Multirobot path-aware global optimization

We propose Voronoi Simultaneous Optimistic Optimization (VSOO), a divide-the-best-based method for multirobot global optimization of a Lipschitz-continuous physical objective (e.g., quantity of material, density of litter, signal power), whose Lipschitz constant is unknown. In this problem, a team of mobile robots must autonomously navigate as quickly as possible to all global optima of the objective function defined over their operating area. The objective can have multiple local and global optima, is initially unknown, and can only be evaluated online at robot locations. VSOO utilizes Voronoi partitions driven by the samples collected so far by the robots, which allows them to incrementally refine the search space in their simultaneous search for the optima. We guarantee everywhere-dense and global convergence for any function, and analyze convergence rates for some representative classes of function shapes. Extensive numerical simulations, performed on established classes of benchmark test functions, demonstrate that VSOO approaches all global optima faster than a series of representative source/extremum seeking techniques that – similarly to VSOO – are global optimizers designed for mobile robots. In terms of execution time, VSOO is competitive with these baselines. We finally validate VSOO in real-robot experiments in which TurtleBot3 robots successfully search for the strongest antenna signals indoors.