Optimal control of plant root tip dynamics in soil

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.