Cooperative Autonomous Mobile Marine Geophysical Sensing Using Robust Formation Control Theory

The development of autonomous vehicles has revolutionized geophysical sensing. Many emerging applications require deployment of a large fleet of unmanned vehicles moving collectively in a formation constrained to maintain a fixed geometric shape while maneuvering. Such a restriction can be quite challenging for underwater platforms where GPS signals are unavailable and alternative localization strategies can be rather costly. In this context, we consider two research problems: (1) Design a control algorithm which guarantees that the fleet maintains the desired formation positions at all time within a user-specified acceptable tolerance without access to a global coordinate system. (2) Assuming that a fraction of the sensors may fail randomly, select a robust network topology for node communication that guarantees that the surviving sensors maintain the desired formation positions.

To address the first question, we propose a leader-following displacement-based formation control law which corrects the trajectory of each vehicle based on the relative errors in position and velocity signals collected through communication with its neighbors. We analyze the resulting dynamic system, prove its ability to achieve the required performance specifications, demonstrate its feasibility through numerical simulations, and compare the results with other approaches reported in the literature. Our algorithm can accommodate a large number of network topologies representing various ways in which neighboring nodes can communicate. To select the most robust topology, we derive a formula based on graph theory to specify the number of "crossline" communication links needed to guarantee that the fleet maintains its formation shape, given an expected number of node failures. We illustrate feasibility via several numerical simulations. Our framework is pertinent to a diverse set of underwater sensing applications, but for concreteness we use a streamer-free mobile marine seismic survey as an illustrative example. The approach can be tailored to handle a wide spectrum of hardware constraints in terms of motion control, communication capacity, power requirements, etc., and will thus contribute to the efficiency of future autonomous sensing capabilities.