Three-Dimensional Enclosing Guidance Law with Entry Time Constraint

This paper proposes a three-dimensional entry time-constrained enclosing guidance law that enables an unmanned aerial vehicle (UAV) to enter a desired orbit at a prescribed time and subsequently maintain stable encircling flight. The enclosing guidance law comprises two distinct commands: the radius-convergence time-constrained encircling guidance (RCTCEG) command and the arrival time-constrained plane pursuit guidance (ATCPPG) command. The RCTCEG and ATCPPG commands are, respectively, designed to control the UAV to make the relative distance converge to a desired radius and to reach a specified circling plane at prescribed times. Consequently, the entry time can be regulated by coordinating the prescribed radius-convergence and plane-arrival times. Furthermore, this paper accounts for the coupling between the radius convergence and plane pursuit motions and addresses it in the command design to ensure that both the radius-convergence time and plane-arrival time can be prescribed independently. The stability of the system is theoretically proven, and various numerical simulations are conducted to demonstrate the effectiveness of the proposed method.