Tracking and Vibration Control of Flexible Robots Using Shape Memory Alloys

This paper considers the tracking control problem for flexible robots with active vibration suppression by shape memory alloys (SMAs). With a singular perturbation technique, the flexible modes and joint angles are modeled as fast and slow variables, respectively. The fast subsystem comprising the nonlinear SMA dynamics is obtained in a strict feedback form feasible for the backstepping design. The SMA actuators are configured in redundant pairs for an active suppression of vibrations. For the slow subsystem, asymptotically stable tracking is ensured, while for the fast subsystem, uniform exponential stability is guaranteed. By invoking Tikhonov's theorem, it is shown that the error arising from the nonideal time-scale separation in the singular perturbation model is small. Simulation demonstrates the effectiveness of the proposed control