Formation control simplifies minimizing multi-robot cost functions by encoding a cost function as a shape the robots maintain. However, by reducing complex cost functions to formations, discrepancies arise between maintaining the shape and minimizing the original cost function. For example, a Diamond or Box formation shape is often used for protecting all members of the formation. When more information about the surrounding environment becomes available, a static shape often no longer minimizes the original protection cost. We propose a formation planner to reduce mismatch between a formation and the cost function while still leveraging efficient formation controllers. Our formation planner is a two-step optimization problem that identifies desired relative robot positions. We first solve a constrained problem to estimate non-linear and non-differentiable costs with a weighted sum of surrogate cost functions. We theoretically analyze this problem and identify situations where weights do not need to be updated. The weighted, surrogate cost function is then minimized using relative positions between robots. The desired relative positions are realized using a non-cooperative formation controller derived from Lyapunov's direct approach. We then demonstrate the efficacy of this approach for military-like costs such as protection and obstacle avoidance. In simulations, we show a formation planner can reduce a single cost by over 75%. When minimizing a variety of cost functions simultaneously, using a formation planner with adaptive weights can reduce the cost by 20-40%. Formation planning provides better performance by minimizing a surrogate cost function that closely approximates the original cost function instead of relying on a shape abstraction.

翻译：编队控制通过将成本函数编码为机器人维持的队形，简化了多机器人成本函数的最小化问题。然而，将复杂成本函数简化为编队时，维持队形与最小化原始成本函数之间会出现差异。例如，菱形或矩形编队形状常用于保护编队中的所有成员。当获得更多关于周围环境的信息时，静态形状往往不再能最小化原始的保护成本。我们提出了一种编队规划器，以减少编队与成本函数之间的不匹配，同时仍利用高效的编队控制器。我们的编队规划器是一个两步优化问题，用于确定期望的机器人相对位置。首先，我们解决一个约束问题，通过代理成本函数的加权和来估计非线性和不可微成本。我们对此问题进行了理论分析，并识别了无需更新权重的情况。然后，使用机器人之间的相对位置最小化加权代理成本函数。期望的相对位置通过基于李雅普诺夫直接法推导的非合作编队控制器实现。随后，我们展示了该方法在军事类成本（如保护和避障）中的有效性。在仿真中，我们表明编队规划器可将单一成本降低超过75%。当同时最小化多种成本函数时，使用具有自适应权重的编队规划器可将成本降低20-40%。编队规划通过最小化紧密逼近原始成本函数的代理成本函数，而非依赖形状抽象，提供了更好的性能。