While there has been significant progress in expanding the capabilities of multi-agent systems a key challenge is developing controllers and motion planners for robotic systems severely constrained by limited computational, sensing, and memory resources. These robots must operate with minimal environmental information and onboard resources, complicating the provision of theoretical guarantees for their collective behavior. This situation poses several interesting questions: given a task, how minimal can a robot’s abilities be to guarantee the desired behavior while ensuring safety and robustness? Is it possible to design a framework that adjusts to a robot’s constraints, such as memory or sensory limitations, in line with task demands? Moreover, what quantifiable trade-offs emerge when balancing onboard capabilities with the control design for minimal robots? In this dissertation, I explore these questions, focusing on providing theoretical guarantees to ensure the globally desired behavior of the collective. I show how we can design reactive controllers that are provably correct, utilizing only simple sensory inputs to form an environmental understanding. This approach is focused on multi-robotic tasks such as target search and encapsulation in unknown, unstructured, and dynamic environments. I provide quantifiable trade-offs between task objectives, system constraints, and control design parameters, paving the way for scalable, distributed robotic systems where traditional sensing and processing methods fall short.