Equivalence of learnability to output-dissipativity and application for control of nonlinear mechanical systems

Abstract

This paper attempts to explicate why a simple iterative learning control scheme for complicated robots dynamics with strong nonlinearities works well in acquiring any given desired motion over a finite time duration or any periodic motion. First, a class of linear dynamical system with specified input and output of the same dimension is treated by defining two properties: output-dissipativity and learnability. Next, extended arguments are developed for a class of nonlinear mechanical systems governed by the variational principle. Once an appropriate output that satisfies output-dissipativity is chosen for such a robotic system with strong nonlinearity, the proof of convergence of the proposed learning control law becomes straightforward from the property of learnability. Finally, by illustrating nonlinear dynamics of a set of multiple robot fingers of multi-joints and soft finger-tips it is shown that passivity plays a crucial role in dexterous motion of grasping and manipulating an objective object.