SYMPLECTIC METHOD FOR INSTANTANEOUS OPTIMAL CONTROL OF MULTIBODY SYSTEM TRAJECTORY TRACKING

With the wide application of robot in various fields, the new requirement on dynamics and control performance for robot has been continually proposed. Especially for the intelligent robot with much more complex system and flexibility of operation, the high accuracy of trajectory tracking should be satisfied for practical mission requirement. Therefore, the aim of this paper is to satisfy the requirement of trajectory tracking mission of robot multibody system, and then the symplectic method based on differential-algebraic equations for instantaneous optimal control is proposed. First, the general dynamic equation of robot should be established by absolute coordinates of multibody system, i.e., differential-algebraic equations; then, the differential-algebraic equations are discretized in the domain of continuoustime by symplectic method, and then the present position/velocity/Lagrange multiplier are taken as unknown variables of nonlinear equations; afterward, the combination of objective tracking trajectory and weighted control input are introduced as the performance of instantaneous optimal control. The optimal control input is obtained by the theory of instantaneous optimal control; finally, the tracking mission for the objective trajectory can be continuously implemented with the updated time step. In order to test the effectiveness of the proposed method, the trajectory tacking problem of double pendulum is taken as an example, and numerical simulations show that the proposed symplectic method for instantaneous optimal control can obtain high accuracy tracking results, meanwhile, the proposed symplectic method based on differential-algebraic equations can be applied for other trajectory tracking mission of complex multibody system.