# Scenario-Based Motion Planning with Bounded Probability of Collision

arXiv: https://arxiv.org/abs/2307.01070 · HTML: https://mlsanity.com/paper/2307.01070/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2023.

## Built on by (most cited first, 7 of 7)

- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Generalizing Multi-Objective Search via Objective-Aggregation Functions](https://mlsanity.com/paper/2509.22085/) (2025)
- [TRANS: Terrain-aware Reinforcement Learning for Agile Navigation of Quadruped Robots under Social Interactions](https://mlsanity.com/paper/2602.12724/) (2026)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)
- [XR-DT: Extended Reality-Enhanced Digital Twin for Safe Motion Planning via Human-Aware Model Predictive Path Integral Control](https://mlsanity.com/paper/2512.05270/) (2025)
- [MoMo: Conditioned Contrastive Representation Learning for Preference-Modulated Planning](https://mlsanity.com/paper/2605.08512/) (2026)
- [Dijkstra as an Oracle for Online Stochastic Shortest Path Navigation with Provable Guarantees](https://mlsanity.com/paper/2608.17703/) (2026)

## Abstract (arXiv)

Robots will increasingly operate near humans that introduce uncertainties in the motion planning problem due to their complex nature. Typically, chance constraints are introduced in the planner to optimize performance while guaranteeing probabilistic safety. However, existing methods do not consider the actual probability of collision for the planned trajectory, but rather its marginalization, that is, the independent collision probabilities for each planning step and/or dynamic obstacle, resulting in conservative trajectories. To address this issue, we introduce a novel real-time capable method termed Safe Horizon MPC, that explicitly constrains the joint probability of collision with all obstacles over the duration of the motion plan. This is achieved by reformulating the chance-constrained planning problem using scenario optimization and predictive control. Our method is less conservative than state-of-the-art approaches, applicable to arbitrary probability distributions of the obstacles' trajectories, computationally tractable and scalable. We demonstrate our proposed approach using a mobile robot and an autonomous vehicle in an environment shared with humans.