Uncertainty Guided Exploratory Trajectory Optimization for Sampling-Based Model Predictive Control

2026-04-13

AI Summary

Sampling-based trajectory optimization is highly sensitive to initial solutions and exhibits limited exploration capability in complex environments, often converging to suboptimal local minima. To address this, this work proposes the UGE-TO algorithm, which, for the first time, explicitly models trajectory uncertainty in configuration space as a probability distribution induced by uncertainty ellipsoids. By incorporating the effects of system dynamics and action selection, the method enforces distributional separation via the Hellinger distance to generate diverse trajectory samples. Integrated into a model predictive control framework as UGE-MPC, the approach achieves a 72.1% faster convergence rate in obstacle-free environments and, in cluttered settings, converges 66% faster with a 6.7% higher success rate under the same sampling budget. Both simulation and real-world experiments validate its superior performance.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Trajectory optimization depends heavily on initialization. In particular, sampling-based approaches are highly sensitive to initial solutions, and limited exploration frequently leads them to converge to local minima in complex environments. We present Uncertainty Guided Exploratory Trajectory Optimization (UGE-TO), a trajectory optimization algorithm that generates well-separated samples to achieve a better coverage of the configuration space. UGE-TO represents trajectories as probability distributions induced by uncertainty ellipsoids. Unlike sampling-based approaches that explore only in the action space, this representation captures the effects of both system dynamics and action selection. By incorporating the impact of dynamics, in addition to the action space, into our distributions, our method enhances trajectory diversity by enforcing distributional separation via the Hellinger distance between them. It enables a systematic exploration of the configuration space and improves robustness against local minima. Further, we present UGE-MPC, which integrates UGE-TO into sampling-based model predictive controller methods. Experiments demonstrate that UGE-MPC achieves higher exploration and faster convergence in trajectory optimization compared to baselines under the same sampling budget, achieving 72.1% faster convergence in obstacle-free environments and 66% faster convergence with a 6.7% higher success rate in the cluttered environment compared to the best-performing baseline. Additionally, we validate the approach through a range of simulation scenarios and real-world experiments. Our results indicate that UGE-MPC has higher success rates and faster convergence, especially in environments that demand significant deviations from nominal trajectories to avoid failures. The project and code are available at https://ogpoyrazoglu.github.io/cuniform_sampling/.

Problem

• trajectory optimization
• sampling-based MPC
• local minima
• exploration
• initialization sensitivity

Innovation

• Uncertainty-guided exploration
• Trajectory optimization
• Sampling-based MPC
• Distributional separation
• Hellinger distance