Boundary following using gyroscopic control

Recent work in the study of interacting particles has demonstrated the effectiveness of gyroscopic interactions in producing desired stable spatial patterns (formations) of motion of a collective of particles. In this paper, we discuss the problem of how a single particle might interact with a fixed structure in space by exploiting gyroscopic feedback laws. We derive a gyroscopic feedback law modeling the interaction of a particle in the plane with an image particle representing the closest point on a simple closed curve bounding an obstacle and show that this law produces boundary-following behavior. We also provide a preliminary discussion of the three-dimensional case.