Fast fixed-time three-dimensional terminal guidance with non-concave trajectory constraint

Focusing on the non-concave trajectory constraint, a sliding-mode-based nonsingular feedback fast fixed-time three-dimensional terminal guidance of rotor unmanned aerial vehicle landing, planetary landing and spacecraft rendezvous and docking terminal phase with external disturbance is investigated in this paper. Firstly, a fixed-time observer based on real-time differentiator is developed to compensate for the external disturbance, whose estimation error can converge to zero after a time independent of the initial state. Then, a sliding surface ensuring fixed-time convergence is presented. This sliding surface can guarantee that the vehicle achieves a non-concave trajectory, which is better for avoiding collision and maintaining the visibility of the landing site or docking port. Next, the nonsingular guidance ensuring the fixed-time convergence of the sliding surface is proposed, which is continuous and chatter free. At last, three numerical simulations of Mars landing are performed to validate the effectiveness and correctness of the designed scheme.