A Prior Design Scheme of Constraint Space of Ajustable Parameters for Guaranteeing Positive Deniteness of Estimated Inertia Matrix Used in Adaptive Trajectory Control of 2 Link Rigid Robot Arm

Abstract

An improved adaptive trajectory control of a rigid link robot manipulator in which Middleton’s control input[4] and the adaptation law with a certain smooth projection algorithm to ensure the positive definiteness of estimated inertia matrix are used was proposed by Sawada[9]. However, it cannot be applied when the manipulator is composed of the links whose length are extremely different with each and the tip load varies significantly. Using prior knowledge about upper bound of tip load and range of robot arm,manipulator’s parameters without tip load, we propose a method to extend the class of robot arm that can be applied by designing the special convex set of adjustable parameters in which the positive definiteness of the estimated inertia matrix is ensured and true parameters are contained.