Header logo is

12 results (View BibTeX file of all listed publications)

2008

no image
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)

am

link (url) [BibTex]

2008

am Hoffmann, H., Schaal, S. Human movement generation based on convergent flow fields: A computational model and a behavioral experiment In Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (inproceedings)

link (url) [BibTex]

no image
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)

am

PDF [BibTex]

am Park, D., Hoffmann, H., Pastor, P., Schaal, S. Movement reproduction and obstacle avoidance with dynamic movement primitives and potential fields In IEEE International Conference on Humanoid Robots, 2008., 2008, clmc (inproceedings)

PDF [BibTex]

no image
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.

am

[BibTex]

am Mistry, M., Theodorou, E., Hoffmann, H., Schaal, S. The dual role of uncertainty in force field learning In Abstracts of the Eighteenth Annual Meeting of Neural Control of Movement (NCM), Naples, Florida, April 29-May 4, 2008, clmc (inproceedings)

[BibTex]

no image
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)

am

PDF [BibTex]

am Hoffmann, H., Pastor, P., Schaal, S. Dynamic movement primitives for movement generation motivated by convergent force fields in frog In Adaptive Motion of Animals and Machines (AMAM), 2008, clmc (inproceedings)

PDF [BibTex]

no image
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

am

[BibTex]

am Hoffmann, H., Theodorou, E., Schaal, S. Behavioral experiments on reinforcement learning in human motor control In Abstracts of the Eighteenth Annual Meeting of Neural Control of Movement (NCM), Naples, Florida, April 29-May 4, 2008, clmc (inproceedings)

[BibTex]

no image
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)

am

PDF [BibTex]

am Pastor, P., Hoffmann, H., Schaal, S. Movement generation by learning from demonstration and generalization to new targets In Adaptive Motion of Animals and Machines (AMAM), 2008, clmc (inproceedings)

PDF [BibTex]

no image
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)

am

link (url) [BibTex]

am Park, D., Hoffmann, H., Schaal, S. Combining dynamic movement primitives and potential fields for online obstacle avoidance In Adaptive Motion of Animals and Machines (AMAM), Cleveland, Ohio, 2008, 2008, clmc (inproceedings)

link (url) [BibTex]

no image
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.

am

[BibTex]

am Theodorou, E., Hoffmann, H., Mistry, M., Schaal, S. Computational model for movement learning under uncertain cost In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

[BibTex]

no image
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.

am

link (url) [BibTex]

am Ting, J., D’Souza, A., Vijayakumar, S., Schaal, S. A Bayesian approach to empirical local linearizations for robotics In International Conference on Robotics and Automation (ICRA2008), Pasadena, CA, USA, May 19-23, 2008, 2008, clmc (inproceedings)

link (url) [BibTex]

no image
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.

am

[BibTex]

am Hoffmann, H., Schaal, S. Do humans plan continuous trajectories in kinematic coordinates? In Abstracts of the Society of Neuroscience Meeting (SFN 2008), Washington, DC 2008, 2008, clmc (inproceedings)

[BibTex]

1995

no image
A kendama learning robot based on a dynamic optimization theory

Miyamoto, H., Gandolfo, F., Gomi, H., Schaal, S., Koike, Y., Osu, R., Nakano, E., Kawato, M.

In Preceedings of the 4th IEEE International Workshop on Robot and Human Communication (RO-MAN’95), pages: 327-332, Tokyo, July 1995, clmc (inproceedings)

am

[BibTex]

1995

am Miyamoto, H., Gandolfo, F., Gomi, H., Schaal, S., Koike, Y., Osu, R., Nakano, E., Kawato, M. A kendama learning robot based on a dynamic optimization theory In Preceedings of the 4th IEEE International Workshop on Robot and Human Communication (RO-MAN’95), pages: 327-332, Tokyo, July 1995, clmc (inproceedings)

[BibTex]