Multi-agent pursuit-evasion games can be used to model a variety of different real world problems including surveillance, search-and-rescue, and defense-related scenarios. However, many pursuit-evasion problems are computationally difficult, which can be problematic for domains with complex geometry or large numbers of agents. To compound matters further, practical applications often require planning methods to operate under high levels of uncertainty or meet strict running-time requirements. These challenges strongly suggest that heuristic methods are needed to address pursuit-evasion problems in the real world.

In this dissertation I present heuristic planning techniques for three related problem domains: visibility-based pursuit-evasion, target following with differential motion constraints, and distributed asset guarding with unmanned sea-surface vehicles. For these domains, I demonstrate that heuristic techniques based on problem relaxation and model-predictive simulation can be used to efficiently perform low-level control action selection, motion goal selection, and high-level task allocation.

In particular, I introduce a polynomial-time algorithm for control action selection in visibility-based pursuit-evasion games, where a team of pursuers must minimize uncertainty about the location of an evader. The algorithm uses problem relaxation to estimate future states of the game. I also show how to incorporate a probabilistic opponent model learned from interaction traces of prior games into the algorithm. I verify experimentally that by performing Monte Carlo sampling over the learned model to estimate the location of the evader, the algorithm performs better than existing planning approaches based on worst-case analysis.

Next, I introduce an algorithm for motion goal selection in pursuit-evasion scenarios with unmanned boats. I show how a probabilistic model accounting for differential motion constraints can be used to project the future positions of the target boat. Motion goals for the pursuer boat can then be selected based on those projections. I verify experimentally that motion goals selected with this technique are better optimized for travel time and proximity to the target boat when compared to motion goals selected based on the current position of the target boat.

Finally, I introduce a task-allocation technique for a team of unmanned sea-surface vehicles (USVs) responsible for guarding a high-valued asset. The team of USVs must intercept and block a set of hostile intruder boats before they reach the asset. The algorithm uses model-predictive simulation to estimate the value of high-level task assignments, which are then realized by a set of learned low-level behaviors. I show experimentally that using model-predictive simulations based on Monte-Carlo sampling is more effective than hand-coded evaluation heuristics.