# Real-time Trajectory Generation for Quadrotors using B-spline based Non-uniform Kinodynamic Search

## TL;DR

This paper introduces a fast, safe, and smooth trajectory planning method for quadrotors in cluttered environments using B-spline representation and a novel non-uniform kinodynamic search, enabling online replanning.

## Contribution

It presents a new non-uniform kinodynamic search strategy combined with B-spline control point graph-search for efficient, feasible trajectory generation in complex environments.

## Key findings

- Outperforms state-of-the-art methods in simulation and hardware tests.
- Ensures dynamical feasibility through B-spline convex hull property.
- Supports online local and global replanning with dynamic initial and goal states.

## Abstract

In this paper, we propose a time-efficient approach to generate safe, smooth and dynamically feasible trajectories for quadrotors in obstacle-cluttered environment. By using the uniform B-spline to represent trajectories, we transform the trajectory planning to a graph-search problem of B-spline control points in discretized space. Highly strict convex hull property of B-spline is derived to guarantee the dynamical feasibility of the entire trajectory. A novel non-uniform kinodynamic search strategy is adopted, and the step length is dynamically adjusted during the search process according to the Euclidean signed distance field (ESDF), making the trajectory achieve reasonable time-allocation and be away from obstacles. Non-static initial and goal states are allowed, therefore it can be used for online local replanning as well as global planning. Extensive simulation and hardware experiments show that our method achieves higher performance comparing with the state-of-the-art method.