This article examines the problems of multi-robot coverage and persistent monitoring of regions of interest with limited sensing robots. A group of robots, each equipped with only contact sensors and a clock, execute a simple trajectory by repeatedly moving straight and then bouncing at perimeter boundaries by rotating in place. We introduce an approach by finding a joint trajectory for multiple robots to cover a given environment and generating cycles for the robots to persistently monitor the target regions in the environment. From a given initial configuration, our approach iteratively finds the joint trajectory of all the robots that covers the entire environment. Our approach also computes periodic trajectories of all the robots for monitoring of some regions, where trajectories overlap but do not involve robot-robot collisions. We present experimental results from multiple simulations and physical experiments demonstrating the practical utility of our approach.