# Monte Carlo Motion Planning for Robot Trajectory Optimization Under Uncertainty

arXiv: https://arxiv.org/abs/1504.08053 · HTML: https://mlsanity.com/paper/1504.08053/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2015.

## Built on by (most cited first, 12 of 12)

- [Reinforced Refinement with Self-Aware Expansion for End-to-End Autonomous Driving](https://mlsanity.com/paper/2506.09800/) (2025)
- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [ComTraQ-MPC: Meta-Trained DQN-MPC Integration for Trajectory Tracking with Limited Active Localization Updates](https://mlsanity.com/paper/2403.01564/) (2024)
- [Exact and Bounded Collision Probability for Motion Planning under Gaussian Uncertainty](https://mlsanity.com/paper/2110.06348/) (2021)
- [Safe motion planning with environment uncertainty](https://mlsanity.com/paper/2305.06004/) (2023)
- [An Integrated Localisation, Motion Planning and Obstacle Avoidance Algorithm in Belief Space](https://mlsanity.com/paper/2101.11566/) (2021)
- [Learning Provably Robust Motion Planners Using Funnel Libraries](https://mlsanity.com/paper/2111.08733/) (2021)
- [Learned Risk Metric Maps for Kinodynamic Systems](https://mlsanity.com/paper/2302.14803/) (2023)
- [Real-Time Tube-Based Non-Gaussian Risk Bounded Motion Planning for Stochastic Nonlinear Systems in Uncertain Environments via Motion Primitives](https://mlsanity.com/paper/2303.01631/) (2023)
- [IBBT: Informed Batch Belief Trees for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2304.10984/) (2023)
- [Convex Risk Bounded Continuous-Time Trajectory Planning and Tube Design in Uncertain Nonconvex Environments](https://mlsanity.com/paper/2305.17291/) (2023)
- [Risk-aware Integrated Task and Motion Planning for Versatile Snake Robots under Localization Failures](https://mlsanity.com/paper/2502.19690/) (2025)

## Abstract (arXiv)

This article presents a novel approach, named MCMP (Monte Carlo Motion Planning), to the problem of motion planning under uncertainty, i.e., to the problem of computing a low-cost path that fulfills probabilistic collision avoidance constraints. MCMP estimates the collision probability (CP) of a given path by sampling via Monte Carlo the execution of a reference tracking controller (in this paper we consider LQG). The key algorithmic contribution of this paper is the design of statistical variance-reduction techniques, namely control variates and importance sampling, to make such a sampling procedure amenable to real-time implementation. MCMP applies this CP estimation procedure to motion planning by iteratively (i) computing an (approximately) optimal path for the deterministic version of the problem (here, using the FMT* algorithm), (ii) computing the CP of this path, and (iii) inflating or deflating the obstacles by a common factor depending on whether the CP is higher or lower than a target value. The advantages of MCMP are threefold: (i) asymptotic correctness of CP estimation, as opposed to most current approximations, which, as shown in this paper, can be off by large multiples and hinder the computation of feasible plans; (ii) speed and parallelizability, and (iii) generality, i.e., the approach is applicable to virtually any planning problem provided that a path tracking controller and a notion of distance to obstacles in the configuration space are available. Numerical results illustrate the correctness (in terms of feasibility), efficiency (in terms of path cost), and computational speed of MCMP.