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

We present a distributed formation control strategy for agents with a variety of dynamics to achieve a desired planar formation. The proposed strategy is fully distributed, does not require inter-agent communication or a common sense of orientation, and can be implemented using relative position measurements acquired by agents in their local coordinate frames. We show how the control designed for agents with the simplest dynamical model, i.e., the single-integrator dynamics, can be extended to holonomic agents with higher-order dynamics such as quadrotors, and nonholonomic agents such as unicycles and cars. We prove that the proposed strategy is robust to saturations in the input, unmodeled dynamics, and switches in the sensing topology. We further show that the control is relaxed in the sense that agents can move along a rotated and scaled control direction without affecting the convergence to the desired formation. This observation is used to design a distributed collision avoidance strategy. We demonstrate the proposed approach in simulations and further present a distributed robotic platform to test the strategy experimentally. Our experimental platform consists of off-the-shelf equipment that can be used to test and validate other multi-agent algorithms. The code and implementation instructions for this platform are available online and free.