Formation Control With Time-Varying Formations, Bounded Controls, and Local Collision Avoidance

Abstract

We present a formation control algorithm for double-integrator agents, where the formation is time-varying and the agents’ controls satisfy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> bounds (e.g., the controls can accommodate actuator saturation). We assume that each agent has relative-position-and-velocity feedback of its neighbor agents, where the communication structure is a quasi-strongly connected graph, and at least one agent has a measurement of its position and velocity relative to the leader (if applicable). The main analytic results provide sufficient conditions such that all agents converge to the desired time-varying relative positions with one another and the leader and have <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> bounded controls (if applicable). Next, we extend the formation control algorithm to include collision-avoidance terms that, for a set of initial conditions, prevent each agent from colliding with the agents in its neighbor set or colliding with the leader (if applicable). Finally, we present results from rotorcraft experiments that demonstrate the algorithm with time-varying formations and bounded controls. These experimental results include indoor experiments using a motion-capture system and outdoor experiments demonstrating the algorithm in a real-world environment with disturbances (e.g., wind) and only onboard feedback.