An optimization-based approach to control of robotic manipulators

This paper proposes a method to suboptimally tune the control parameters in a conventional Lyapunov-based method which shares the same concept of control design with sliding mode approach as applied to the robot manipulators. Optimal tuning of such parameters involves handling of nonlinearities in system dynamics and cost functions, which makes the problem challenging. We propose a step-by-step numerical algorithm that select suboptimal parameters while ensuring system stability. The controller is, suboptimal due to the facts that (1) it is in the form of a Slotine-type sliding mode control, (2) the numerical recursive algorithm might fall into a local minimum, and (3) the controller coefficients depend on the initial conditions of the system. The method is successfully applied to a two-link robot manipulator and the results are compared in simulation with those of a conventional controller.