Tendon-based modelling, estimation and control for a simulated high-DoF anthropomorphic hand model

TL;DR

The paper tackles estimating joint postures in a high-DoF tendon-driven anthropomorphic hand without joint encoders by combining a Denavit–Hartenberg-based kinematic model with a nonlinear feasibility solver to recover joint angles from tendon tensions and motor elongations. It augments a Jacobian-based PI controller with a data-driven feedforward term to improve gesture tracking, and validates the approach in MuJoCo using the Anatomically Correct Biomechatronic Hand. The work provides an analytical framework for tendon-branch and junction interactions, demonstrates improved transient performance, and discusses observability and constraint-related challenges in highly articulated hands. The findings have practical implications for dexterous manipulation and human–robot interaction where compact sensing limits joint sensing, and they highlight the need for constraint-aware control and potential data-driven enhancements.

Abstract

Tendon-driven anthropomorphic robotic hands often lack direct joint angle sensing, as the integration of joint encoders can compromise mechanical compactness and dexterity. This paper presents a computational method for estimating joint positions from measured tendon displacements and tensions. An efficient kinematic modeling framework for anthropomorphic hands is first introduced based on the Denavit-Hartenberg convention. Using a simplified tendon model, a system of nonlinear equations relating tendon states to joint positions is derived and solved via a nonlinear optimization approach. The estimated joint angles are then employed for closed-loop control through a Jacobian-based proportional-integral (PI) controller augmented with a feedforward term, enabling gesture tracking without direct joint sensing. The effectiveness and limitations of the proposed estimation and control framework are demonstrated in the MuJoCo simulation environment using the Anatomically Correct Biomechatronic Hand, featuring five degrees of freedom for each long finger and six degrees of freedom for the thumb.

Figures (7)

• Figure 1: Bone structure of the ACB Hand at rest position. Abbreviations of the bones are given in the left figure, whereas, the right figure illustrate the joints with their names, and their degrees of freedom (i.e., the axes of free rotations). This illustration is a slightly modified version of that appeared in 2024_Polcz.etal.
• Figure 2: Tendon structure of the index finger. $J_1$--$J_8$ are the labels of the joints, whereas, the numbers correspond to the tendon segments.
• Figure 5: Desired, achieved, and observed gestures under observer-based PI control with feedforward compensation. Red phantom bodies represent the desired gestures, grey bodies correspond to the achieved gestures produced by observer-based PI feedback with an additional feedforward term, and yellow phantom bodies depict the observed gestures. With the exception of Gesture G5, the desired, achieved, and observed gestures exhibit only minor discrepancies, making them nearly indistinguishable to the human eye.
• Figure 6: Posture estimation during the PI-based tracking controller with feedforward term. Red lines show to the desired angles, the black illustrate achieved angles, the yellow highlight the estimated angles. The labels (G1)--(G6) in the top of each plot highlight the current gesture to be achieved.
• Figure 7: Posture tracking using the PI-based controller with and without feedforward compensation. Red lines show to the desired angles, the black illustrate achieved angles with compensation, the green lines show the achieved angles without compensation.

Theorems & Definitions (2)

• Remark 1
• Remark 2