Throwing motion control of the Pendubot and instability analysis of the zero dynamics

This paper presents systematic methods for throwing motion control of the Pendubot based on the concept of explosively unstable zero dynamics. The Pendubot, an underactuated two-link planar robot, is investigated as a dynamic model of the superior limbs for imitation of human throwing motion whose models are fundamentally underactuated in nature. The controller is designed based on input-output linearization and output zeroing control since the Pendubot is not input-state linearizable. The originality of this paper is to intentionally destabilize the zero dynamics, a nonlinear dynamics which remains unobservable from the output when the partially linearized dynamics converges exponentially to zero, to generate dynamic acceleration of the ball. Mathematical analysis of ordinary differential equations guarantees the explosive instability of the zero dynamics. Numerical simulations verify the effectiveness of the proposed control strategy.