This article examines the selection of a robot’s actuation and sensing hardware to minimize the cost of that design while ensuring that the robot is capable of carrying out a plan to complete a task. Its primary contribution is in the study of the hardness of reasonable formal models for that minimization problem. Specifically, for the case in which sensing hardware is held fixed, we show that this algorithmic design problem is NP-hard even for particularly simple classes of cost functions, confirming what many perhaps have suspected about this sort of design-time optimization. We also introduce a formalism, based on the notion of label maps, for the broader problem in which the design space encompasses choices for both actuation and sensing components. As a result, for several questions of interest, having both optimality and efficiency of solution is unlikely. However, we also show that, for some specific types of cost functions, the problem is either polynomial-time solvable or fixed-parameter tractable. Note to Practitioners—Despite the primary results being theoretical and, further, taking the form of bad news, this article still has considerable value to practitioners. Specifically, assuming that one has been employing heuristic or approximate solutions to robot design problems, this article serves as a justification for doing so. Moreover, it delineates some circumstances in which one can, in a sense, do better and achieve genuine optima with practical algorithms.

中文翻译：

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能够解决规划问题的最小机器人的设计


本文研究了机器人驱动和传感硬件的选择，以最大限度地降低设计成本，同时确保机器人能够执行计划来完成任务。它的主要贡献是研究最小化问题的合理形式模型的硬度。具体来说，对于传感硬件固定的情况，我们表明即使对于特别简单的成本函数类别，这种算法设计问题也是 NP 困难的，这证实了许多人可能对这种设计时优化的怀疑。我们还引入了一种基于标签图概念的形式主义，以解决更广泛的问题，其中设计空间包含驱动和传感组件的选择。因此，对于几个感兴趣的问题，不太可能同时具有解决方案的最优性和效率。然而，我们还表明，对于某些特定类型的成本函数，问题要么是多项式时间可解的，要么是固定参数可处理的。从业者须知——尽管主要结果是理论上的，并且以坏消息的形式出现，但本文对从业者仍然具有相当大的价值。具体来说，假设人们一直采用启发式或近似解决方案来解决机器人设计问题，本文将作为这样做的理由。此外，它还描述了一些情况，在某些情况下，人们可以在某种意义上做得更好，并通过实用算法实现真正​​的优化。