Direct collocation for two dimensional motion camouflage with non-holonomic, velocity and acceleration constraints

Motion camouflage is a stealth behaviour observed in hover-flies and dragonflies, where a shadower (predator) moves in the presence of a shadowee (prey) while appearing stationary for the later at a fix point, called focal point. This paper presents a new way of obtaining motion camouflage trajectories for unicycle motion models assuming a known trajectory of the shadowee, when the velocities and accelerations of the shadower have to be bounded. Even though there are multiple solutions for a given configuration, the problem is highly challenging since the camouflage trajectories form a very small subset of all the interception trajectories. We use the angular deviation between the shadower and the focal point, as view by the shadowee, to define cost functional to minimise. Simulation results show that when the desired interception time is too short, the target can be reached but the camouflage quality is degraded. We also show through simulations that an increase in the maximum allowed velocity of the shadower produces longer trajectories, but with a better camouflage quality. This method is suitable for implementation in non-holonomic real robots.