# Using Uncertainty Data in Chance-Constrained Trajectory Planning

## TL;DR

This paper presents a method for trajectory planning under obstacle location uncertainty, learning distribution moments online and providing high-confidence feasible solutions through a convex reformulation.

## Contribution

It introduces a novel approach that learns distribution moments online and derives tight bounds for trajectory planning with uncertain obstacle locations.

## Key findings

- Provides a convex reformulation of the planning problem
- Achieves high-confidence feasible trajectories in autonomous driving case study
- Derives tight concentration bounds on moment estimation errors

## Abstract

We consider the problem of trajectory planning in an environment comprised of a set of obstacles with uncertain locations. While previous approaches model the uncertainties with a prescribed Gaussian distribution, we consider the realistic case in which the distribution's moments are unknown and are learned online. We derive tight concentration bounds on the error of the estimated moments. These bounds are then used to derive a tractable and tight mixed-integer convex reformulation of the trajectory planning problem, assuming linear dynamics and polyhedral constraints. The solution of the resulting optimization program is a feasible solution for the original problem with high confidence. We illustrate the approach with a case study from autonomous driving.