Coupling Numerical Deformable Models in Global and Reduced Coordinates for the Simulation of the Direct and the Inverse Kinematics of Soft Robots

• Published in: IEEE robotics and automation letters Vol. 6; no. 2; pp. 3910 - 3917
• Main Authors: Adagolodjo, Yinoussa, Renda, Federico, Duriez, Christian
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Series: IEEE Robotics and Automation Letters
• Subjects: Actuation; Cables; Computer Science; Constraint modelling; contact modeling; control; Coupling; Deformable models; Deformation; Engineering Sciences; Finite element analysis; Finite element method; Flexible robotics; Formability; grasping; Inverse kinematics; Kinematics; learning for soft robots; Mathematical analysis; Mathematical model; Mathematics; modeling; Numerical models; Optimization; Parameterization; Physics; Robot kinematics; Robots; simulation and animation; soft robot applications; Soft robotics; Solid modeling; Strain; tendon/wire mechanism; Tubes; Flexible Robotics; Tendon/Wire Mechanism; Control and Learning for Soft Robots; Grasping; Soft Robot Applications; Simulation and Animation; Modeling; Contact Modeling
• ISSN: 2377-3766; 2377-3766
• DOI: 10.1109/LRA.2021.3061977

In this letter, 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.