Learning gravity compensation in robots: Rigid arms, elastic joints, flexible links

The setpoint regulation problem for robotic manipulators is a basic task that can be solved either by PID control or by model-based gravity compensation. These approaches are commonly applied both to rigid arms and to robots with flexible links and/or elastic joints. However, PID control requires fine and lengthy tuning of gains in order to achieve good performance over the whole workspace. Moreover, no global convergence proof has yet been given for this control law in the case of flexible links or elastic joints. On the other hand, a constant or even a configuration-dependent gravity compensation is only an approximate solution when an unknown payload is present or when model parameters are poorly estimated. In this paper a simple iterative scheme is proposed for generating exact gravity compensation at the desired setpoint without the knowledge of dynamic model terms. The resulting control law is shown to be global asymptotically stable for rigid arms as well as for manipulators with elastic joints or flexible links. Starting with a PD action on the error at the joint (i.e. motor) level, an additional feedforward term is built and updated at discrete instants. Convergence of the scheme is proved under a mild condition on the proportional gain, related to a bound on the gravity terms. In the presence of concentrated or distributed flexibility a structural property of the joint or of the link stiffness is further required, largely satisfied in practice. Simulation results are given for a three-link rigid arm and experimental results are also presented for a two-link robot with a flexible forearm.