Online Trajectory Planning Control for a Class of Underactuated Mechanical Systems

Efficient control of underactuated systems has always been a great challenge, since one has to stabilize both actuated and unactuated states with fewer control inputs. During the past decades, great efforts have been devoted to improving the transient performance and robustness of the system, which are very crucial in plenty of application scenarios. To motivate corresponding research, an online trajectory planning method is proposed for a class of underactuated mechanical systems in this article. Specifically, reference trajectories are first generated for actuated states. Based on that, appropriate online adjustments are made to these reference trajectories, so as to realize efficient stabilization of the unactuated states. Different from traditional offline planning methods, the proposed one utilizes real-time feedback to counteract various unfavorable conditions, which endows it stronger robustness and better transient performance. Rigorous Lyapunov-based analysis is performed to show that the closed-loop system is asymptotically stable around the desired equilibrium point. Finally, the proposed method is applied to two underactuated mechanical systems, with simulation/experiment results provided to demonstrate its superior performance.