Variable structure control of a robotic arm in the presence of uncertainty

Abstract

Abstract Based on the theory of variable structure systems (VSS), control system design for the trajectory control of robotic systems is presented. It is assumed that the parameters of the system are uncertain and unknown frictional torques are acting at the various joints of the arm. For simplicity, the control of a three‐link PUMA arm is considered. For trajectory following, two control laws, C H and C θ , based on the choice of coordinates of the end effector or joint angles as the controlled outputs, respectively, are derived. It is seen that whereas control C θ has no singularity, certain singular surfaces arise where feedback elements of C H become infinity. These singular surfaces describe the boundary of the reachable region (workspace). Digital simulation results are presented to show that accurate trajectory following can be accomplished using the control C H or C θ for large maneuvers of the arm in spite of the uncertainty in the system.