Dijkstra algorithm based minimum acceleration/snap quadrotor UAV trajectory planning

Abstract

This paper focuses on path planning using the Dijkstra/A* algorithm and addresses the trajectory generation problem using the minimum acceleration/snap approach. Firstly, the mathematical model of the optimization problem is formulated, specifically utilizing the Euler-Lagrange equation to derive the necessary conditions for achieving minimum acceleration/snap trajectories, which are represented by either 3rd or 7th order polynomials. The coefficients of these polynomials are determined by imposing appropriate constraints on velocity, acceleration, and higher-order derivatives. Subsequently, a detailed comparison of the performances of the two optimization methods in complex environments is conducted, evaluating differences in position and velocity. Based on the deterministic analysis, conclusive results are obtained.