Heterogeneous Pursuit of Multiple Translating Targets

We address the minimum-time intercept problem for multiple mobile targets translating in a fixed direction at identical constant speeds. Each target must be intercepted by a heterogeneous pursuer assembly - a mobile vehicle carrying identical pursuers, each capable of moving faster than the vehicle. Beyond this novel formulation, our key contributions are as follows. First, we establish that the optimal intercept problem is equivalent to solving an appropriately defined Euclidean minimum Hamiltonian path through neighborhoods (EMHPN), where each neighborhood is an ellipse defined by its center and axis lengths. Second, we derive novel upper bounds on the optimal path length as a function of key parameters: number of targets, speed ratios between agents, region geometry, and interception time. Notably, our derived bounds on path length do not require prior knowledge of the targets' current exact locations. Finally, we illustrate our approach numerically and discuss potential improvements to the bounds.