Joint‐space orthogonalization and passivity for physical interpretations of dextrous robot motions under geometric constraints

Abstract

Abstract A principle of ‘joint‐space orthogonalization’ is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric constraints. The principle realizes the hybrid control in a strict sense by letting position feedback signals be orthogonal in joint space to the contact force vector whose components exert at corresponding joints. This orthogonalization is executed via a projection matrix computed in real‐time from a Jacobian matrix of the constraint equation in joint coordinates. To show the important role of the principle in control of robot manipulators, two basic set‐point control problems are analysed. One is a hybrid PID control problem for robot manipulators under geometric endpoint constraint and another is a coordinated control problem of two arms. It is shown that passivity properties of residual dynamics of robots follow from the introduction of a quasi‐natural potential and the joint‐space orthogonalization. Various stability problems of PID‐type feedback control schemes without compensating for the gravity force and with or without use of a force sensor are discussed from passivity properties of robot dynamics with the aid of the hyper‐stability theory.