EXPONENTIAL TRAJECTORY TRACKING CONTROL IN THE WORKSPACE OF A CLASS OF FLEXIBLE ROBOTS

In this paper, we present a control strategy that ensures the exponent ial stability of the tracking error in the virtual joint space of a cl ass of mechanical systems made up of rigid links that form a chain tha t ends with a flexible beam. Virtual joints are defined so as to be re lated kinematically to the workspace. Thus, when the inverse kinematic s is nonsingular, trajectory tracking in the virtual joint space is eq uivalent to trajectory tracking in the workspace. The method proposed in this paper calls for the transformation of the trajectory from the virtual joint space to Me joint and deformation space. The robot is a non-minimum-phase system in the virtual joint space. However, this tra nsformation, which involves the dynamics of the flexible part, can be solved using a causal-anticausal iterative approach. The controller is then designed using an input-output feedback Linearization scheme, wi th regard to the joints, and two linear control laws with regard to th e joint and to me deformation variable tracking errors. Analysis based on the passivity theorem, hierarchical systems stability, and linear matrix inequalities then allows us to determine the controller gains t hat ensure that the tracking errors in the virtual joint space are wel l damped and exponentially stable. Finally, the strategy is validated by simulating a controller that incorporates the proposed laws and tha t drives a two-link manipulator that has one rigid and one flexible Li nk. The simulation results demonstrate the good performance of the pro posed control system. (C) 1998 John Wiley & Sons, Inc.