DRPA-MPPI: Dynamic Repulsive Potential Augmented MPPI for Reactive Navigation in Unstructured Environments

TL;DR

This work introduces dynamic repulsive potential augmented MPPI (DRPA-MPPI), which dynamically detects potential entrapments on the predicted trajectories and automatically switches between standard goal-oriented optimization and a modified cost function that generates repulsive forces away from local minima.

Abstract

Reactive mobile robot navigation in unstructured environments is challenging when robots encounter unexpected obstacles that invalidate previously planned trajectories. Model predictive path integral control (MPPI) enables reactive planning, but still suffers from limited prediction horizons that lead to local minima traps near obstacles. Current solutions rely on heuristic cost design or scenario-specific pre-training, which often limits their adaptability to new environments. We introduce dynamic repulsive potential augmented MPPI (DRPA-MPPI), which dynamically detects potential entrapments on the predicted trajectories. Upon detecting local minima, DRPA-MPPI automatically switches between standard goal-oriented optimization and a modified cost function that generates repulsive forces away from local minima. Comprehensive testing in simulated obstacle-rich environments confirms DRPA-MPPI's superior navigation performance and safety compared to conventional methods with less computational burden.

Figures (4)

• Figure 1: Overview of the DRPA-MPPI framework. The framework switches between target-directed and detour-inducing guidance costs based on local minima detection and local minima passage detection.
• Figure 2: Comparison of guidance functions with a convex obstacle between robot and target. Left: The target-directed guidance function lacks detour gradients along the obstacle edge, which can trap the robot in local minima. Right: The proposed detour-inducing guidance function combines repulsive forces from detected local minima with attractive forces toward a virtual target to create effective obstacle circumnavigation gradients.
• Figure 3: DRPA-MPPI in a U-shaped obstacle configuration. Green circles, red stars, and blue shading represent start and target positions, and the top 10% of sampled rollouts, respectively. The sequence shows: (a) initial target-directed movement, (b) detection of local minimum (×) and function switch, (c) obstacle avoidance with detour function, (d) continued detour until passage criteria are met, (e) return to target-directed function after obstacle bypass.
• Figure 4: Example trajectories in a $6 \times 6$ grid non-convex obstacle scenario. Green dots, red stars, and color gradients respectively show start and target positions, and linear velocity magnitude. Results: (a) MPPI (horizon: 50) and (b) Log-MPPI (horizon: 50) both trapped at same local minima; (c) MPPI (horizon: 100) escapes the initial local minimum but encounters another trap, failing to reach the target; (d) Log-MPPI (horizon: 100) reaches the target but with inefficient navigation and velocity degradation; and (e) DRPA-MPPI (horizon: 50) navigates efficiently to the target without velocity degradation.

Theorems & Definitions (2)

• proof
• proof