C-Free-Uniform: A Map-Conditioned Trajectory Sampler for Model Predictive Path Integral Control

TL;DR

This work tackles the sensitivity of sampling-based MPC to nominal trajectories in cluttered environments by introducing C-Free Uniformity (C-Free-Uniform), an objective that yields a map-conditioned, collision-free sampling distribution uniform over the safe configuration space. A supervised map-conditioned sampler is learned to approximate the optimal C-Free-Uniform policy $oldsymbol{ ho}^*$ by training against a max-flow-derived ground truth $oldsymbol{ ho}_{MF}$, with a local perception pipeline feeding a U-Net-conditioned policy network. The CFU-MPPI controller integrates this sampler into MPPI, enabling variable-speed navigation and yielding superior performance in challenging end-to-end navigation tasks, with 4–8× more collision-free samples and robust generalization to varying velocity, time-step, and horizon. Real-world experiments on a scale robot validate the approach, achieving shorter paths at comparable success rates and maintaining real-time performance (~4 ms inference per batch). Overall, the study demonstrates that environment-aware sampling substantially improves exploration efficiency and navigation reliability in cluttered environments, with practical applicability to real-time robotic control.

Abstract

Trajectory sampling is a key component of sampling-based control mechanisms. Trajectory samplers rely on control input samplers, which generate control inputs u from a distribution p(u | x) where x is the current state. We introduce the notion of Free Configuration Space Uniformity (C-Free-Uniform for short) which has two key features: (i) it generates a control input distribution so as to uniformly sample the free configuration space, and (ii) in contrast to previously introduced trajectory sampling mechanisms where the distribution p(u | x) is independent of the environment, C-Free-Uniform is explicitly conditioned on the current local map. Next, we integrate this sampler into a new Model Predictive Path Integral (MPPI) Controller, CFU-MPPI. Experiments show that CFU-MPPI outperforms existing methods in terms of success rate in challenging navigation tasks in cluttered polygonal environments while requiring a much smaller sampling budget.

Figures (4)

• Figure 1: Comparison of trajectory sampling distributions (512 samples per method) in a cluttered environment, with obstacles in black, collision-free/colliding trajectories in blue/gray, the goal marked by a star, and the selected path in dashed orange. MPPI and Log-MPPI get stuck in a local minimum. While both C-Uniform and C-Free-Uniform find a solution, C-Free-Uniform shows a better path quality.
• Figure 2: The C-Free-Uniform System Architecture. The input is the robot's initial state and a signed distance function (SDF) representation of the environment. A U-Net extracts a dense feature map from the environment, which is used to condition a policy network inside an iterative planning loop. After training, the network outputs a control input probability distribution $p(u|x)$ which can be sampled to obtain uniform trajectories across the free space. In the diagram, blue components are neural networks, green are data representations, and orange are processing operations.
• Figure 3: Global map conversion to local perception map visualization. The complete map is shown on the left, and the extracted local map is shown on the right.
• Figure 4: The physical experiment setup. The robot navigated from a start position (bottom left) to a goal (top right) through a constrained environment requiring a severe S-turn. A foam pad on the ground is placed to generate perturbations.