EXACT-MPPI: Exact Signed-Distance Navigation for Arbitrary-Footprint Robots from Point Clouds via Path Integral Control

2026-05-28

AI Summary

This work addresses the loss of feasible paths in dense environments caused by oversimplified robot footprint representations in traditional navigation methods. It proposes a training-free local navigation framework that embeds an analytical, exact signed distance function directly into an MPPI controller, generating motion commands from raw point cloud observations and sparse guidance. The approach natively supports arbitrary convex or concave polygonal and rectangular footprints without requiring convex decomposition, inflation, or learned encodings. For the first time in sampling-based predictive control, it enables analytically precise distance evaluation. Combined with JAX-accelerated batched GPU computation, dynamic point cloud transformation, and configurable kinematic models, the method significantly improves distance computation efficiency, preserves feasible paths where convex approximations fail, and maintains robustness in both static and dynamic obstacle environments. It has been successfully deployed on differential, Ackermann, omnidirectional, and hybrid-drive mobile bases.

Abstract

Ground robots often carry payloads, implements, or other attachments that turn their effective footprint into complex, non-convex shapes. Navigating safely through clutter then requires reasoning about this true geometry, yet most local planners simplify it with convex or inflated proxies and rasterize sensor data into occupancy grids or distance fields. Both choices eliminate feasible motions when clearance is comparable to the footprint geometry. We present EXACT-MPPI, a training-free local navigation framework that maps local point-cloud observations and sparse guidance directly to motion commands, without any intermediate map representation. The framework embeds an analytic, exact signed-distance evaluator into a Model Predictive Path Integral (MPPI) controller. The footprint is represented as a simple polygon for general convex or concave planar shapes, with a rectangle-cover specialization for faster evaluation of rectilinear footprints, enabling footprint-aware collision costs without convex decomposition, inflation, or learned encoders. During each MPPI rollout, observed obstacle points are transformed into the predicted body frame and evaluated against the footprint. All operations are batched in JAX, leveraging GPU parallelism for real-time receding-horizon control. Experiments show that EXACT-MPPI accelerates batched distance evaluation over a learned point-to-robot baseline, preserves feasible motion where convex-footprint planners fail, and remains robust under dense static and moving obstacles. The same framework deploys on differential-drive, Ackermann, omnidirectional, and hybrid-mode platforms by changing only the footprint description and motion model without per-platform training. Pairing exact footprint geometry with sampling-based predictive control thus offers a practical, training-free path to footprint-aware local navigation across diverse robots.

Problem

• footprint-aware navigation
• non-convex robot footprint
• local motion planning
• signed-distance evaluation
• point cloud-based navigation

Innovation

• exact signed-distance
• footprint-aware navigation
• Model Predictive Path Integral (MPPI)
• point cloud
• training-free control