This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton’s method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

中文翻译：

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二阶多智能体系统最优时不变分布式编队跟踪

本文解决了最优时不变编队跟踪问题，旨在为具有二阶积分器动力学的多智能体系统提供分布式解决方案。在文献中，大多数与多智能体编队跟踪相关的结果在研究分布式反馈控制律时都没有考虑能量问题。为了考虑到这一关键的设计方面，我们通过对优化成本中潜在函数的具体和关键选择，形式化并提出了一个优化问题的解决方案，该解决方案封装了轨迹跟踪、基于距离的编队控制和输入能量最小化。为此，我们展示了如何通过基于投影算子的牛顿轨迹优化方法（PRONTO）以集中方式计算逆动力学，更重要的是，我们利用这种离线解决方案作为设计的一般参考稳定的在线分布式控制律。最后，提供了涉及在 3D 空间中遵循类似弯道路径的立方体编队的数值示例，以验证所提出的控制策略。