Speed-Varying Minimum Time Rendezvous with Moving Goal

A minimum-time intercept path from a kinematic vehicle to a moving maneuvering target may be solved as a scalar root-finding problem, which is conducive to real-time implementation. Motivated by the advent of automated aerial refueling, we extend these methods to incorporate a variable speed into the problem definition to compute a rendezvous path for a kinematic vehicle (the receiver) to a moving maneuvering goal state (the tanker). We vary the receiver speed with piecewise constant acceleration commands which maximize the receiver’s speed without interfering with the turn radius constraint used to compute the Dubins path. We also develop a feedback guidance law for the receiver with theoretical guarantees that the receiver reaches the end of its path with the correct speed at the expected final time. Through simulation in a constant wind field and with first-order autopilot dynamics, the efficacy of the feedback law is demonstrated. The reference path generation and tracking algorithm is thereby shown to be useful for the application of minimum time rendezvous.