Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

Abstract

Pursuit-evasion games have been used for modeling various forms of conflict arising between two agents modeled as dynamical systems. Although analytical solutions of some simple pursuit-evasion games are known, most interesting instances can only be solved using numerical methods requiring significant offline computation. In this paper, a novel incremental sampling-based algorithm is presented to compute optimal open-loop solutions for the evader, assuming worst-case behavior for the pursuer. It is shown that the algorithm has probabilistic completeness and soundness guarantees. As opposed to many other numerical methods tailored to solve pursuit-evasion games, incremental sampling-based algorithms offer anytime properties, which allow their real-time implementations in online settings.

Robust Sampling-based Motion Planning with Asymptotic Optimality Guarantees

“…28 Additional simulation and hardware results will be explored for more complex scenarios and dynamics, including nonholonomic vehicles; 29 dynamic obstacles, including pursuit-evasion scenarios; 30 and dynamic realtime operations.…”

“…Since P xt can be computed off-line, the tightened constraints (25), (30) can be computed off-line, implying that the complexity of the nominal formulation need not increase when chance constraints are incorporated. In a similar manner as in Blackmore et al, 2 probabilistic feasibility of any state or state sequence can be checked via these tightened, deterministic constraints.…”

Pursuit-evasion games: a tractable framework for antijamming games in aerial attacks

“…We also solve the pursuit-evasion game-without taking into account the communications capacity-and we show that both problems have very similar solutions. Hence, we show that it is possible, under certain circumstances, to approximate the hard capacity problem by an easier pursuit-evasion game, which could be solved either analytically-as we do-or using numerical methods, as in [9].…”

“…(5), and the third point is the adjoint equation which Isaacs includes in Eq. (9). Pontryagin uses costate functions, that he calls (t), which can be identified with the gradient of the value function ∇V that Isaacs uses.…”

Multi-robot target detection and tracking: taxonomy and survey

“…Facing this complexity, Karaman and Frazzoli propose an incremental sampling based algorithm for the evader strategy, using on numerical methods instead of analytical ones (Karaman and Frazzoli, 2011). Indeed, "although analytical solutions of some simple pursuit-evasion games are known, most interesting instances can only be solved using numerical methods requiring significant off-line computation."…”