# Chance Constrained Motion Planning for High-Dimensional Robots

arXiv: https://arxiv.org/abs/1811.03073 · HTML: https://mlsanity.com/paper/1811.03073/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2018.

## Built on by (most cited first, 5 of 5)

- [Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing](https://mlsanity.com/paper/2508.12166/) (2025)
- [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)
- [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)
- [MoMo: Conditioned Contrastive Representation Learning for Preference-Modulated Planning](https://mlsanity.com/paper/2605.08512/) (2026)

## Abstract (arXiv)

This paper introduces Probabilistic Chekov (p-Chekov), a chance-constrained motion planning system that can be applied to high degree-of-freedom (DOF) robots under motion uncertainty and imperfect state information. Given process and observation noise models, it can find feasible trajectories which satisfy a user-specified bound over the probability of collision. Leveraging our previous work in deterministic motion planning which integrated trajectory optimization into a sparse roadmap framework, p-Chekov shows superiority in its planning speed for high-dimensional tasks. P-Chekov incorporates a linear-quadratic Gaussian motion planning approach into the estimation of the robot state probability distribution, applies quadrature theories to waypoint collision risk estimation, and adapts risk allocation approaches to assign allowable probabilities of failure among waypoints. Unlike other existing risk-aware planners, p-Chekov can be applied to high-DOF robotic planning tasks without the convexification of the environment. The experiment results in this paper show that this p-Chekov system can effectively reduce collision risk and satisfy user-specified chance constraints in typical real-world planning scenarios for high-DOF robots.