Differential Dynamic Programming-based Path Planning and Control Using Stochastic Initialization

This paper presents an integrated model predictive path integral (MPPI) and differential dynamic programming (DDP) framework for real-time local planning and trajectory tracking in unstructured, obstacle-rich environments. While DDP provides fast convergence and smooth control via second-order optimization, it is sensitive to initialization and prone to local-minima in non-convex settings. MPPI offers robustness through stochastic sampling but may require high computational effort and produce oscillatory controls under limited samples. To leverage their complementary strength MPPI is first used to generate a collision-free warm-start control sequence based on occupancy-grid collision checking. This sequence is then refined using DDP with adaptive regularization for improved convergence and smoothness. Obstacle avoidance is incorporated through an exponential repulsive potential derived from local costmap information, while control constraints on acceleration and steering are handled through penalty-based formulations. Experiments in robot operating system (ROS) Gazebo environments with static obstacles demonstrate that MPPI-based initialization enhances robustness, reduces convergence iterations, and mitigates control oscillations compared to standalone methods, while maintaining real-time performance.