Invertibility and robust nonlinear control of robotic systems

Based on the theory of invertibility and functional reproducibility in multivariable nonlinear systems, a unified framework for the trajectory control of robotic systems is presented. An inversion algorithm is used to derive a decoupling control law such that independent control of certain desired outputs is accomplished. For obtaining robustness in the control system under large variation of payloads, design of a servocompensator around the inner decoupled-loop using servomechanism theory is suggested. These results are applied for the trajectory control of a three degrees of freedom robot arm. For trajectory following two control laws, C?? and CH, based on the choice of joint angles or coordinates of the end effector as the controlled outputs, respectively, are derived. It is seen that, whereas control C?? has no singularity, certain singular surfaces arise where feedback elements of CH become infinity. Digital simulation results are presented to show the capability of the controls C?? and CH.