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

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.

💡 Research Summary

This paper addresses the challenge of sensing joint angles in tendon‑driven anthropomorphic robotic hands, where installing encoders compromises compactness and dexterity. The authors propose a fully physics‑based framework that estimates joint postures from measured tendon displacements and tensions, and then uses those estimates for closed‑loop control without any direct joint sensing.

First, an extended Denavit‑Hartenberg (DH) convention is introduced to describe the irregular, three‑degree‑of‑freedom (3‑DoF) rotary joints of the Anatomically Correct Biomechatronic (ACB) Hand. Each bone is characterized by six parameters (three fixed offsets and three free rotations), allowing systematic generation of DH tables for both long fingers (5 DoF) and the thumb (6 DoF).

The tendon network is modeled as a directed acyclic graph with three vertex types: muscle start sites, junctions, and bone attachment sites. The authors derive combinatorial relationships between the numbers of root segments, connected segments, junctions, and branches, and they construct a sparse incidence matrix C_{b,s} that maps individual tendon segment lengths to whole‑tendon branch lengths. Each segment’s length L_{s,i}(θ) is expressed as a function of the joint vector θ, while its tension follows a linear spring law f_i = k_i·ℓ_i with stiffness k_i = E·A/L_{s0,i} (E = Young’s modulus, A = cross‑section).

Given measured motor currents (tendon forces) and motor encoder readings (root segment excursions), the only unknowns are the free joint angles θ and the excursions of the connected (non‑root) tendon segments. By equating two expressions for branch excursion—one derived from segment‑wise geometry and the other from measured root excursions plus spring forces—the authors obtain a set of nonlinear equations (Eq. 10). These are solved in real time using a Levenberg‑Marquardt optimizer, yielding an estimate \hat{θ}.

For control, the estimated posture is used to compute the Jacobian J(\hat{θ}) of the hand. A proportional‑integral (PI) controller is augmented with a feed‑forward torque term τ_{ff}=J^T·f_{ref}, where f_{ref} is the desired tendon force vector. The feed‑forward component anticipates the required tendon forces, reducing latency and overshoot inherent in pure feedback control.

The framework is evaluated in the MuJoCo simulator with the full ACB Hand model (five fingers, each with 5 DoF, and a thumb with 6 DoF). Experiments include tracking of smooth curves, rapid gesture transitions, and grasping motions. Results show that the feed‑forward‑enhanced controller reduces average joint‑angle error by roughly 30 % and shortens settling time by about 40 % compared with a baseline PI controller. However, the authors note degradation in estimation accuracy for gestures that heavily couple MCP roll and yaw motions, highlighting the limitation of the linear spring tendon model and the need for more sophisticated friction/non‑linear elasticity modeling.

The paper concludes that a physics‑based, analytically tractable approach can replace data‑driven black‑box methods for high‑DoF tendon‑driven hands, offering transparency, interpretability, and the ability to perform offline tendon placement optimization. Future work is suggested on incorporating non‑linear tendon dynamics, adaptive optimization for faster convergence, and validation on physical hardware.