Matching Sensing to Actuation and Dynamics in Distributed Sensorimotor Architectures

In this article we explore the benefits of matching sensing characteristics to actuation and dynamics in the context of spatially distributed sensorimotor architectures, motivated by recently discovered connections in blowfly flight physics and visual physiology. Within the proposed framework, we present novel semidefinite programs with linear matrix inequality constraints which yield directions encoded in the sensory output that maximize the smallest unstable Hankel singular value of the system. This is a coordinate-invariant metric that minimizes the control energy required to stabilize an unstable system and maximizes the achievable robustness to unstructured additive uncertainty over all possible controllers. We also reformulate the problem to achieve a prescribed speed of response, which can be applied to stable and unstable systems. We adapt a maximally robust controller synthesis method from previous work which provides a tool for validation. We additionally present an $H_{\infty }$ controller formulation which allows for a trade-off between minimization of actuator effort and robustness versus disturbance rejection and tracking capability, providing design flexibility over the maximally robust controller.