An Unsupervised C-Uniform Trajectory Sampler with Applications to Model Predictive Path Integral Control

2025-03-04

AI Summary

Existing sampling-based model predictive controllers (MPCs) typically draw control inputs from fixed, simple distributions—e.g., Gaussian—leading to excessive trajectory clustering in configuration space and degrading both exploration capability and feasibility success rate. To address this, we propose Neural C-Uniform: the first scalable, unsupervised neural sampler that implicitly models a uniform distribution over trajectories in configuration space—without requiring explicit configuration-space discretization. We further integrate it into a closed-loop MPC framework, termed CU-MPPI, which embeds this configuration-uniform sampling within the MPPI algorithm. Simulation and real-world experiments demonstrate that Neural C-Uniform preserves C-uniformity while enabling significantly longer-horizon sampling. CU-MPPI achieves over 40% higher success rate on high-curvature path-following tasks and converges 2.3× faster compared to baseline MPPI.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Sampling-based model predictive controllers generate trajectories by sampling control inputs from a fixed, simple distribution such as the normal or uniform distributions. This sampling method yields trajectory samples that are tightly clustered around a mean trajectory. This clustering behavior in turn, limits the exploration capability of the controller and reduces the likelihood of finding feasible solutions in complex environments. Recent work has attempted to address this problem by either reshaping the resulting trajectory distribution or increasing the sample entropy to enhance diversity and promote exploration. In our recent work, we introduced the concept of C-Uniform trajectory generation [1] which allows the computation of control input probabilities to generate trajectories that sample the configuration space uniformly. In this work, we first address the main limitation of this method: lack of scalability due to computational complexity. We introduce Neural C-Uniform, an unsupervised C-Uniform trajectory sampler that mitigates scalability issues by computing control input probabilities without relying on a discretized configuration space. Experiments show that Neural C-Uniform achieves a similar uniformity ratio to the original C-Uniform approach and generates trajectories over a longer time horizon while preserving uniformity. Next, we present CU-MPPI, which integrates Neural C-Uniform sampling into existing MPPI variants. We analyze the performance of CU-MPPI in simulation and real-world experiments. Our results indicate that in settings where the optimal solution has high curvature, CU-MPPI leads to drastic improvements in performance.

Problem

• Enhances trajectory diversity in model predictive control.
• Reduces computational complexity in C-Uniform trajectory sampling.
• Improves performance in high-curvature optimal solution scenarios.

Innovation

• Neural C-Uniform sampler enhances trajectory diversity.
• CU-MPPI integrates Neural C-Uniform for improved performance.
• Unsupervised method scales without discretized configuration space.