Cascaded Nonlinear Control Design for Highly Underactuated Balance Robots

This paper presents a nonlinear control design for highly underactuated balance robots, where the number of unactuated degree-of-freedom is greater than that of actuated one. To address the challenge of simultaneously trajectory tracking and balancing, the control converts a robot dynamics into a series of cascaded subsystems and each of them is con-sidered virtually actuated. We sequentially design and update the virtual and actual control inputs to incorporate the balance task such that the unactuated coordinates are balanced to their instantaneous equilibrium. The closed-loop dynamics are shown to be stable and the tracking errors exponentially converge towards a neighborhood near the origin. The simulation results demonstrate the effectiveness of the proposed control design by using a triple-inverted pendulum cart system.