A monolithic optimal control method for displacement tracking of Cosserat rod with application to reconstruction of C. elegans locomotion
A monolithic optimal control method for displacement tracking of Cosserat rod with application to reconstruction of C. elegans locomotion
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DOI：
10.1007/s00466-022-02247-x
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发表时间：
2022-11
影响因子：
4.1
通讯作者：
Yongxing Wang;T. Ranner;Thomas P. Ilett;Yan Xia;N. Cohen
中科院分区：
文献类型：
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作者：
Yongxing Wang;T. Ranner;Thomas P. Ilett;Yan Xia;N. Cohen
本文考虑了一个反问题的Cosserat杆，我们只给的位置的中心线的杆，必须解决外力和扭矩，以及方向的横截面的中心线。我们制定的逆问题作为一个最优控制问题，使用的中心线的位置作为目标函数的外力和扭矩作为控制变量，有意义的正规化的方向。提出了一种整体隐式数值格式，它将原方程和伴随方程以完全耦合的方式求解，并将控制偏微分方程的所有非线性系数更新为当前状态变量。正向制定，确定杆配置从外力和扭矩，首先验证了数值基准;的可解性和稳定性的反问题，然后使用正向模拟的数据进行测试。建议的最优控制方法的动机是重建的方向杆的横截面，其中心线被捕获通过成像协议。作为一个案例研究，我们采取的运动的线虫，秀丽隐杆线虫。在这项研究中，我们采取实验室数据的中心线，并推断其横截面方向（肌肉位置）的控制力和扭矩被解释为反作用力，激活C。elegans'肌肉，from the surrounding周围fluids液体.因此，该方法结合了数学模型和实验室数据来研究C。elegans，这让我们深入了解蠕虫的潜在解剖方向，超越了通过实验室数据可以观察到的。本文完成了几个额外的注释解释模型的理论和技术细节。
This article considers an inverse problem for a Cosserat rod where we are given only the position of the centreline of the rod and must solve for external forces and torques as well as the orientation of the cross sections of the centreline. We formulate the inverse problem as an optimal control problem using the position of the centreline as an objective function with the external force and torque as control variables, with meaningful regularisation of the orientations. A monolithic, implicit numerical scheme is proposed in the sense that primal and adjoint equations are solved in a fully-coupled manner and all the nonlinear coefficients of the governing partial differential equations are updated to the current state variables. The forward formulation, determining rod configuration from external forces and torques, is first validated by a numerical benchmark; the solvability and stability of the inverse problem are then tested using data from forward simulations. The proposed optimal control method is motivated by reconstruction of the orientations of a rod’s cross sections, with its centreline being captured through imaging protocols. As a case study, we take the locomotion of the nematode,Caenorhabditis elegans. In this study we take laboratory data for its centreline and infer its cross-section orientation (muscle locations) with the control force and torque being interpreted as the reaction force, activated byC. elegans’ muscles, from the surrounding fluids. This method thus combines the mathematical modelling and laboratory data to study the locomotion ofC. elegans, which gives us insights into the potential anatomical orientation of the worm beyond what can be observed through the laboratory data. The paper is completed with several additional remarks explaining the theoretical and technical details of the model.