Model predictive control of a manipulator arm with frictional/unilateral contact.

Abstract

Controlling mechanisms whose equations of motion involve nonlinear discontinuous terms is difficult. A robot manipulator doing a task requiring intermittent contacts with the environment is such a system. Historically, the difficulty was avoided by splitting the global control problem into subproblems defined by the smooth structures of the piecewise discontinuous model. As a result, algorithms for controlling robot manipulators in free motion, transition to contact (impact control) and force/motion in contact were obtained separately and implementation was done using a switching law. In this thesis, nonlinear Model Predictive Control (MPC) is proposed as a unified solution for controlling robot manipulators with intermittent contacts. The use of a model-based prediction over a receding horizon allows MPC to foresee discontinuous changes in the dynamics and smoothly adjust the control command. Therefore, it was used extensively in the process industry where state and control command saturations are often present. The first contribution in this thesis lies in the use of MPC for controlling systems with discontinuities in the equations of motion. Through analysis and simulation, the ability of the nonlinear MPC approach to provide a unifying solution is demonstrated. The literature on nonlinear MPC being almost inexistent, the work presented herein also contributes to the understanding of how MPC can be applied to nonlinear systems. Because the complete analytical solution of the nonlinear MPC problem is not prone to real-time applications, two implementation alternatives are also proposed. Both use the operational space information about the task to perform to reduce considerably how much computation is necessary for a solution. The first approach is similar to the resolved-acceleration algorithm with the resolved acceleration being computed from a reduced MPC problem. The second is called the predictive impedance algorithm since its formulation is similar to impedance control with the impedance being replaced by the output of a reduced MPC problem. The applicability of both algorithms has been demonstrated through simulation. Experimental results were also obtained for the predictive impedance solution.