Make it Safer and Stabler: Model Predictive Path Integral Control Strategy Using Lyapunov Function

Trajectory planning is the basis of motion control for mobile manipulator and its performance has a significant impact on the stability and safety for the motion of mobile manipulator. Model Predictive Path Integral (MPPI) control strategy, which samples different trajectories and fits them into a good trajectory, can be applied in it. However, for randomization of the sampling process, stability and safety of the generated trajectory can't be guaranteed. In this paper, we propose a new improved control strategy, called LF-MPPI, introducing Lyapunov Function(LF) into classic MPPI control strategy, which significantly improves stability of the generated trajectory in terms of guaranteeing safety. The key point is to use Lyapunov Function constraints to optimize the control inputs generated by classic MPPI control strategy. First, different trajectories are sampled from Gaussian function under forward kinematics and Lyapunov Function constraints are used to penalize trajectories lacking sufficient stability. Then, the sampling trajectories are fitted into one excellent trajectory through importance sampling. Finally, Lyapunov Function constraints are introduced to solve the actual control inputs executed to the mobile manipulator which is closest to the control inputs generated before. We validate the feasibility and practicability of our proposed control strategy through extensive simulations of trajectory planning for mobile manipulator. Results show that LF-MPPI control strategy guarantees the safety with avoiding exceeding limits and helps improve the stability with 100% task success rate and an approximate 12% time savings.