Modeling and control of a planar manipulator with an elastic forearm

A complete nonlinear dynamic model for a planar 2-DOF manipulator with an elastic forearm is derived. A nonlinear strain-displacement relationship is used to describe the kinematic foreshortening of the forearm. This effect is important in obtaining a correct derivation of the nonlinear terms that depend on the first-order generalised elastic coordinates. Using a Lyapunov stability theorem, the global asymptotic stability of an independent proportional-derivative (PD) feedback law is demonstrated. Simulation results compare the performance of the PD control law to that of a full-state feedback law. An experimental testbed in development is described, and preliminary experimental results are discussed