We present a distributed formation control strategy for agents with a variety of dynamics to achieve a desired planar formation. Our approach is based on the barycentric-coordinate-based (BCB) control, which is fully distributed, does not require inter-agent communication or a common sense of orientation, and can be implemented using relative position measurements acquired by agents in their local coordinate frames. This removes the need for global positioning or alignment of local coordinate frames, which are required across several existing strategies. We show how the BCB control for agents with the simplest dynamical model, i.e., the single-integrator dynamics, can be extended to agents with higher-order dynamics such as quadrotors, and nonholonomic agents such as unicycles and cars. Specifically, our extension preserves the desired convergence and robustness guarantees of the BCB approach and is provably robust to saturations in the input and unmodeled linear actuator dynamics for unicycle and car agents. We further show that under our proposed BCB control design, the agents can move along a rotated and scaled control direction without affecting the convergence to the desired formation. This observation is used to design a fully distributed collision avoidance strategy, which is often not considered in the formation control literature. We demonstrate the proposed approach in simulations and further present a distributed robotic platform to test the strategy experimentally. Our experimental platform consists of off-the-shelf equipment that can be used to test and validate other multi-agent algorithms. The code and implementation instructions for this platform are available online.

中文翻译：

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高阶完整和非完整代理的鲁棒分布式平面形成控制

我们为具有各种动态的代理提出了一种分布式编队控制策略，以实现所需的平面编队。我们的方法基于基于重心坐标 (BCB) 的控制，它是完全分布式的，不需要代理间通信或方向常识，并且可以使用代理在其本地坐标中获取的相对位置测量值来实现帧。这消除了对全局定位或局部坐标系对齐的需要，这在几个现有策略中都是必需的。我们展示了对具有最简单动力学模型（即单积分器动力学）的代理的 BCB 控制如何扩展到具有高阶动力学（例如四旋翼）和非完整代理（例如独轮车和汽车）的代理。具体来说，我们的扩展保留了 BCB 方法所需的收敛性和鲁棒性保证，并且可以证明对独轮车和汽车代理的输入和未建模线性执行器动力学的饱和具有鲁棒性。我们进一步表明，在我们提出的 BCB 控制设计下，代理可以沿旋转和缩放的控制方向移动，而不会影响到所需编队的收敛。这种观察被用来设计一个完全分布式的防撞策略，这在编队控制文献中通常没有考虑到。我们在模拟中演示了所提出的方法，并进一步提出了一个分布式机器人平台来实验测试该策略。我们的实验平台由现成的设备组成，可用于测试和验证其他多代理算法。