Passivity of robot dynamics implies capability of motor program learning

Abstract

Learning control is a new approach to the problem of skill refinement for robot arms by iterative training. It is considered to be a mathematical model of motor program learning for skilled motions in the central nervous system.

This paper proposes a class of learning control algorithms with a forgetting factor 1»α>0 and without differention of velocity signals, which updates the input command by μ _k+1=(1−α)μ _k + αμ ₀ + Φe _k , where μ _k and e _k stand for command input and velocity error at k-th exercise respectively. The robustness of this learning control with respect to reinitialization errors, fluctuations of robot dynamics, and measurement noises is studied in detail. It is shown that not only the passivity of robot dynamics but also the exponential passivity of displacement dynamics on errors and difference dynamics between consecutive trials play a crucial role in proving the uniform boundedness of transient behaviors and the convergence in the progress of learning. Furthermore, two methods of learning called “interval training” and “selective learning” are proposed, which updates μ ₀ in the long-term memory every after several trials by the current command input μ _k or by the best command input among the past trials. The effectiveness of these methods in acceleration of the speed of convergence is also discussed.