Time-optimal Bezier Curves for Straight-line and Circular Path Convergence 3D Space

This work constructs near-optimal continuous curvature paths for convergence to a straight line or a circular path in three-dimensional (3D) space to minimize tracking errors arising out of constraints on speed and turn radius of Unmanned Air vehicles (UAVs). It is developed in two stages: (i) determination of the optimal CSC path (Circular path of minimum turn radius (C)-Straight line path (S)-Circular path of minimum turn radius (C)) (3D Dubins path) from the initial pose to the target path, and (ii) construction of the continuous curvature path using Bezier curves with the aid of the Dubins reference path. This algorithm solves the problem of curvature discontinuity inherent with the CSC path for path convergence problems with minimal compromise in its optimal length by maintaining the maximum curvature limit. Simulation results demonstrate the efficacy of the proposed approach.