Adaptive Robot Deployment Algorithms

In robot deployment problems, the fundamental issue is to optimize a steady state performance measure that depends on the spatial configuration of a group of robots. For static deployment problems, a classical way of designing high- level feedback motion planners is to implement a gradient descent scheme on a suitably chosen objective function. This can lead to computationally expensive deployment algorithms that may not be adaptive to uncertain dynamic environments. We address this challenge by showing that algorithms for a variety of deployment scenarios in stochastic environments and with noisy sensor measurements can be designed as stochastic gradient descent algorithms, and their convergence properties analyzed via the theory of stochastic approximations. This approach yields often surprisingly simple algorithms that can accommodate complicated objective functions, and adapt to slow temporal variations in environmental parameters. To illustrate the richness of the framework, we discuss several applications, including searching for a field extrema, deployment with stochastic connectivity constraints, coverage, and vehicle routing scenarios.