Trajectory formation for imitation with nonlinear dynamical systems

Explores an approach to learning by imitation and trajectory formation by representing movements as mixtures of nonlinear differential equations with well-defined attractor dynamics. An observed movement is approximated by finding a best fit of the mixture model to its data by a recursive least squares regression technique. In contrast to non-autonomous movement representations like splines, the resultant movement plan remains an autonomous set of nonlinear differential equations that forms a control policy which is robust to strong external perturbations and that can be modified by additional perceptual variables. This movement policy remains the same for a given target, regardless of the initial conditions, and can easily be re-used for new targets. We evaluate the trajectory formation system in the context of a humanoid robot simulation that is part of the Virtual Trainer project, which aims at supervising rehabilitation exercises in stroke-patients. A typical rehabilitation exercise was collected with a Sarcos Sensuit, a device to record joint angular movement from human subjects, and approximated and reproduced with our imitation techniques. Our results demonstrate that multijoint human movements can be encoded successfully, and that this system allows robust modifications of the,movement policy through external variables.

[1]  F. Delcomyn Neural basis of rhythmic behavior in animals. , 1980, Science.

[2]  Daniel Bullock,et al.  Chapter 11 Vite and Flete: Neural Modules for Trajectory Formation and Postural Control , 1989 .

[3]  Haim Sompolinsky,et al.  Associative network models for central pattern generators , 1989 .

[4]  S. Wolf,et al.  Forced use of hemiplegic upper extremities to reverse the effect of learned nonuse among chronic stroke and head-injured patients , 1989, Experimental Neurology.

[5]  F. A. Mussa-lvaldi,et al.  Convergent force fields organized in the frog's spinal cord , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[6]  Robert A. Jacobs,et al.  Hierarchical Mixtures of Experts and the EM Algorithm , 1993, Neural Computation.

[7]  S. Schaal,et al.  A Kendama Learning Robot Based on Bi-directional Theory , 1996, Neural Networks.

[8]  Mitsuo Kawato,et al.  TRAJECTORY FORMATION IN ARM MOVEMENTS: MINIMIZATION PRINCIPLES AND PROCEDURES , 1996 .

[9]  Ferdinando A. Mussa-Ivaldi,et al.  Nonlinear force fields: a distributed system of control primitives for representing and learning movements , 1997, Proceedings 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA'97. 'Towards New Computational Principles for Robotics and Automation'.

[10]  Christopher G. Atkeson,et al.  Constructive Incremental Learning from Only Local Information , 1998, Neural Computation.

[11]  S. Schaal,et al.  Programmable Pattern Generators , 1998 .

[12]  Perry Y. Li,et al.  Passive velocity field control of mechanical manipulators , 1995, IEEE Trans. Robotics Autom..

[13]  Joshua G. Hale,et al.  Using Humanoid Robots to Study Human Behavior , 2000, IEEE Intell. Syst..

[14]  Shinya Kotosaka,et al.  Submitted to: IEEE International Conference on Humanoid Robotics Nonlinear Dynamical Systems as Movement Primitives , 2022 .