Simulation and trajectory optimization of articulated robots via spectral variational integrators

This paper presents an arbitrary high -order structure -preserving numerical method for the simulation and optimization of the articulated robot dynamics. The proposed numerical scheme is derived by using spectral variational integrators (SVI) to discretize the Lagrangian of multibody robot systems which are calculated by an efficient parallel Lie group formulation. The linear stability conditions of SVI for the simulation of the robot dynamics are given and proofed. The resulting algorithms are examined in a simplified industrial Selective Compliance Assembly Robot Arm (SCARA) and a wheel -leg hybrid mechanism. They exhibit salient advantages over conventional numerical methods. The algorithms converge exponentially, preserve the symplectic form and momentum automatically and exhibit excellent energy stability, which yield more qualitative simulation and optimization results for articulated multibody robot systems.