# Density Planner: Minimizing Collision Risk in Motion Planning with Dynamic Obstacles using Density-based Reachability

arXiv: https://arxiv.org/abs/2210.02131 · HTML: https://mlsanity.com/paper/2210.02131/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2022.

## Built on by (most cited first, 2 of 2)

- [Hi-Drive: Hierarchical POMDP Planning for Safe Autonomous Driving in Diverse Urban Environments](https://mlsanity.com/paper/2409.18411/) (2024)
- [Dynamic Risk Assessment for Autonomous Vehicles from Spatio-Temporal Probabilistic Occupancy Heatmaps](https://mlsanity.com/paper/2501.16480/) (2025)

## Abstract (arXiv)

Uncertainty is prevalent in robotics. Due to measurement noise and complex dynamics, we cannot estimate the exact system and environment state. Since conservative motion planners are not guaranteed to find a safe control strategy in a crowded, uncertain environment, we propose a density-based method. Our approach uses a neural network and the Liouville equation to learn the density evolution for a system with an uncertain initial state. We can plan for feasible and probably safe trajectories by applying a gradient-based optimization procedure to minimize the collision risk. We conduct motion planning experiments on simulated environments and environments generated from real-world data and outperform baseline methods such as model predictive control and nonlinear programming. While our method requires offline planning, the online run time is 100 times smaller compared to model predictive control.