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2008


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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.

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link (url) [BibTex]

2008


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.

am

[BibTex]

[BibTex]

2002


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Learning rhythmic movements by demonstration using nonlinear oscillators

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

In IEEE International Conference on Intelligent Robots and Systems (IROS 2002), pages: 958-963, Piscataway, NJ: IEEE, Lausanne, Sept.30-Oct.4 2002, 2002, 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.

am

link (url) [BibTex]

2002


link (url) [BibTex]


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Movement imitation with nonlinear dynamical systems in humanoid robots

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

In International Conference on Robotics and Automation (ICRA2002), Washinton, May 11-15 2002, 2002, 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.

am

link (url) [BibTex]

link (url) [BibTex]


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A locally weighted learning composite adaptive controller with structure adaptation

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

In IEEE International Conference on Intelligent Robots and Systems (IROS 2002), Lausanne, Sept.30-Oct.4 2002, 2002, clmc (inproceedings)

Abstract
This paper introduces a provably stable adaptive learning controller which employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and the working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using a nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized on-line. Inspired by composite adaptive control methods, the pro-posed learning adaptive control algorithm uses both the tracking error and the estimation error to up-date the parameters. We provide Lyapunov analyses that demonstrate the stability properties of the learning controller. Numerical simulations illustrate rapid convergence of the tracking error and the automatic structure adaptation capability of the function approximator. This paper introduces a provably stable adaptive learning controller which employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and the working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using a nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized on-line. Inspired by composite adaptive control methods, the pro-posed learning adaptive control algorithm uses both the tracking error and the estimation error to up-date the parameters. We provide Lyapunov analyses that demonstrate the stability properties of the learning controller. Numerical simulations illustrate rapid convergence of the tracking error and the automatic structure adaptation capability of the function approximator

am

link (url) [BibTex]

link (url) [BibTex]

1993


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Roles for memory-based learning in robotics

Atkeson, C. G., Schaal, S.

In Proceedings of the Sixth International Symposium on Robotics Research, pages: 503-521, Hidden Valley, PA, 1993, clmc (inproceedings)

am

[BibTex]

1993


[BibTex]


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Open loop stable control strategies for robot juggling

Schaal, S., Atkeson, C. G.

In IEEE International Conference on Robotics and Automation, 3, pages: 913-918, Piscataway, NJ: IEEE, Georgia, Atlanta, May 2-6, 1993, clmc (inproceedings)

Abstract
In a series of case studies out of the field of dynamic manipulation (Mason, 1992), different principles for open loop stable control are introduced and analyzed. This investigation may provide some insight into how open loop control can serve as a useful foundation for closed loop control and, particularly, what to focus on in learning control. 

am

link (url) [BibTex]

link (url) [BibTex]