Simulation of flexible-link manipulators: basis functions and nonlinear terms in the motion equations

Two important issues relevant to modeling of flexible-link robotic manipulators are addressed. The authors examine the question of which terms should be included in the equations of motion for purposes of simulation. A complete model incorporating all nonlinearities that couple rigid-body and elastic motions is presented, along with a rational scheme for classifying their inclusion. The issue of basis function selection for spatial discretization of the elastic displacements is discussed. The finite element method and an eigenfunction expansion techniques are presented and compared. Both issues are examined numerically in the context of the Space Shuttle remote manipulator system. It is shown that certain key nonlinear elastic terms are required if numerical instability of the simulation is to be averted. Simulation results for two discretization schemes are included