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

TL;DR

This paper introduces Density Planner, a novel density-based approach using neural networks and the Liouville equation to minimize collision risk in motion planning under uncertainty, achieving faster online planning times.

Contribution

It presents a new density evolution method for uncertain systems, enabling feasible and safe trajectory planning with significantly reduced online computation.

Findings

Outperforms baseline methods like MPC and nonlinear programming.

Achieves 100 times faster online planning than MPC.

Effective in simulated and real-world environments.

Abstract

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.