Study on Motion Control Problems for 3-DOF Underactuated Cart-Double Pendulum System

A cart-double pendulum (CDP) system is a nonlinear underactuated mechanical system with three degrees of freedom (DOF) and two control inputs. This brief studies two motion control problems for this 3-DOF underactuated system. The first one is to construct a motion trajectory for the system from the lowest energy point to the highest energy point. The design of the trajectory is based on the ideas of energy absorption and inverse motion. The second one is to design tracking controllers that make the CDP system accurately track the planned trajectory. As a result, the CDP system can be stabilized at the highest energy point along a planned trajectory. And the motion process and settling time of the entire control system can be accurately known. Finally, numerical simulation results verify the effectiveness of our developed control strategy.