Visibility-Based Pursuit-Evasion in an Unknown Planar Environment

Abstract

We address an on-line version of the visibility-based pursuit-evasion problem. We take a minimalist approach in modeling the capabilities of a pursuer robot. A point pursuer moves in an unknown, simplyconnected, piecewise-smooth planar environment, and is given the task of locating any unpredictable, moving evaders that have unbounded speed. The evaders are assumed to be points that move continuously. To solve the problem, the pursuer must for each target have an unobstructed view of it at some time during execution. The pursuer is equipped with a range sensor that measures the direction of depth discontinuities, but cannot provide precise depth measurements. All pursuer control is specified either in terms of this sensor or wall-following movements. The pursuer does not have localization capability or perfect control. We present a complete algorithm that enables the limited pursuer to clear the same environments that a pursuer with a complete map, perfect localization, and perfect control can clear (under certain general position assumptions). Theoretical guarantees that the evaders will be found are provided. The resulting algorithm to compute this strategy has been implemented in simulation. Results are shown for several examples. The approach is efficient and simple enough to be useful towards the development of real robot systems that perform visual searching.

Gap Navigation Trees: Minimal Representation for Visibility-based Tasks

“…In terms of visual events, an strategy should dictate the sequence of inflection rays and bitangent complements to cross in order to clear the whole environment. In [29] a strategy is presented that explicitly avoids some visual events of being triggered to clear an unknown environment. The order of how the visual events should occur also dictates the structure of the "T", "S" and "Z" patterns in [15], in which a 6-state automaton restricted to move along the environment boundary serves as a pursuer.…”

Multiagent Pursuit Evasion, or Playing Kabaddi

“…This is indeed the case in all graph searching [2,11,14] or visibility based pursuit evasion [5,7,15]. In the lion-and-the-man game also there are known results that show that multiple lions can capture the man when the man lies inside the convex hull of the lions [10].…”

Probabilistic Graph-Clear

“…, ∞} [13], [8]. Sachs et al present in [12] an online algorithm to solve the visibility-based pursuit-evasion problem for a point pursuer moving in an unknown, simply-connected, piecewise-smooth planar environment. The pursuer is assumed to be equipped only with a sensor that measures depth-discontinuities, and can perform only wall-following or a movements along the perceived depth-discontinuities.…”