The design of multi-agent robotic systems involves tightly coupled decisions spanning heterogeneous domains, including robot design, fleet composition, and planning. Much effort has been devoted to isolated improvements in these domains, while system-level co-design considering trade-offs and task requirements remains underexplored. In this work, we present a formal and compositional framework for the task-driven co-design of heterogeneous multi-robot systems, and propose robotic phase diagrams as a qualitative design guideline. Building on monotone co-design theory, we introduce general abstractions of robots, fleets, planners, executors, and evaluators as interconnected design problems with well-defined interfaces that are agnostic to both implementations and tasks. This structure enables efficient joint optimization of robot design, fleet composition, and planning under task-specific performance constraints. A series of case studies demonstrates the capabilities of the framework. New component solutions can be seamlessly incorporated, including robot types, task profiles, and probabilistic sensing objectives, while non-obvious design alternatives are systematically uncovered with optimality guarantees. The results highlight the flexibility, scalability, and interpretability of the proposed approach, illustrate how formal co-design enables principled reasoning about complex heterogeneous multi-robot systems, and how a robotic phase diagram qualitatively guides the design.

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