Design and Nonlinear Modeling of a Modular Cable Driven Soft Robotic Arm

TL;DR

This work tackles the nonlinear actuation–deformation coupling in cable-driven soft robots by introducing an octopus-inspired modular arm with decoupled sections fabricated through 3D-printed endcaps and silicone casting. It develops an analytical static model that accounts for transverse deformation of cables pushing into the soft body, and couples this with a multi-section kinematic framework using homogeneous transforms and the Jacobian $J_v$ for inverse kinematics. Experimental validation shows substantial improvements over a baseline, with end-effector tracking errors reduced by up to about $52\%$ in two-section configurations. The approach is generalizable to a broad class of soft cable-driven actuators and supports low-cost fabrication, planning, and potential sensor integration for real-time control.

Abstract

We propose a novel multi-section cable-driven soft robotic arm inspired by octopus tentacles along with a new modeling approach. Each section of the modular manipulator is made of a soft tubing backbone, a soft silicon arm body, and two rigid endcaps, which connect adjacent sections and decouple the actuation cables of different sections. The soft robotic arm is made with casting after the rigid endcaps are 3D-printed, achieving low-cost and convenient fabrication. To capture the nonlinear effect of cables pushing into the soft silicon arm body, which results from the absence of intermediate rigid cable guides for higher compliance, an analytical static model is developed to capture the relationship between the bending curvature and the cable lengths. The proposed model shows superior prediction performance in experiments over that of a baseline model, especially under large bending conditions. Based on the nonlinear static model, a kinematic model of a multi-section arm is further developed and used to derive a motion planning algorithm. Experiments show that the proposed soft arm has high flexibility and a large workspace, and the tracking errors under the algorithm based on the proposed modeling approach are up to 52$\%$ smaller than those with the algorithm derived from the baseline model. The presented modeling approach is expected to be applicable to a broad range of soft cable-driven actuators and manipulators.

Figures (13)

• Figure 1: Structures of the soft robotic arm. (A). A two-section modular soft robotic arm. (B). The structure for one section of the robotic arm. (C). Connection of two endcaps. (D) One endcap at the tip side of the section. (E). Cable paths for different sections of the soft robotic arm.
• Figure 2: Fabrication process for one section of the soft robotic arm. (A). 3D printing of the rigid parts. (B). Assembling of mold for one section. (C). Wrapping fiber coils around the rods for cavities. (D). Inserting the rods for cavities into the mold. (E). Injecting silicone glue into the mold and curing. (F). Adding another layer of silicone glue to the inner surface of the cavities. (G). Removing the mold and getting one section of the soft robotic arm.
• Figure 3: Modeling of one section of the arm driven by a single cable. (A). Bending configuration for one section driven by a single cable. (B). External forces and moments applied by the cable to the soft section. (C) The total transverse force applied by the cable and its arm. (D). Actuation cable considering transverse deformation (red) and without transverse deformation (blue).
• Figure 4: Modeling of one section of the arm driven by multiple cables. (A). Bending configuration for one section of the arm driven by multiple cables. (B). External moments applied by multiple cables to the soft section in the $P$ direction.
• Figure 5: Modeling of a multi-section soft robotic arm. (A). Variables of bending configuration for one section. (B). Local frames for different sections. (C). The inverse kinematics solver for the bending configurations of different sections based on the reference of the end position. (D). Open loop control of the soft robotic arm based on the proposed model. $\bm{x}$ and $\bm{l}$ are the end position of the soft robotic arm and the actuation cable lengths, respectively, for which $\bm{x}_d$ and $\bm{l}_d$ are the corresponding target values.