Impact Modeling and Control for Industrial Manipulators

or arobotic manipulator, the impact of the end-effector on the F environment occurs in the transition from unconstrained (free) motion to constrained motion. Contact force at impact is difficult to control and oscillatory behavior (or, worse still, instability) can easily occur. Several kinds of models have been proposed to explain impact-force behavior. For instance, in [ 171 a rigid, six-degree-of-freedom (d.0.f.) model of the manipulator is assumed for a geared PUMA 560 arm; in [13] a sixth-order model is derived for a direct-drive manipulator (CMU DD arm 11) in single-joint operations, accounting for the arm, sensor, and environment compliances and whose dominant dynamics is due to the environment. In [ 191 a sixth-order model that takes into account the joint compliance inherent in reduction gears and the sensor and environment dynamics is adopted for a prototype single-joint geared arm. In this article. the impact-force behavior is experimentally studied on a six-d.0.f. commercial manipulator interacting with a very hard granite surface. The arm was manufactured with standard components and is representative of current industrial products. It is shown that the elastic-joint robot model proposed by Spong [ 161 completely explains frequency and damping of impact-force oscillations, so that oscillations can be totally ascribed to joint compliance, while links behave as rigid bodies. The initial part of the impact transient is also affected by Coulomb friction in the joints, which contributes to the dissipation of the kinetic energy of the arm at impact. Several control strategies have been proposed in the literature for impact and force control. A nonlinear feedback control law was proposed in [ 171 to decouple and linearize the system, so that the motion of the manipulator and the contact force can be controlled independently along each unconstrained (motion) and constrained (force) direction. In [ 191 an integral gain control was used for permanent (bounceless) contact and throughout transition, but bounces took place. In [13] a discontinuous explicit force control was implemented to avoid bounces, which led to a proportional positive gain (smaller than unity) for the transient phase of impact and to an integral gain for tracking the force setpoint once a bounceless contact had been established. In fact, [ 131 highlights that integral control, widely recognized (see, e.g., [8], [lo], [14], [19]) as the most suitable choice for permanent contact, is not suitable for the transition phase as bounce and instability might occur because of integrator wind-up [2]. This article shows, through analysis and experiments, how to effectively employ integral control even in the transition phase, Fig. I . SMART 3s robot.