n -th Order Sensor Output to Control k -DoF Serial Robot Arms

Abstract

Currently, zero-order sensors are commonly used as positioning feedback for the closed-loop control in robotics; thus, in order to expand robots’ control alternatives, other paths in sensing should be investigated more deeply. Conditions under which the $n$ -th order sensor output can be used to control $k$ -DoF serial robot arms are formally studied in this work. In obtaining the mentioned control conditions, the Pickard-Lindeloff theorem has been used to prove the existence and uniqueness of the robot’s mathematical model solution with $n$ order sensory systems included. To verify that the given conditions and claims guarantee controllability for both continuous-based and variable structure-based systems, two types of control strategies are used in obtaining simulation results: the conventional PID control and a second-order Sliding Mode control.