The Constructing UAV Trajectories Method Using Bezier Curves and Pythagorean Hodograph

Abstract

In the proposed work, an algorithm for constructing the smooth trajectory of one UAV in a three-dimensional space is developed. To construct and approximate the trajectory, the extended Bernstein polynomials with the Pythagorean hodograph are used. The provided method uses an RRT∗ algorithm for path generation, and spatial Bezier curves for further trajectory smoothing. The proposed method makes UAVs apply less energy after calling the replanning procedure which is necessary for obstacle avoidance. Here we provide a quaternion representation of the Bernstein-basis Pythagorean-Hodograph curves and the proposed algorithm. We introduce simulation data that shows the pure RRT∗ path and the final approximated trajectory in the environment with obstacles.