Cascaded Nonlinear Control Design for Highly Underactuated Balance Robots

TL;DR

This paper introduces a nonlinear control strategy for highly underactuated balance robots, enabling simultaneous trajectory tracking and balancing of unactuated degrees of freedom through a cascaded virtual control approach.

Contribution

It proposes a novel cascaded control design that converts complex robot dynamics into manageable subsystems with virtual actuators, ensuring stability and convergence.

Findings

Closed-loop system is stable with exponential convergence.

Simulation on a triple-inverted pendulum cart system demonstrates effectiveness.

Control method handles more unactuated than actuated DOFs successfully.

Abstract

This paper presents a nonlinear control design for highly underactuated balance robots, which possess more numbers of unactuated degree-of-freedom (DOF) than actuated ones. To address the challenge of simultaneously trajectory tracking of actuated coordinates and balancing of unactuated coordinates, the proposed control converts a robot dynamics into a series of cascaded subsystems and each of them is considered virtually actuated. To achieve the control goal, 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.