Energy-efficient optimal control of robotic leg by indirect methods

Abstract

Since its beginning around 50 years ago [1], the research on biped robotics developed many successful prototypes, however the conventional strategies of gait generation and control have diverse performance issues. Between the promising alternatives of strategies is Optimal Control, which offers a clear definition of performance criteria and precise methods for achieving it. To highligh the possibilities of Optimal Control, this work solves the minimization of energy expenditure in the swing trajectory of a leg with 2 degrees of freedom, using an optimization method based on Pontryagin's Minimum Principle. The method applied is an indirect method that solves the optimal control of an exact non-linear model. The energy expenditure is compared with the expenditure of an intuitive Inverse Kinematics solution for the same model and task, demonstrating the minimization of energy expenditure. Unlike common optimization methods, this method relies on the use of an exact model of a non-linear system, eliminating modeling errors and generating a precise open loop control solution.