal, S.

International Journal of Robotics Research, 27, pages: 197-212, 2008, clmc (article)

Abstract
One of the most general frameworks for phrasing control problems for complex, redundant robots is operational space control. However, while this framework 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 com- plex robots, e.g., humanoid robots. In this paper, we suggest a learning approach for opertional space control as a direct inverse model learning problem. A first important insight for this paper is that a physically cor- rect solution to the inverse problem with redundant degrees-of-freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on the insight that many operational space controllers can be understood in terms of a constrained optimal control problem. The cost function as- sociated with this optimal control problem allows us to formulate a learn- ing algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the machine learning point of view, this learning problem corre- sponds to a reinforcement learning problem that maximizes an immediate reward. We employ an expectation-maximization policy search algorithm in order to solve this problem. Evaluations on a three degrees of freedom robot arm are used to illustrate the suggested approach. The applica- tion to a physically realistic simulator of the anthropomorphic SARCOS Master arm demonstrates feasibility for complex high degree-of-freedom robots. We also show that the proposed method works in the setting of learning resolved motion rate control on real, physical Mitsubishi PA-10 medical robotics arm.

link (url) DOI [BibTex]

2008

link (url) DOI [BibTex]


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Adaptation to a sub-optimal desired trajectory

M. Mistry, E. A. G. L. T. Y. S. S. M. K.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

PDF [BibTex]

PDF [BibTex]


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Human movement generation based on convergent flow fields: A computational model and a behavioral experiment

Hoffmann, H., Schaal, S.

In Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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Operational space control: A theoretical and emprical comparison

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

International Journal of Robotics Research, 27(6):737-757, 2008, clmc (article)

Abstract
Dexterous manipulation with a highly redundant movement system is one of the hallmarks of hu- man motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e., they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space con- trol in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics imple- mentations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in face of inevitable modeling errors.

link (url) [BibTex]

link (url) [BibTex]


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Movement reproduction and obstacle avoidance with dynamic movement primitives and potential fields

Park, D., Hoffmann, H., Pastor, P., Schaal, S.

In IEEE International Conference on Humanoid Robots, 2008., 2008, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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The dual role of uncertainty in force field learning

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

In Abstracts of the Eighteenth Annual Meeting of Neural Control of Movement (NCM), Naples, Florida, April 29-May 4, 2008, clmc (inproceedings)

Abstract
Force field experiments have been a successful paradigm for studying the principles of planning, execution, and learning in human arm movements. Subjects have been shown to cope with the disturbances generated by force fields by learning internal models of the underlying dynamics to predict disturbance effects or by increasing arm impedance (via co-contraction) if a predictive approach becomes infeasible. Several studies have addressed the issue uncertainty in force field learning. Scheidt et al. demonstrated that subjects exposed to a viscous force field of fixed structure but varying strength (randomly changing from trial to trial), learn to adapt to the mean disturbance, regardless of the statistical distribution. Takahashi et al. additionally show a decrease in strength of after-effects after learning in the randomly varying environment. Thus they suggest that the nervous system adopts a dual strategy: learning an internal model of the mean of the random environment, while simultaneously increasing arm impedance to minimize the consequence of errors. In this study, we examine what role variance plays in the learning of uncertain force fields. We use a 7 degree-of-freedom exoskeleton robot as a manipulandum (Sarcos Master Arm, Sarcos, Inc.), and apply a 3D viscous force field of fixed structure and strength randomly selected from trial to trial. Additionally, in separate blocks of trials, we alter the variance of the randomly selected strength multiplier (while keeping a constant mean). In each block, after sufficient learning has occurred, we apply catch trials with no force field and measure the strength of after-effects. As expected in higher variance cases, results show increasingly smaller levels of after-effects as the variance is increased, thus implying subjects choose the robust strategy of increasing arm impedance to cope with higher levels of uncertainty. Interestingly, however, subjects show an increase in after-effect strength with a small amount of variance as compared to the deterministic (zero variance) case. This result implies that a small amount of variability aides in internal model formation, presumably a consequence of the additional amount of exploration conducted in the workspace of the task.

[BibTex]

[BibTex]


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Dynamic movement primitives for movement generation motivated by convergent force fields in frog

Hoffmann, H., Pastor, P., Schaal, S.

In Adaptive Motion of Animals and Machines (AMAM), 2008, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Efficient inverse kinematics algorithms for highdimensional movement systems

Tevatia, G., Schaal, S.

CLMC Technical Report: TR-CLMC-2008-1, 2008, clmc (techreport)

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-offreedom robot, and were evaluated on an actual 30 degree-of-freedom full-body humanoid robot.

link (url) [BibTex]

link (url) [BibTex]


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Behavioral experiments on reinforcement learning in human motor control

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

In Abstracts of the Eighteenth Annual Meeting of Neural Control of Movement (NCM), Naples, Florida, April 29-May 4, 2008, clmc (inproceedings)

Abstract
Reinforcement learning (RL) - learning solely based on reward or cost feedback - is widespread in robotics control and has been also suggested as computational model for human motor control. In human motor control, however, hardly any experiment studied reinforcement learning. Here, we study learning based on visual cost feedback in a reaching task and did three experiments: (1) to establish a simple enough experiment for RL, (2) to study spatial localization of RL, and (3) to study the dependence of RL on the cost function. In experiment (1), subjects sit in front of a drawing tablet and look at a screen onto which the drawing pen's position is projected. Beginning from a start point, their task is to move with the pen through a target point presented on screen. Visual feedback about the pen's position is given only before movement onset. At the end of a movement, subjects get visual feedback only about the cost of this trial. We choose as cost the squared distance between target and virtual pen position at the target line. Above a threshold value, the cost was fixed at this value. In the mapping of the pen's position onto the screen, we added a bias (unknown to subject) and Gaussian noise. As result, subjects could learn the bias, and thus, showed reinforcement learning. In experiment (2), we randomly altered the target position between three different locations (three different directions from start point: -45, 0, 45). For each direction, we chose a different bias. As result, subjects learned all three bias values simultaneously. Thus, RL can be spatially localized. In experiment (3), we varied the sensitivity of the cost function by multiplying the squared distance with a constant value C, while keeping the same cut-off threshold. As in experiment (2), we had three target locations. We assigned to each location a different C value (this assignment was randomized between subjects). Since subjects learned the three locations simultaneously, we could directly compare the effect of the different cost functions. As result, we found an optimal C value; if C was too small (insensitive cost), learning was slow; if C was too large (narrow cost valley), the exploration time was longer and learning delayed. Thus, reinforcement learning in human motor control appears to be sen

[BibTex]

[BibTex]


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Movement generation by learning from demonstration and generalization to new targets

Pastor, P., Hoffmann, H., Schaal, S.

In Adaptive Motion of Animals and Machines (AMAM), 2008, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Combining dynamic movement primitives and potential fields for online obstacle avoidance

Park, D., Hoffmann, H., Schaal, S.

In Adaptive Motion of Animals and Machines (AMAM), Cleveland, Ohio, 2008, 2008, clmc (inproceedings)

link (url) [BibTex]

link (url) [BibTex]


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A library for locally weighted projection regression

Klanke, S., Vijayakumar, S., Schaal, S.

Journal of Machine Learning Research, 9, pages: 623-626, 2008, clmc (article)

Abstract
In this paper we introduce an improved implementation of locally weighted projection regression (LWPR), a supervised learning algorithm that is capable of handling high-dimensional input data. As the key features, our code supports multi-threading, is available for multiple platforms, and provides wrappers for several programming languages.

link (url) [BibTex]

link (url) [BibTex]


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Computational model for movement learning under uncertain cost

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

In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

Abstract
Stochastic optimal control is a framework for computing control commands that lead to an optimal behavior under a given cost. Despite the long history of optimal control in engineering, it has been only recently applied to describe human motion. So far, stochastic optimal control has been mainly used in tasks that are already learned, such as reaching to a target. For learning, however, there are only few cases where optimal control has been applied. The main assumptions of stochastic optimal control that restrict its application to tasks after learning are the a priori knowledge of (1) a quadratic cost function (2) a state space model that captures the kinematics and/or dynamics of musculoskeletal system and (3) a measurement equation that models the proprioceptive and/or exteroceptive feedback. Under these assumptions, a sequence of control gains is computed that is optimal with respect to the prespecified cost function. In our work, we relax the assumption of the a priori known cost function and provide a computational framework for modeling tasks that involve learning. Typically, a cost function consists of two parts: one part that models the task constraints, like squared distance to goal at movement endpoint, and one part that integrates over the squared control commands. In learning a task, the first part of this cost function will be adapted. We use an expectation-maximization scheme for learning: the expectation step optimizes the task constraints through gradient descent of a reward function and the maximizing step optimizes the control commands. Our computational model is tested and compared with data given from a behavioral experiment. In this experiment, subjects sit in front of a drawing tablet and look at a screen onto which the drawing-pen's position is projected. Beginning from a start point, their task is to move with the pen through a target point presented on screen. Visual feedback about the pen's position is given only before movement onset. At the end of a movement, subjects get visual feedback only about the cost of this trial. In the mapping of the pen's position onto the screen, we added a bias (unknown to subject) and Gaussian noise. Therefore the cost is a function of this bias. The subjects were asked to reach to the target and minimize this cost over trials. In this behavioral experiment, subjects could learn the bias and thus showed reinforcement learning. With our computational model, we could model the learning process over trials. Particularly, the dependence on parameters of the reward function (Gaussian width) and the modulation of movement variance over time were similar in experiment and model.

[BibTex]

[BibTex]


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Optimization strategies in human reinforcement learning

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

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

PDF [BibTex]

PDF [BibTex]


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A Bayesian approach to empirical local linearizations for robotics

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

In International Conference on Robotics and Automation (ICRA2008), Pasadena, CA, USA, May 19-23, 2008, 2008, clmc (inproceedings)

Abstract
Local linearizations are ubiquitous in the control of robotic systems. Analytical methods, if available, can be used to obtain the linearization, but in complex robotics systems where the the dynamics and kinematics are often not faithfully obtainable, empirical linearization may be preferable. In this case, it is important to only use data for the local linearization that lies within a ``reasonable'' linear regime of the system, which can be defined from the Hessian at the point of the linearization -- a quantity that is not available without an analytical model. We introduce a Bayesian approach to solve statistically what constitutes a ``reasonable'' local regime. We approach this problem in the context local linear regression. In contrast to previous locally linear methods, we avoid cross-validation or complex statistical hypothesis testing techniques to find the appropriate local regime. Instead, we treat the parameters of the local regime probabilistically and use approximate Bayesian inference for their estimation. This approach results in an analytical set of iterative update equations that are easily implemented on real robotics systems for real-time applications. As in other locally weighted regressions, our algorithm also lends itself to complete nonlinear function approximation for learning empirical internal models. We sketch the derivation of our Bayesian method and provide evaluations on synthetic data and actual robot data where the analytical linearization was known.

link (url) [BibTex]

link (url) [BibTex]


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Do humans plan continuous trajectories in kinematic coordinates?

Hoffmann, H., Schaal, S.

In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

Abstract
The planning and execution of human arm movements is still unresolved. An ongoing controversy is whether we plan a movement in kinematic coordinates and convert these coordinates with an inverse internal model into motor commands (like muscle activation) or whether we combine a few muscle synergies or equilibrium points to move a hand, e.g., between two targets. The first hypothesis implies that a planner produces a desired end-effector position for all time points; the second relies on the dynamics of the muscular-skeletal system for a given control command to produce a continuous end-effector trajectory. To distinguish between these two possibilities, we use a visuomotor adaptation experiment. Subjects moved a pen on a graphics tablet and observed the pen's mapped position onto a screen (subjects quickly adapted to this mapping). The task was to move a cursor between two points in a given time window. In the adaptation test, we manipulated the velocity profile of the cursor feedback such that the shape of the trajectories remained unchanged (for straight paths). If humans would use a kinematic plan and map at each time the desired end-effector position onto control commands, subjects should adapt to the above manipulation. In a similar experiment, Wolpert et al (1995) showed adaptation to changes in the curvature of trajectories. This result, however, cannot rule out a shift of an equilibrium point or an additional synergy activation between start and end point of a movement. In our experiment, subjects did two sessions, one control without and one with velocity-profile manipulation. To skew the velocity profile of the cursor trajectory, we added to the current velocity, v, the function 0.8*v*cos(pi + pi*x), where x is the projection of the cursor position onto the start-goal line divided by the distance start to goal (x=0 at the start point). As result, subjects did not adapt to this manipulation: for all subjects, the true hand motion was not significantly modified in a direction consistent with adaptation, despite that the visually presented motion differed significantly from the control motion. One may still argue that this difference in motion was insufficient to be processed visually. Thus, as a control experiment, we replayed control and modified motions to the subjects and asked which of the two motions appeared 'more natural'. Subjects chose the unperturbed motion as more natural significantly better than chance. 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 adaptation under such transformation.

[BibTex]

[BibTex]

2003


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Dynamic movement primitives - A framework for motor control in humans and humanoid robots

Schaal, S.

In The International Symposium on Adaptive Motion of Animals and Machines, Kyoto, Japan, March 4-8, 2003, March 2003, 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]

2003

link (url) [BibTex]


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Bayesian backfitting

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

In Proceedings of the 10th Joint Symposium on Neural Computation (JSNC 2003), Irvine, CA, May 2003, 2003, clmc (inproceedings)

Abstract
We present an algorithm aimed at addressing both computational and analytical intractability of Bayesian regression models which operate in very high-dimensional, usually underconstrained spaces. Several domains of research frequently provide such datasets, including chemometrics [2], and human movement analysis [1]. The literature in nonparametric statistics provides interesting solutions such as Backfitting [3] and Partial Least Squares [4], which are extremely robust and efficient, yet lack a probabilistic interpretation that could place them in the context of current research in statistical learning algorithms that emphasize the estimation of confidence, posterior distributions, and model complexity. In order to achieve numerical robustness and low computational cost, we first derive a novel Bayesian interpretation of Backfitting (BB) as a computationally efficient regression algorithm. BBÕs learning complexity scales linearly with the input dimensionality by decoupling inference among individual input dimensions. We embed BB in an efficient, locally variational model selection mechanism that automatically grows the number of backfitting experts in a mixture-of-experts regression model. We demonstrate the effectiveness of the algorithm in performing principled regularization of model complexity when fitting nonlinear manifolds while avoiding the numerical hazards associated with highly underconstrained problems. We also note that this algorithm appears applicable in various areas of neural computation, e.g., in abstract models of computational neuroscience, or implementations of statistical learning on artificial systems.

link (url) [BibTex]

link (url) [BibTex]


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Reinforcement learning for humanoid robotics

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

In IEEE-RAS International Conference on Humanoid Robots (Humanoids2003), Karlsruhe, Germany, Sept.29-30, 2003, clmc (inproceedings)

Abstract
Reinforcement learning offers one of the most general framework to take traditional robotics towards true autonomy and versatility. However, applying reinforcement learning to high dimensional movement systems like humanoid robots remains an unsolved problem. In this paper, we discuss different approaches of reinforcement learning in terms of their applicability in humanoid robotics. Methods can be coarsely classified into three different categories, i.e., greedy methods, `vanilla' policy gradient methods, and natural gradient methods. We discuss that greedy methods are not likely to scale into the domain humanoid robotics as they are problematic when used with function approximation. `Vanilla' policy gradient methods on the other hand have been successfully applied on real-world robots including at least one humanoid robot. We demonstrate that these methods can be significantly improved using the natural policy gradient instead of the regular policy gradient. A derivation of the natural policy gradient is provided, proving that the average policy gradient of Kakade (2002) is indeed the true natural gradient. A general algorithm for estimating the natural gradient, the Natural Actor-Critic algorithm, is introduced. This algorithm converges to the nearest local minimum of the cost function with respect to the Fisher information metric under suitable conditions. The algorithm outperforms non-natural policy gradients by far in a cart-pole balancing evaluation, and for learning nonlinear dynamic motor primitives for humanoid robot control. It offers a promising route for the development of reinforcement learning for truly high dimensionally continuous state-action systems.

link (url) [BibTex]

link (url) [BibTex]


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Discovering imitation strategies through categorization of multi-cimensional data

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

In IEEE International Conference on Intelligent Robots and Systems (IROS 2003), Las Vegas, NV, Oct. 27-31, 2003, clmc (inproceedings)

Abstract
An essential problem of imitation is that of determining Ówhat to imitateÓ, i.e. to determine which of the many features of the demonstration are relevant to the task and which should be reproduced. The strategy followed by the imitator can be modeled as a hierarchical optimization system, which minimizes the discrepancy between two multidimensional datasets. We consider imitation of a manipulation task. To classify across manipulation strategies, we apply a probabilistic analysis to data in Cartesian and joint spaces. We determine a general metric that optimizes the policy of task reproduction, following strategy determination. The model successfully discovers strategies in six different manipulation tasks and controls task reproduction by a full body humanoid robot. or the complete path followed by the demonstrator. We follow a similar taxonomy and apply it to the learning and reproduction of a manipulation task by a humanoid robot. We take the perspective that the features of the movements to imitate are those that appear most frequently, i.e. the invariants in time. The model builds upon previous work [3], [4] and is composed of a hierarchical time delay neural network that extracts invariant features from a manipulation task performed by a human demonstrator. The system analyzes the Carthesian trajectories of the objects and the joint

link (url) [BibTex]

link (url) [BibTex]


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Scaling reinforcement learning paradigms for motor learning

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

In Proceedings of the 10th Joint Symposium on Neural Computation (JSNC 2003), Irvine, CA, May 2003, 2003, clmc (inproceedings)

Abstract
Reinforcement learning offers a general framework to explain reward related learning in artificial and biological motor control. However, current reinforcement learning methods rarely scale to high dimensional movement systems and mainly operate in discrete, low dimensional domains like game-playing, artificial toy problems, etc. This drawback makes them unsuitable for application to human or bio-mimetic motor control. In this poster, we look at promising approaches that can potentially scale and suggest a novel formulation of the actor-critic algorithm which takes steps towards alleviating the current shortcomings. We argue that methods based on greedy policies are not likely to scale into high-dimensional domains as they are problematic when used with function approximation Ð a must when dealing with continuous domains. We adopt the path of direct policy gradient based policy improvements since they avoid the problems of unstabilizing dynamics encountered in traditional value iteration based updates. While regular policy gradient methods have demonstrated promising results in the domain of humanoid notor control, we demonstrate that these methods can be significantly improved using the natural policy gradient instead of the regular policy gradient. Based on this, it is proved that KakadeÕs Ôaverage natural policy gradientÕ is indeed the true natural gradient. A general algorithm for estimating the natural gradient, the Natural Actor-Critic algorithm, is introduced. This algorithm converges with probability one to the nearest local minimum in Riemannian space of the cost function. The algorithm outperforms nonnatural policy gradients by far in a cart-pole balancing evaluation, and offers a promising route for the development of reinforcement learning for truly high-dimensionally continuous state-action systems.

link (url) [BibTex]

link (url) [BibTex]


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Learning attractor landscapes for learning motor primitives

Ijspeert, A., Nakanishi, J., Schaal, S.

In Advances in Neural Information Processing Systems 15, pages: 1547-1554, (Editors: Becker, S.;Thrun, S.;Obermayer, K.), Cambridge, MA: MIT Press, 2003, clmc (inproceedings)

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

link (url) [BibTex]

link (url) [BibTex]


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Learning from demonstration and adaptation of biped locomotion with dynamical movement primitives

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

In Workshop on Robot Learning by Demonstration, IEEE International Conference on Intelligent Robots and Systems (IROS 2003), Las Vegas, NV, Oct. 27-31, 2003, clmc (inproceedings)

Abstract
In this paper, we report on our research for learning biped locomotion from human demonstration. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like locomotion. We suggest dynamical movement primitives as a CPG of a biped robot, an approach we have previously proposed for learning and encoding complex human movements. Demonstrated trajectories are learned through the movement primitives by locally weighted regression, and the frequency of the learned trajectories is adjusted automatically by a novel frequency adaptation algorithm based on phase resetting and entrainment of oscillators. Numerical simulations demonstrate the effectiveness of the proposed locomotion controller.

link (url) [BibTex]

link (url) [BibTex]


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Movement planning and imitation by shaping nonlinear attractors

Schaal, S.

In Proceedings of the 12th Yale Workshop on Adaptive and Learning Systems, Yale University, New Haven, CT, 2003, clmc (inproceedings)

Abstract
Given the continuous stream of movements that biological systems exhibit in their daily activities, an account for such versatility and creativity has to assume that movement sequences consist of segments, executed either in sequence or with partial or complete overlap. Therefore, a fundamental question that has pervaded research in motor control both in artificial and biological systems revolves around identifying movement primitives (a.k.a. units of actions, basis behaviors, motor schemas, etc.). What are the fundamental building blocks that are strung together, adapted to, and created for ever new behaviors? This paper summarizes results that led to the hypothesis of Dynamic Movement Primitives (DMP). DMPs are units of action that are formalized as stable nonlinear attractor systems. They are useful for autonomous robotics as they are highly flexible in creating complex rhythmic (e.g., locomotion) and discrete (e.g., a tennis swing) behaviors that can quickly be adapted to the inevitable perturbations of a dy-namically changing, stochastic environment. Moreover, DMPs provide a formal framework that also lends itself to investigations in computational neuroscience. A recent finding that allows creating DMPs with the help of well-understood statistical learning methods has elevated DMPs from a more heuristic to a principled modeling approach, and, moreover, created a new foundation for imitation learning. Theoretical insights, evaluations on a humanoid robot, and behavioral and brain imaging data will serve to outline the framework of DMPs for a general approach to motor control and imitation in robotics and biology.

link (url) [BibTex]

link (url) [BibTex]


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Computational approaches to motor learning by imitation

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

Philosophical Transaction of the Royal Society of London: Series B, Biological Sciences, 358(1431):537-547, 2003, clmc (article)

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

link (url) [BibTex]

link (url) [BibTex]

1999


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Is imitation learning the route to humanoid robots?

Schaal, S.

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

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

link (url) [BibTex]

1999

link (url) [BibTex]