Symbolic modeling and dynamic simulation of robotic manipulators with compliant links and joints

The explicit, non-recursive symbolic form of the dynamic model of robotic manipulators with compliant links and joints are developed based on a Lagrangian-assumed mode of formulation. This form of dynamic model is suitable for controller synthesis, as well as accurate simulations of robotic applications. The final form of the equations is organized in a form similar to rigid manipulator equations. This allows one to identify the differences between rigid and flexible manipulator dynamics explixitly. Therefore, current knowledge on control of rigid manipulators is likely to be utilized in a maximum way in developing new control algorithms for flexible manipulators.

Computer automated symbolic expansion of the dynamic model equations for any desired manipulator is accomplished with programs written based on commercial symbolic manipulation programs (SMP, MACSYMA, REDUCE). A two-link manipulator is used as an example. Computational complexity involved in real-time control, using the explicit, non-recursive form of equations, is studied on single CPU and multi-CPU parallel computation processors.