Throwing Motion Control of the Pendubot via Explosively Unstable Zero Dynamics

The objective of this paper is to present systematic methods for throwing motion control of underactuated robots. 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. Exact analysis of ordinary differential equations guarantees the explosive instability of the zero dynamics. Numerical simulations confirm the effectiveness of the proposed control strategy.