Nonlinear dynamical systems for imitation with humanoid robots

This article explores a new approach to learning by imitation and trajectory formation by representing movements as control policies (CPs) based on a set of nonlinear differential equations with well-defined attractor dynamics. An observed movement is approximated by locally linear models using an incremental locally weighted 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 system in the context of a humanoid robot simulation and an actual humanoid robot. Typical reaching movements were 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 (a) that multijoint human movements can be encoded successfully by the CPs, (b) that a learned movement policy can readily be reused to produce robust trajectories towards different targets, (c) that a policy fitted for one particular target provides a good predictor of human reaching movements towards neighboring targets, and (d) that the parameter space which encodes a policy is suitable for measuring to which extent two trajectories are qualitatively similar.