Tendon-Actuated Robots with a Tapered, Flexible Polymer Backbone: Design, Fabrication, and Modeling

Technical Deep Dive

Overview

This work presents the design, modeling, and fabrication of a tendon-actuated continuum robot featuring a flexible, tapered backbone made of thermoplastic polyurethane (TPU). The key contributions are:

• A scalable, 3D-printed robot design with an integrated electronics base for tendon actuation and sensing
• A generalized Cosserat rod model that captures the effects of spatially varying cross-sectional geometry and stiffness along the backbone
• Experimental validation of the model's shape prediction accuracy using motion capture and load cell data

The proposed design prioritizes customizability, rapid assembly, and low cost while enabling high curvature and enhanced distal compliance through the tapered backbone geometry.

Problem and Context

Tendon-actuated continuum robots with flexible backbones offer intrinsic compliance and compactness, making them suitable for tasks in confined spaces. However, existing designs often rely on rigid discs or supporting structures, limiting their configuration space and adaptability.

The authors address this by developing a tendon-actuated robot with a tapered, compliant TPU backbone. The tapering enables greater curvature under tip loading compared to a uniform-diameter backbone, yielding a system with decreasing stiffness towards the tip for enhanced dexterity and compliance.

Methodology

Design and Fabrication

• The robot's backbone is 3D-printed with a tapered, logarithmic spiral shape when fully curled
• The disc radii, thicknesses, and spacing vary according to the same logarithmic ratio
• An integrated electronics base houses the tendon actuation system, with motors driving spools that apply tension to the tendons
• Compression load cells measure the tendon tensions, enabling closed-loop control

Modeling

• The authors extend Cosserat rod theory to explicitly model the spatially varying cross-sectional area and second moments of area along the tapered backbone
• This yields a generalized forward kinetostatic model that captures the effects of tapering on the robot's configuration
• The model is augmented to include the effects of tendon actuation, with tendons following arbitrary non-straight paths

Inverse Design

• The kinetostatic model is used to formulate an optimization problem that maps a desired curvature profile to the optimal backbone taper angle
• This allows practitioners to select geometric parameters that yield a desired configuration space

Data and Experimental Setup

• The 3D-printed robot has a 34.5 cm long backbone with a base radius of 1.11 cm and a tip radius of 0.45 cm (1.08° taper angle)
• The backbone is made of TPU 95A with a reported Young's modulus of 67 MPa
• Ten rigid discs are spaced along the backbone, with radii ranging from 3.7 cm at the base to 1.6 cm at the tip
• Three tendons are routed through the discs and actuated from the base
• Vicon motion capture cameras track the positions of markers affixed to the discs
• Load cells in the base measure the tendon tensions

Results

• The model was validated against the Vicon-measured backbone positions, with a line search used to calibrate the TPU Young's modulus
• After calibration, the model achieves centimeter-level accuracy in predicting the backbone shape on a held-out test set
• The taper angle optimization demonstrates that increasing the taper angle expands the robot's configuration space at modest tendon tensions

Limitations and Uncertainties

• The load cell resolution (0.125 N/bit) limits the detection of subtle shape changes, introducing errors near the upright, unactuated configuration
• Nonlinear TPU material behavior and manufacturing imperfections may contribute to modeling errors

What Comes Next

• Efforts are underway to improve sensor integration and resolution to mitigate the impact of limited load cell sensitivity
• Incorporating residual learning methods could further improve model accuracy by compensating for unmodeled effects

Sources: [1] Tendon-Actuated Robots with a Tapered, Flexible Polymer Backbone: Design, Fabrication, and Modeling (arXiv cs.RO preprint)