Newton-type algorithms for robot motion optimization

Abstract

The paper presents a class of Newton-type algorithms for the optimization of robot motions that take into account the dynamics. Using techniques from the theory of Lie groups and Lie algebras, the equations of motion of a rigid multibody system can be formulated in such a way that both the first and second derivatives of the dynamic equations with respect to arbitrary joint variables can be computed analytically. The result is that one can formulate the exact gradient and Hessian of an objective function involving the dynamics, and develop efficient second-order Newton-type optimization algorithms for generating optimal robot motions. The methodology is illustrated with a nontrivial example.