Kinematic and dynamic modelling and simulation of soft continuous arm based on modal method

Inspired by the muscle structures of elephant’s trunk, octopus’ arm and tongue, the soft continuous arm developed based on bionics can extend, contract and bend along any point of its structure. Compared with the rigid manipulator, it has the characteristics of high flexibility, complex environment adaptability and safe human-machine interactivity. In this work, a three-dimensional (3D) kinematic and dynamic model of the soft continuous arm based on the modal method is presented and analyzed. The spatial kinematics model of the soft continuous arm is established based on the modal method first, in which the deformation of the soft continuous arm is assumed to be an arc without torsion, and the complex nonlinear function is approximated by a simple mathematical function. The accurate, singularity free and unique modal transformation matrix can be deduced conveniently. Also, it overcomes the limitations of the previous models in which the curve parameters are used and the curvature of the cross section assumes to be not zero as well as the dynamic model does not include the pure linear motion. The modal method can be used to simulate the spatial bending motion, but also effectively overcome the singularity problem caused by using the curve parameters for simulating the pure linear motion. Then, the dynamics model of the soft continuous arm is established using the Lagrange method. Due to large number of complex nonlinear integral operations is inevitably involved, and the computational efficiency is low in the numerical solution, the modal method is used in the numerical simulation, which greatly simplifies the complex nonlinear integral operation and improves the efficiency of numerical calculation. The simulation results of the pure elongation and bending of the soft continuous arm show that the modal method has the characteristics of fast and accurate response.