Operation of microrobots in swarms is a crucial challenge facing their translation to real-world applications. Without integrated electronics for sensing and actuation, current microrobotic systems should rely on physical interactions among individual microrobots for local communication and cooperation. In this project, we are developing a design approach for programming collective behavior in mobile microrobotic swarms by controlling magnetic interactions between individual units. Collective order and stability results from imposed interactions, which enables parallel operation of microrobotic swarms over macroscale distances and through confining obstacles. The proposed approach will enable other researchers to design a wide range of novel interaction strategies for guiding collective behavior in microrobotic and active matter systems under external fields.