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𝐂𝐨𝐮𝐩𝐥𝐢𝐧𝐠 𝐧𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥 𝐝𝐞𝐟𝐨𝐫𝐦𝐚𝐛𝐥𝐞 𝐦𝐨𝐝𝐞𝐥𝐬 𝐢𝐧 𝐠𝐥𝐨𝐛𝐚𝐥 𝐚𝐧𝐝 𝐫𝐞𝐝𝐮𝐜𝐞𝐝 𝐜𝐨𝐨𝐫𝐝𝐢𝐧𝐚𝐭𝐞𝐬 𝐟𝐨𝐫 𝐭𝐡𝐞 𝐬𝐢𝐦𝐮𝐥𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐭𝐡𝐞 𝐝𝐢𝐫𝐞𝐜𝐭 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐢𝐧𝐯𝐞𝐫𝐬𝐞 𝐤𝐢𝐧𝐞𝐦𝐚𝐭𝐢𝐜𝐬 𝐨𝐟 𝐒𝐨𝐟𝐭 𝐑𝐨𝐛𝐨𝐭𝐬 :
In this paper, we propose a method to combine the Finite Element Method (FEM) with Discrete Cosserat Modeling (DCM) to capture the mechanics and the actuation of soft robots.
The FEM is used to simulate the non-linear behavior of the volume of the soft structure while the cable/rod used for the actuation is modeled using the DCM.
The two models are linked using kinematic constraints without imposing meshing rules.
We demonstrate that both direct and inverse kinematic models can be obtained by quadratic optimization.
The originality of this coupling is that the FEM model uses global coordinates (the position of the nodes of its mesh in space) where the Cosserat model uses local coordinates (successive strain values).
The coupling of these mechanical models allows to combine the best of each parametrization.
On the one hand, FEM allows to capture the behavior of the volume structure of the robot while accounting for its geometry with a complex mesh.
On the other hand, the DCM allows efficient modeling of 1D structures such as rods, (concentric) tubes, cables, etc. that are used to deform the volume structure of the soft robots. DCM handles large deformation, torsion and (in)-extensibility and is efficient to compute.
Moreover, the approach is compatible with complementarity constraints introduced when modeling contact and friction of the robot with its environment as well as the self-collision.
𝐋𝐢𝐧𝐤 𝐭𝐨 𝐏𝐝𝐟 𝐟𝐢𝐥𝐞 : https://hal.archives-ouvertes.fr/hal-...
𝐊𝐞𝐲𝐰𝐨𝐫𝐝𝐬 : 𝕊𝕠𝕗𝕥 ℝ𝕠𝕓𝕠𝕥𝕤, 𝕊𝕠𝕗𝕥 ℝ𝕠𝕓𝕠𝕥 ℂ𝕠𝕟𝕥𝕣𝕠𝕝, 𝕊𝕠𝕗𝕥 ℝ𝕠𝕓𝕠𝕥 𝔸𝕡𝕡𝕝𝕚𝕔𝕒𝕥𝕚𝕠𝕟𝕤, ℂ𝕠𝕟𝕥𝕒𝕔𝕥 𝕄𝕠𝕕𝕖𝕝𝕚𝕟𝕘, 𝔾𝕣𝕒𝕤𝕡𝕚𝕟𝕘, 𝕄𝕠𝕕𝕖𝕝𝕚𝕟𝕘, 𝕊𝕚𝕞𝕦𝕝𝕒𝕥𝕚𝕠𝕟 𝕒𝕟𝕕 𝔸𝕟𝕚𝕞𝕒𝕥𝕚𝕠𝕟, 𝕋𝕖𝕟𝕕𝕠𝕟/𝕎𝕚𝕣𝕖 𝕄𝕖𝕔𝕙𝕒𝕟𝕚𝕤𝕞, 𝕃𝕖𝕒𝕣𝕟𝕚𝕟𝕘 𝕗𝕠𝕣 𝕊𝕠𝕗𝕥 ℝ𝕠𝕓𝕠𝕥𝕤, 𝔻𝕚𝕤𝕔𝕣𝕖𝕥𝕖 ℂ𝕠𝕤𝕤𝕖𝕣𝕒𝕥 𝕄𝕠𝕕𝕖𝕝, 𝔽𝔼𝕄 , 𝔻𝕖𝕗𝕠𝕣𝕞𝕒𝕓𝕝𝕖 M𝕠𝕕𝕖𝕝 𝕒𝕟𝕕 𝕊𝕆𝔽𝔸 𝔽𝕣𝕒𝕞𝕖𝕨𝕠𝕣𝕜