Strict Lyapunov function for sliding mode control of manipulator using quasi-velocities

This paper describes proposition of sliding mode control using strict Lyapunov function for robot manipulators described in terms of some quasi-velocities (QV). The considered here quasi-velocities contain both kinematical and dynamical parameters of a manipulator. Introducing QV together with joint position leads to one first-order dynamic equations with diagonal mass matrix instead of a second-order differential equation and one first-order equation which describes transformation between joint velocities and QV. The presented controller based on strict Lyapunov function guarantees closed-loop stability and global positioning. Differences between classical sliding mode control scheme and the considered here were shown on 3 d.o.f., 3-D Yasukawa-like robot.