Optimal Control Concepts for Robots with Varying Stiffness Joints

Abstract

This work will focus on the performance limits of robots consisting elastic elements in their joints. In order to derive these limits, Optimal Control (OC) Theory is applied as the tool for solving this problem. This theory yields optimality conditions for the controls, which minimize a cost functional that describes the goal. Since OC Theory is mainly a mathematical tool, physical interpretation of the results is often not easy to make, especially if the problem is solved numerically. For that reason, most of the work will discuss a robot arm with one joint, for which analytical solutions could be obtained. This simple nonlinear model, where the nonlinearity occurs because of the varying joint stiffness, will reveal many interesting properties of this class of systems. These properties will then be investigated for robots with multiple joints.