A SIMPLE ITERATIVE SCHEME FOR LEARNING GRAVITY COMPENSATION IN ROBOT ARMS A. DE LUCA, S. PANZIERI Dipartimento di Informatica e Sistemistica Universit` a degli Studi di Roma “La Sapienza” ABSTRACT The set-point regulation problem for robot manipulators under gravity is usually solved by either model-based compensation or PID control. The former cannot be applied if an unknown payload is present or when model parameters are poorly esti- mated, while the latter requires fine and lengthy tuning of gains in order to achieve good performance on the whole workspace. A simple iterative scheme is proposed for generating exact gravity compensation at the desired set-point, without the knowl- edge of the robot dynamic model. The control law starts with a PD action on the joint error, updating at discrete instants an additional feedforward term. Global con- vergence of the scheme is proved under a mild condition on the proportional gains. Simulations are presented for a 3R rigid robot arm moving in a vertical plane. 1. Introduction It is well known that a rigid robot arm can be asymptotically stabilized around a given joint configuration via a PD controller on the joint errors, provided that gravity is exactly cancelled by feedback [1]. This result holds globally, i.e. starting from any joint configuration, and requires only positive definite gain matrices. However, on- line cancellation of gravity effects leads to a nonlinear control law, which may be difficult to implement. Under a mild condition on the proportional gain, this scheme can be simplified to constant gravity compensation , evaluated only at the desired configuration [2]; a purely linear feedback law with a feedforward action is then obtained. In this case, the proportional gain should be chosen so to dominate the gradient of the gravity forces in the whole robot workspace. Similar conditions have been found also for robots with elastic joints [3] or with flexible links [4], under a further assumption on the arm stiffness. In all cases, an exact knowledge of the gravity vector is required. This condition is difficult to be realized, e.g. for a robot picking up multiple unknown payloads, and