# Trajectory Replanning for Quadrotors Using Kinodynamic Search and Elastic Optimization

## TL;DR

This paper introduces a real-time kinodynamic search algorithm using B-splines for quadrotor trajectory replanning, combined with elastic optimization to refine control points, enabling efficient, feasible, and adaptable flight paths.

## Contribution

The paper presents a novel RBK search algorithm that transforms position-only shortest path search into kinodynamic planning, and an elastic optimization method for trajectory refinement, advancing real-time quadrotor replanning.

## Key findings

- The RBK search efficiently generates dynamically feasible trajectories.
- Elastic optimization improves trajectory quality within free space constraints.
- Systematic comparison shows superior performance over existing methods.

## Abstract

We focus on a replanning scenario for quadrotors where considering time efficiency, non-static initial state and dynamical feasibility is of great significance. We propose a real-time B-spline based kinodynamic (RBK) search algorithm, which transforms a position-only shortest path search (such as A* and Dijkstra) into an efficient kinodynamic search, by exploring the properties of B-spline parameterization. The RBK search is greedy and produces a dynamically feasible time-parameterized trajectory efficiently, which facilitates non-static initial state of the quadrotor. To cope with the limitation of the greedy search and the discretization induced by a grid structure, we adopt an elastic optimization (EO) approach as a post-optimization process, to refine the control point placement provided by the RBK search. The EO approach finds the optimal control point placement inside an expanded elastic tube which represents the free space, by solving a Quadratically Constrained Quadratic Programming (QCQP) problem. We design a receding horizon replanner based on the local control property of B-spline. A systematic comparison of our method against two state-of-the-art methods is provided. We integrate our replanning system with a monocular vision-based quadrotor and validate our performance onboard.