Trajectory Tracking Control for Robotics Manipulators Based on Passivity

This paper present a synthesized design for asymptotic stable feedback control approach based in Euler-Lagrange passivity properties, hyperbolic trigonometric functions, and the Lyapunov theory (specially second method) for a robot manipulator. Control systems of robot manipulators (tracking trajectory set point) offer many challenges in education where the students must learn robot dynamics and control structures, the solution of regulation and tracking control problem of Euler-Lagrange systems has been known for many years, for a literature review. The classic control systems that are used in robotics manipulators as a mechanical system, don´t allow to compensate the no linear dynamics performance, for example, inertia, Coriolis, gravity and tribology forces. To this end, we propose a nonlinear control design, based on the Euler-Lagrange formulation andits dynamics properties, the passivity injection, and the Lyapunov stability theory (second method). To this goal, we present the tracking set point, the stability proof and an illustrative example.