Direct Vector Field Guidance for Path Following

Abstract

This paper presents a path-following guidance framework for a turn-rate-constrained unmanned aerial vehicle (UAVs). The proposed guidance strategy uses commanded course angle as a tanh-hyperbolic shaping function of the lateral deviation from the desired path. Stability characteristics illustrating asymptotic convergence to the desired path are established using Lyapunov analysis. Analytical expressions for the turn-rate and corresponding maximum turn-rate bound are derived, enabling direct gain selection for a turn-rate-limited vehicle. Numerical simulations are performed for straight-line following scenarios under both ideal and non-ideal initial heading conditions. Furthermore, a comparative study against representative arctan-, arcsine-, and arccos-based vector-field guidance laws is conducted using analytically feasible gains selected from their respective turn-rate bounds. Comparative numerical results demonstrate the proposed formulation achieves reliable boundary convergence while maintaining smooth steering behavior and a compact analytical gain-design framework.