This paper aims to propose a novel approach to model the dynamics of objects that move within the soil, e.g. plants roots. One can assume that external forces are significant only at the tip of the roots, where the plant’s growth is actuated. We formulate an optimal control problem that minimises the energy spent by a growing root subject to physical constraints imposed by the surrounding soil at the tip. We study the motion strategy adopted by plant roots to facilitate penetration into the soil, which we hypothesize to be a circumnutation movement. By solving the proposed optimal control problem numerically, we validate the hypothesis that plant roots adopt a circumnutation motion pattern to reduce soil penetration resistance during growth. The proposed formalisation could be applied to replicate such a biological behaviour in robotic systems, to adopt the most efficient strategy for autonomous devices in soil exploration.

中文翻译：

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土壤中植物根尖动力学的优化控制。

本文旨在提出一种新方法来模拟在土壤中移动的物体（例如植物根部）的动力学。人们可以假设外力只在根尖处显着，在那里植物的生长被驱动。我们制定了一个最优控制问题，以最大限度地减少受周围土壤在尖端施加的物理约束的生长根所消耗的能量。我们研究了植物根系为促进土壤渗透而采用的运动策略，我们假设这是一种环绕运动。通过数值求解所提出的最优控制问题，我们验证了植物根系采用环绕运动模式以降低生长过程中土壤渗透阻力的假设。提议的形式化可以应用于在机器人系统中复制这种生物行为，