In this work, we propose a method to solve the interaction planning problem for a set of mobile agents with obstacles and agent collisions via a core path planner and constrained random position sampling approach. The interaction constraint is posed in the form of an arbitrary number of discretized times in which we enforce a desired topological condition. The general objective function, to be maximized subject to the interaction constraint, is coverage of an environmental process here modeled as a Gaussian mixture model. The main tool we use to select positions and the times of interaction is the greedy algorithm, along with a submodular objective function and matroid constraint. Through this we guarantee strong theoretical lower bounds on sub-optimality. Simulations, including several Monte Carlo trials, are presented to corroborate our proposed methods.

中文翻译：

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通过对位置样本的顺序贪婪选择进行多代理间歇交互规划

在这项工作中，我们提出了一种方法，通过核心路径规划器和受约束的随机位置采样方法来解决一组具有障碍物和代理碰撞的移动代理的交互规划问题。交互约束以任意数量的离散时间的形式提出，我们在其中强制执行所需的拓扑条件。在相互作用约束下最大化的一般目标函数是覆盖这里建模为高斯混合模型的环境过程。我们用来选择位置和交互次数的主要工具是贪心算法，以及一个子模块目标函数和拟阵约束。通过这一点，我们保证了次优性的强大理论下限。模拟，包括几个蒙特卡罗试验，