Calculus of Variations and Geometric Measure Theory

F. Ancona - A. Bressan - M. T. Chiri

Soil searching by an artificial root

created by chiri on 13 May 2020
modified on 10 Feb 2022


Accepted Paper

Inserted: 13 may 2020
Last Updated: 10 feb 2022

Journal: SIAM Journal on Applied Mathematics
Year: 2022


We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integro-partial differential equations: one for the growth of the body and the other for the elongation of the tip. At any given time, the angular velocity of the root is obtained by solving a minimization problem with state constraints. We prove the existence of solutions to the evolution problem, up to the first time where a "breakdown configuration" is reached. Some numerical simulations are performed, to test the effectiveness of our feedback control algorithm.