Time-optimal control of robotic manipulators with uncertain dynamics and constraints

Abstract

The issues of the development of a nonlinear mathematical model and robust time-optimal control of rigid-link robotic manipulators are addressed. Constraints, nonlinearities and uncertainties, of manipulators and electric motors affect the performance characteristics of robotic systems and should be studied in detail. The nonlinear dynamical model of manipulators actuated by DC motors is derived on the basis of the Euler-Lagrange formulation. The constraints represent physical and kinematical bounds of mechanical components and electric motors. In this paper, the robust control issues for manipulators are investigated using the Hamilton-Jacobi theory. For robotic systems with unknown but bounded parameters and constraints on the state variables and control inputs we develop the robust time-optimal control strategy. A procedure for designing the robust bang-bang controllers is given and the nonquadratic performance measure is minimized. The proposed control methodology is feasible, reliable and provides the computational efficiency. The first joint of a manipulator with permanent-magnet DC motor is studied to demonstrate the efficiency of the robust control procedure and the bang-bang control algorithm. Experimental results are presented to verify the robustness and dynamic performance.