Distributed Optimal Formation Control for an Uncertain Multiagent System in the Plane

Abstract

In this paper, we present a distributed optimal multiagent control scheme for quadrotor formation tracking under localization errors. Our control architecture is based on a leader-follower approach, where a single leader quadrotor tracks a desired trajectory while the followers maintain their relative positions in a triangular formation. We begin by modeling the quadrotors as particles in the YZ-plane evolving under dynamics with uncertain state information. Next, by formulating the formation tracking task as an optimization problem -with a constraint-augmented Lagrangian subject to dynamic constraints -we solve for the control law that leads to an optimal solution in the control and trajectory error costminimizing sense. Results from numerical simulations show that for the planar quadrotor model considered -with uncertainty in sensor measurements modeled as Gaussian noise -the resulting optimal control is able to drive each agent to achieve the desired global objective: leader trajectory tracking with formation maintenance. Finally, we evaluate the performance of the control law using the tracking and formation errors of the multiagent system.