Inverse dynamics and Fourier-based approach to solve optimal control problems for multi-link mechanisms

Paper in proceeding, 1997

This paper is concerned with the investigation of multi-link mechanism controlled mo­tion between fixed boundary conditions and given constraints on the phase coordinates. The mo­­duli of the controlling moments at the hinges between the links are bounded. A com­pu­ta­ti­o­nal method to the mathematical modeling of the optimal control laws which govern multi-link mechanism reaching motion is presented. This method is based on Fourier and spline appro­xi­ma­tions of the independently variable functions and inverse-dynamics approach. The me­­thod proposed makes it possible to satisfy the boundary conditions and some constraints on the phase coordinates automatically and accurately. The efficiency of the proposed method is illustrated by the solution of the energy-optimal control problem of a plane mobile three-link manipulator with a load on the grip.