Control of Vehicular Formations
Supported in part by NSF Award CMMI-09-27720
There is a growing interest in controlling formations of autonomous vehicles. I have discovered fundamental limitations in the control of large-scale formations and quantified how key system properties, such as stabilizability and detectability, deteriorate with the number of vehicles. Furthermore, I established that convergence of merge and split maneuvers scales poorly with the system size. My research also shows that in one and two spatial dimensions, with only local feedback, it is impossible to have coherent large formations, that behave like rigid lattices. Yet I prove that this is possible in three spatial dimensions. The observed phenomenon is a consequence of the fact that, in 1D and 2D, local feedback laws are ineffective in guarding against disturbances with large spatial wavelength, resulting in an accordion-like motion of the entire formation. Similar phenomenon also arises in several other problems including distributed estimation from relative measurements, distributed averaging algorithms, global mean first passage time of random walks, effective resistance in electrical networks, and statistical mechanics of harmonic solids.
Currently, I am designing optimal and robust localized controllers for formations in which the movement of each vehicle will be formed using only information from nearby vehicles. These controllers are expected to transfer salient features of collective motion observed in nature (swarming, flocking, schooling) to engineering applications. The design is being done at a level of abstraction that will allow use of localized feedback strategies in control of fluid flows, extremely large telescopes, wind farms, power networks, and high density data-storage devices.