Navigation of Multiple Disk-Shaped Robots with Independent Goals within Obstacle-Cluttered Environments

In this work, we propose a hybrid control scheme to address the navigation problem for a team of disk-shaped robotic platforms operating within an obstacle-cluttered planar workspace. Given an initial and a desired configuration of the system, we devise a hierarchical cell decomposition methodology which is able to determine which regions of the configuration space need to be further subdivided at each iteration, thus avoiding redundant cell expansions. Furthermore, given a sequence of free configuration space cells with an arbitrary connectedness and shape, we employ harmonic transformations and harmonic potential fields to accomplish safe transitions between adjacent cells, thus ensuring almost-global convergence to the desired configuration. Finally, we present the comparative simulation results that demonstrate the efficacy of the proposed control scheme and its superiority in terms of complexity while yielding a satisfactory performance without incorporating optimization in the selection of the paths.