Time-Synchronized B-Spline Path Planning for Multi-Agent UAV Systems with Fixed Speed Profiles

Most UAV path planning methods assume that speed is constant or controllable within certain constraints. However, some applications require UAVs to follow predefined speed profiles. This paper proposes a novel offline path planning algorithm for multi-agent UAV systems with fixed speed profiles that facilitates scheduled arrivals at desired final states in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{R}^{2}$</tex> space using uniform B-splines. The B-splines are parameterized by a path variable to decouple the path geometry from the speed profile, and a path extension algorithm is introduced for timely arrival. We present the path planning methods and demonstrate their effectiveness through Monte Carlo simulations of a formation control example. Results show that the proposed algorithm consistently ensures simultaneous arrival within 0.2 seconds in all cases, with an average deviation of only 0.07 seconds, regardless of initial conditions. This approach offers an effective solution for coordinated UAV missions with fixed speed profiles.