Tracking control using optimal discrete-time H∞ for mechanical systems: Applied to Robotics.

In this work, the H∞ control for mechanical systems and its application in Robotics is discussed. The controller is designed in discrete time and it is synthesized for mechanical systems that are modeled by means of the Euler–Lagrange formulation. Making use of the discrete Hamilton–Jacobi–Isaacs equation the control law is derived. The discrete control law is then applied to a continuous-time 6-DoF bipedal robot model in order to track the walking pattern references for each link. The system along with the control law is simulated, with the system subjected to an external disturbance that emulates the action of a group of unknown bounded forces over the links of the bipedal robot. Furthermore, an algorithm to diminish the effect of the disturbance is proposed such that the full knowledge of the plant is not needed but only the linear part of the mass and inertia matrix; this algorithm is combined with the H∞ controller and applied to a robotic arm. Finally, this work is compared to a similar approach that uses H∞ technique in continuous time.