Pursuit problems have attracted considerable attention from biologists, mathematicians and engineers. Guidance/steering laws are essential in robotic systems. In this thesis, we first review the results on steering laws for a specific pursuit process, motion camouflage with respect to infinity. This type of guidance law renders the baseline (line connecting the pursuer and evader) parallel to a fixed line. In observations of prey pursuit trajectories of echolocating bats, it has been noted that the same geometrical condition of eventual parallelism holds.

We hypothesize that a steering law of the same form as discussed here for motion camouflage with respect to infinity, also applies to the trajectories of prey capture behavior by bats. In this thesis, we develop a method to extract curvatures for trajectories and a detailed investigation to validate this hypothesis. In the latter part of the thesis, we discuss the effect of delays on the performance of motion camouflage laws. We derive limits on the feedback gain and an upper bound on the delay that can be allowed in a pursuit evader system, to ensure successful motion camouflage.