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 cost-minimizing 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.

翻译：本文针对存在定位误差的四旋翼编队跟踪问题，提出一种分布式多智能体最优控制方案。我们的控制架构基于领航-跟随方法，其中单架领航四旋翼追踪预期轨迹，而跟随者保持三角形编队中的相对位置。首先，将四旋翼建模为YZ平面上状态信息不确定的动态质点系统。随后，将编队跟踪任务转化为优化问题——通过构建受动态约束的约束增广拉格朗日函数——求解出在控制与轨迹误差代价最小化意义上达成最优解的控制律。数值仿真结果表明：针对所考虑的平面四旋翼模型（其传感器测量不确定性建模为高斯噪声），该最优控制律能够驱动每个智能体实现全局目标——即领航者轨迹跟踪与编队维持。最后，我们利用多智能体系统的跟踪误差和编队误差对控制律性能进行评估。