Funnel-Control in robotics: An introduction

An adaptive (time-varying) MIMO/SISO control strategy - funnel-control - for position control of nonlinear, coupled (rigid) robotic systems is presented and its applicability in robotics introductory shown. The concept is based on the high-gain controllability of minimum-phase systems with relative degree one and known high-frequency gain. The approach allows prescribed transient behavior without identification and/or parameter estimation, although the plant is only structurally known. As most industrial applications - also the considered robotic systems - exhibit higher relative degrees, funnel-control is not directly applicable. Therefore a state-feedback like extension is introduced, which permits the reduction of the relative degree and retains the minimum-phase property. The additional implementation of a Pi-like structure assures good disturbance rejection and asymptotic tracking of the reference position trajectory. Simulation results for a 6-DOF Manutec R3 robot show the achievable performance of one overall MIMO Funnel Controller for all joints and one SISO funnel controller for each joint (6 controllers).