Optimal Control of Constrained Mechanical Systems

摘要: Abstract The equations of motion for a constrained mechanical (or multi-body) system can be obtained from the Hamiltonian description dynamics which leads to Euler-Lagrange's equation. result, in general, is set mixed differential and algebraic involving generalized coordinates system, their derivatives, input forces torques, constraint torques (Lagrange multipliers associated with constraints). It possible, principle, reduce this differential- strictly by eliminating torques. In practice, however, complexity these manipulations prohibitive. Consequently, problem optimal open-loop control systems cannot treated standard optimization packages generally require that time evolution described or difference equations. paper, we obtain procedure calculating systems. This implemented using integration software. We present several examples controls have been computed Basile, specialized software package signal processing developed at INRIA.