Heat Equation Driven Area Coverage (HEDAC) is a state-of-the-art multi-agent ergodic motion control guided by a gradient of a potential field. A finite element method is hereby implemented to obtain a solution of Helmholtz partial differential equation, which models the potential field for surveying motion control. This allows us to survey arbitrarily shaped domains and to include obstacles in an elegant and robust manner intrinsic to HEDAC's fundamental idea. For a simple kinematic motion, the obstacles and boundary avoidance constraints are successfully handled by directing the agent motion with the gradient of the potential. However, including additional constraints, such as the minimal clearance dsitance from stationary and moving obstacles and the minimal path curvature radius, requires further alternations of the control algorithm. We introduce a relatively simple yet robust approach for handling these constraints by formulating a straightforward optimization problem based on collision-free escapes route maneuvers. This approach provides a guaranteed collision avoidance mechanism, while being computationally inexpensive as a result of the optimization problem partitioning. The proposed motion control is evaluated in three realistic surveying scenarios simulations, showing the effectiveness of the surveying and the robustness of the control algorithm. Furthermore, potential maneuvering difficulties due to improperly defined surveying scenarios are highlighted and we provide guidelines on how to overpass them. The results are promising and indiacate real-world applicability of proposed constrained multi-agent motion control for autonomous surveying and potentially other HEDAC utilizations.

中文翻译：

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基于势场有限元逼近的约束多智能体遍历区域测量控制

热方程驱动区域覆盖 (HEDAC) 是一种由势场梯度引导的最先进的多智能体遍历运动控制。在此实施有限元方法以获得亥姆霍兹偏微分方程的解，该解对用于测量运动控制的势场进行建模。这使我们能够调查任意形状的域，并以一种优雅而稳健的方式包含 HEDAC 基本思想固有的障碍。对于简单的运动学运动，通过以势能梯度引导代理运动成功地处理了障碍物和边界回避约束。然而，包括额外的约束，例如与静止和移动障碍物的最小间隙距离以及最小路径曲率半径，需要进一步改变控制算法。我们通过制定一个基于无碰撞逃生路线机动的直接优化问题，引入了一种相对简单但稳健的方法来处理这些约束。这种方法提供了有保证的碰撞避免机制，同时由于优化问题划分而在计算上成本低廉。所提出的运动控制在三个实际测量场景模拟中进行了评估，显示了测量的有效性和控制算法的鲁棒性。此外，突出显示了由于不正确定义的测量场景而导致的潜在机动困难，我们提供了有关如何超越它们的指南。