Coverage patterns generated by two unicycles pursuing each other

This paper studies the trajectory of a pair of unicycles pursuing each other. The control law depends only on the distance between them. The resulting paths trace hypotrochoidal patterns. These patterns are suitable for coverage path planning and can be utilized in surveillance, patrolling, demining, and similar applications. We find the conditions under which unicycles generate the patterns. We also design the controller gain that ensures the patterns cover a region with a specified maximum and minimum radius. The results are validated in simulations.