Robust Distributed Planar Formation Control for Higher-Order Holonomic\n and Nonholonomic Agents

Abstract

We present a distributed formation control strategy for agents with a variety\nof dynamics to achieve a desired planar formation. Our approach is based on the\nbarycentric-coordinate-based (BCB) control, which is fully distributed, does\nnot require inter-agent communication or a common sense of orientation, and can\nbe implemented using relative position measurements acquired by agents in their\nlocal coordinate frames. This removes the need for global positioning or\nalignment of local coordinate frames, which are required across several\nexisting strategies. We show how the BCB control for agents with the simplest\ndynamical model, i.e., the single-integrator dynamics, can be extended to\nagents with higher-order dynamics such as quadrotors, and nonholonomic agents\nsuch as unicycles and cars. Specifically, our extension preserves the desired\nconvergence and robustness guarantees of the BCB approach and is provably\nrobust to saturations in the input and unmodeled linear actuator dynamics for\nunicycle and car agents. We further show that under our proposed BCB control\ndesign, the agents can move along a rotated and scaled control direction\nwithout affecting the convergence to the desired formation. This observation is\nused to design a fully distributed collision avoidance strategy, which is often\nnot considered in the formation control literature. We demonstrate the proposed\napproach in simulations and further present a distributed robotic platform to\ntest the strategy experimentally. Our experimental platform consists of\noff-the-shelf equipment that can be used to test and validate other multi-agent\nalgorithms. The code and implementation instructions for this platform are\navailable online.\n