This paper presents control and coordination algorithms for groups of vehicles, focusing on autonomous vehicle networks performing distributed sensing tasks where each vehicle acts as a mobile tunable sensor. The authors propose gradient descent algorithms for a class of utility functions that encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct. The paper discusses mobile sensing networks, which involve large groups of autonomous vehicles coordinating through ad-hoc communication networks to perform tasks like search and recovery, exploration, and environmental monitoring. These networks offer advantages such as robustness to failures and the ability to adapt to changing environments. The paper also addresses optimal sensor allocation and coverage problems, introducing a notion of sensor coverage that formalizes an optimal sensor placement problem. This is related to locational optimization, which is a broad discipline with applications in various scientific fields. The authors design distributed asynchronous algorithms for coverage control, which are adaptive, distributed, asynchronous, and verifiably asymptotically correct. These algorithms are based on the classic Lloyd algorithm from quantization theory and are adapted for mobile sensing networks. The paper presents two asynchronous distributed implementations of the Lloyd algorithm for ad-hoc networks with communication and sensing capabilities. These implementations account for the constraints imposed by the distributed nature of the vehicle network. The paper also discusses extensions and applications of the algorithms, including variations on vehicle dynamics and discrete-time implementations for vehicles with local motion planners. It also describes ways to design density functions to solve problems unrelated to coverage.This paper presents control and coordination algorithms for groups of vehicles, focusing on autonomous vehicle networks performing distributed sensing tasks where each vehicle acts as a mobile tunable sensor. The authors propose gradient descent algorithms for a class of utility functions that encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct. The paper discusses mobile sensing networks, which involve large groups of autonomous vehicles coordinating through ad-hoc communication networks to perform tasks like search and recovery, exploration, and environmental monitoring. These networks offer advantages such as robustness to failures and the ability to adapt to changing environments. The paper also addresses optimal sensor allocation and coverage problems, introducing a notion of sensor coverage that formalizes an optimal sensor placement problem. This is related to locational optimization, which is a broad discipline with applications in various scientific fields. The authors design distributed asynchronous algorithms for coverage control, which are adaptive, distributed, asynchronous, and verifiably asymptotically correct. These algorithms are based on the classic Lloyd algorithm from quantization theory and are adapted for mobile sensing networks. The paper presents two asynchronous distributed implementations of the Lloyd algorithm for ad-hoc networks with communication and sensing capabilities. These implementations account for the constraints imposed by the distributed nature of the vehicle network. The paper also discusses extensions and applications of the algorithms, including variations on vehicle dynamics and discrete-time implementations for vehicles with local motion planners. It also describes ways to design density functions to solve problems unrelated to coverage.