Formation Control with Bounded Controls and Collision Avoidance: Theory and Application to Quadrotor Unmanned Air Vehicles

This dissertation presents new results on multi-agent formation control and applies the new control algorithms to quadrotor unmanned air vehicles. First, this dissertation presents a formation control algorithm for double-integrator agents, where the formation is time varying and the agents’ controls satisfy a priori bounds (e.g., the controls accommodate actuator saturation). 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 a priori bounded controls (if applicable). We also 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 as well as outdoor experiments demonstrating the algorithm in a real-world environment with disturbances (e.g., wind) and only onboard feedback. Next, the dissertation extends the formation control method to address agents with damped-rigid-body dynamics (rather than double-integrator dynamics). We also use a barrier-function method to prevent collisions, and enforce state and control constraints. This method modifies the desired formation control as little as possible to enforce the constraints, and is implemented as a quadratic program. We then introduce an observer UAV that uses an onboard vision system and detection algorithm to obtain estimates of a leader trajectory, which can be used as feedback for the formation control. Finally, we present results from outdoor rotorcraft experiments that demonstrate the algorithm with time-varying formations, bounded controls, collision avoidance, and leader tracking