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This paper introduces EXACT-MPPI, a novel training-free local navigation framework for robots with arbitrary footprints that directly maps point cloud observations to motion commands using an analytic, exact signed-distance evaluator embedded within a Model Predictive Path Integral (MPPI) controller. By representing the robot's footprint as a simple polygon and leveraging JAX for GPU-accelerated batch processing, the method avoids the limitations of convex approximations and occupancy grids. Experiments demonstrate that EXACT-MPPI achieves faster distance evaluation than learned baselines, preserves feasible motions in cluttered environments, and generalizes across different robot platforms by only modifying the footprint description and motion model.
Ditch the convex approximations: EXACT-MPPI lets robots with complex footprints navigate tight spaces in real-time by directly reasoning about their true shape using point cloud data.
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.