Servo-constraint Generalized Inverse Dynamics for Robot Manipulator Control Design

Novel concept of inverse dynamics for robot manipulator control is developed. The concept is based on generalized inversion, and therefore it avoids limitations and shortcomings of square inversion that are frequently encountered in conventional inverse dynamics. A servo-constraint on the manipulator is defined, the satisfaction of which implies that the desired robot kinematics is satisfied. A prescribed stable linear second-order dynamics in a servo-constraint deviation norm measure variable is evaluated along trajectory solutions of the manipulator, resulting in a linear algebraic relation in the control vector. Generalized inversion of the relation via the Greville formula yields a control law that is linearly parameterized in a free null-control vector. The null-control vector is projected onto nullspace of the controls coefficient in the linear algebraic relation, and therefore it does not affect servo-constraint dynamics. The design freedom offered by the null-control vector is utilized to stabilize manipulator's internal dynamics, and to provide a perturbed feedback linearizing transformation of the global closed loop system dynamics. Generalized inversion singularity avoidance is made by replacing the Moore-Penrose generalized inverse in the Greville formula by a damped generalized inverse, resulting in uniformly ultimately bounded robot manipulator trajectory tracking.