Abstract-For a given robot and a given task, this paper addresses questions about which modifications may be made to the robot's suite of sensors without impacting the robot's behavior in completing its task. Though this is an important design-time question, few principled methods exist for providing a definitive answer in general. Utilizing and extending the language of combinatorial filters, this paper aims to fill that lacuna by introducing theoretical tools for reasoning about sensors and representations of sensors. It introduces new representations for sensors and filters, exploring the relationship between those elements and the specific information needed to perform a task. It then shows how these tools can be used to algorithmically answer questions about changes to a robot's sensor suite. The paper substantially expands the expressiveness of combinatorial filters so that, where they were previously limited to quite simple sensors, our richer filters are able to reasonably model a much broader variety of real devices. We have implemented the proposed algorithms, and describe their application to an example instance involving a series of simplifications to the sensors of a specific, widely deployed mobile robot.

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. 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, and give these graph structures semantics in terms of ideas based in formal language theory. 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 connections between this new approach and existing threads of research, including combinatorial filtering, Erdmann's strategy complexes, and hybrid automata.

Recent research in algorithmic robotics considers combinatorial filters, which concisely capture the discrete structure underlying many reasoning problems for robots. An important recent result is that the filter minimization problem-Given a filter, find the smallest equivalent filter-is NP-hard. This paper extends that result along several dimensions, including hardness proofs for some natural special cases and for approximation, and new results analyzing the only known algorithm for this problem. We show that this problem is not fixedparameter tractable for any of the obvious parameters, but it is fixed-parameter tractable for a certain combination of new parameters.

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