Optimal evasive strategies for groups of interacting agents with motion constraints

Abstract

In this thesis we examine systems of pursuit and evasion with multiple evaders from several perspectives. Through the analysis of mathematical models and the study of field experiments we seek to understand how constraints on individual motion and sensing abilities affect outcomes on the level of the group and the individual.

We present a nonlinear model of pursuit and evasion on the plane for a single pursuer and two evaders. Control laws are defined so that each evader trades off between evasion and herding. We analyze the system dynamics in terms of relative shape variables and derive conditions on the control parameters and initial conditions that determine whether capture occurs.

We consider a system where evaders have heterogeneous limits on speed, turning rate, and lateral acceleration, versus a single pursuer with limited speed but no turning constraints. Optimal strategies are derived for the one-on-one differential game, and these form the basis of strategies for the multiple-evader system. Explicit analytic expressions for open-loop and state-feedback forms of optimal controls are derived in a related minimum-time problem for a single agent with the evader's motion constraints. For the multiple evader system, we propose a pursuer strategy of optimal target selection which leads to capture in bounded time and we prove how any evader not initially targeted can avoid capture with a "reactive evasion" strategy. We consider optimal strategies for agents with radius-limited sensing capabilities. In the case that evader turning rate is unbounded, we prove conditions for evader capture avoidance through a local strategy of "risk reduction," which we show leads to group aggregation.

We present some preliminary results from a field experiment conducted at the Ol Pejeta Conservancy in Laikipia, Kenya in July 2014 to study evasive behaviors in herds of plains zebra under pursuit by an artificial predator, the ``robo-lion.'' Through manual tracking of video from an overhead camera we extract quantitative trajectory data for each zebra in the herd and for the robo-lion. The observed zebra behaviors of efficient evasion and group alignment serve to motivate our modeling efforts.