A visual feedback-based time-optimal motion policy for capturing an unpredictable evader

In this paper, we address the pursuit–evasion problem of capturing an unpredictable omnidirectional evader using a differential drive robot (DDR) in an obstacle-free environment. We present three main contributions. (1) We provide a state feedback-based time-optimal motion policy for the DDR. The motion policy is based on a partition of the state space. One main contribution of this paper is to provide algebraic equations of the regions’ boundaries of this partition in terms of the state-space coordinates. (2) We estimate the state of the evader based on images using the one-dimensional trifocal tensor. We propose a new formulation of the estimation of the evader's state relative to the pursuer. (3) We present a bound, for conventional cameras, over the pursuer's field of view that guarantees that, if the evader is initially visible, it will remain visible (inside the camera's view) regardless of its motion strategy, until the capture condition is achieved. We also present an implementation of the pursuer's motion policy, the estimation of the evader's state and also present simulation results of the pursuit/evasion game.