# Scenario-Based Trajectory Optimization in Uncertain Dynamic Environments

arXiv: https://arxiv.org/abs/2103.12517 · HTML: https://mlsanity.com/paper/2103.12517/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [Active Uncertainty Reduction for Human-Robot Interaction: An Implicit Dual Control Approach](https://mlsanity.com/paper/2202.07720/) (2022)
- [Predictive Control for Autonomous Driving with Uncertain, Multi-modal Predictions](https://mlsanity.com/paper/2310.20561/) (2023)
- [Unified Generation-Refinement Planning: Bridging Guided Flow Matching and Sampling-Based MPC for Social Navigation](https://mlsanity.com/paper/2508.01192/) (2025)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)
- [Learning-Based Motion Planning for Dynamic Environments: From Foundational Algorithms to Emerging Paradigms](https://mlsanity.com/paper/2608.00625/) (2026)
- [Multi-Agent Deferred-Decision Trajectory Optimization with Anytime-Valid Target Retention for Moving Candidates](https://mlsanity.com/paper/2610.17003/) (2026)

## Abstract (arXiv)

We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by incorporating chance constraints into the planning problem. This problem is not suitable for online optimization outright for arbitrary probability distributions. Hence, we sample from these chance constraints using an uncertainty model, to generate "scenarios", which translate the probabilistic constraints into deterministic ones. In practice, each scenario represents the collision constraint for a dynamic obstacle at the location of the sample. The number of theoretically required scenarios can be very large. Nevertheless, by exploiting the geometry of the workspace, we show how to prune most scenarios before optimization and we demonstrate how the reduced scenarios can still provide probabilistic guarantees on the safety of the motion plan. Since our approach is scenario based, we are able to handle arbitrary uncertainty distributions. We apply our method in a Model Predictive Contouring Control framework and demonstrate its benefits in simulations and experiments with a moving robot platform navigating among pedestrians, running in real-time.