Abstract We address problems underlying the algorithmic question of automating the co-design of robot hardware in tandem with its apposite software. Specifically, we consider the impact that degradations of a robot's sensor and actuation suites may have on the ability of that robot to complete its tasks. Expanding upon prior work that addresses similar questions in the context of filtering, we introduce a new formal structure that generalizes and consolidates a variety of well known structures including many forms of plans, planning problems, and filters, into a single data structure called a procrustean graph. We describe a collection of operations on procrustean graphs (both semantics-preserving and semantics-mutating), and show how a family of questions about the destructiveness of a change to the robot hardware can be answered by applying these operations. We also highlight the strong connections between this new approach and existing threads of research, including combinatorial filtering, Erdmann's strategy complexes, and hybrid automata.