Learnability and Adaptability from the Viewpoint of Passivity Analysis

Abstract

Abstract This paper attempts to give a mathematical and physical interpretation of practice-based learning (so-called ‘learning control’) from the passivity viewpoint for a class of linear dynamical systems with passivity and general nonlinear differential equations of robotic motion. It is shown from an axiomatic argument that the passivity of a pair of input and output plays a crucial role in the ability of learning. More precisely in case of robot dynamics it is shown that the passivity between a residual input torque vector and an output as a linear combination of the angular velocity error and the saturated joint angle error enables trajectory tracking errors of the robot motion to converge to zero with repeating practices. For a class of robot tasks when the endpoint is holonomically constrained on a surface, the problem of convergence of residual position and force trajectory tracking errors is also discussed under the joint-space orthogonalization principle.