MPPI-IPDDP: Hybrid Method of Collision-Free Smooth Trajectory Generation for Autonomous Robots

Abstract

This paper presents a hybrid trajectory optimization method designed to generate collision-free, smooth trajectories for autonomous mobile robots. By combining sampling-based Model Predictive Path Integral (MPPI) control with gradient-based Interior-Point Differential Dynamic Programming (IPDDP), we leverage their respective strengths in exploration and smoothing. The proposed method, MPPI-IPDDP, involves three steps: First, MPPI control is used to generate a coarse trajectory. Second, a collision-free convex corridor is constructed. Third, IPDDP is applied to smooth the coarse trajectory, utilizing the collision-free corridor from the second step. To demonstrate the effectiveness of our approach, we apply the proposed algorithm to trajectory optimization for differential-drive wheeled mobile robots and point-mass quadrotors. In comparisons with other MPPI variants and continuous optimization-based solvers, our method shows superior performance in terms of computational robustness and trajectory smoothness. Code: https://github.com/i-ASL/mppi-ipddp Video: https://youtu.be/-oUAt5sd9Bk

Figures (9)

• Figure 1: A method for collision-free smooth path planning. The contents in the red box are subjects in this paper.
• Figure 2: Schematics of for collision-free path corridors.
• Figure 3: The iterations of the MPPI-IPDDP algorithm for generating a collision-free path from $(0,0)$ to $(0,6)$. In the figure, black dots represent the positions of the robot, red circles denote the path corridors, and gray areas indicate obstacles. During the early iterations, the constraints are violated (as the black dots are outside the corridors) because the IPDDP struggled with the infeasible starting point and was terminated by the user-defined maximum iteration limit, as illustrated in ①$\sim$③. However, as the MPPI-IPDDP algorithm continues to iterate, it eventually finds the optimal collision-free trajectory, as shown in ⑧.
• Figure 4: A comparison of control inputs obtained from MPPI and IPDDP.
• Figure 6: The iterations for generating an optimal collision-free path from $(0,0,0)$ to $(0,4,2)$ by MPPI-IPDDP. The black dots are position of the quadrotor, the red spheres are the path corridors, and the gray represents obstacles. The optimal trajectory passes the small hole and reaches the destination. Details can be found in accompanying video.