A Class of Co-Design Problems with Cyclic Constraints and Their Solution

Abstract

Co-design problems in the field of robotics involve the tradeoff of 'resources' usage, such as cost, execution time, and energy, with mission performance, under recursive constraints that involve energetics, mechanics, computation, and communication. This letter shows that a large class of codesign problems have a common structure, as they are described by two posets, representing functionality, and resources. The codesign constraints can be expressed as two maps in opposite directions between the two posets. Finding the most resource-economical feasible solution is equivalent to finding the least fixed point of the composition of those two maps. If the two maps are monotone, results from order theory allow concluding uniqueness and systematically deriving an optimal design or a certificate for infeasibility.