Modeling and Control of a Novel Variable Stiffness Three DoFs Wrist

Abstract

This study introduces an innovative design for a Variable Stiffness 3 Degrees of Freedom actuated wrist capable of actively and continuously adjusting its overall stiffness by modulating the active length of non-linear elastic elements. This modulation is akin to human muscular cocontraction and is achieved using only four motors. The mechanical configuration employed results in a compact and lightweight device with anthropomorphic characteristics, making it potentially suitable for applications such as prosthetics and humanoid robotics. This design aims to enhance performance in dynamic tasks, improve task adaptability, and ensure safety during interactions with both people and objects. The paper details the first hardware implementation of the proposed design, providing insights into the theoretical model, mechanical and electronic components, as well as the control architecture. System performance is assessed using a motion capture system. The results demonstrate that the prototype offers a broad range of motion ($[55, -45]$° for flexion/extension, $\pm48$° for radial/ulnar deviation, and $\pm180$° for pronation/supination) while having the capability to triple its stiffness. Furthermore, following proper calibration, the wrist posture can be reconstructed through multivariate linear regression using rotational encoders and the forward kinematic model. This reconstruction achieves an average Root Mean Square Error of 6.6°, with an $R^2$ value of 0.93.

Figures (18)

• Figure 1: The VS-Wrist compared to a human forearm (model’s size: forearm length 247 mm, forearm circumference 265 mm. Comprised between the 5th and 50th percentile male nasa_dim).
• Figure 2: Panel (a) depicts a schematic architecture of the 2 DoFs VS joint integrated into the VS-Wrist. Its kinematic configuration is a parallel manipulator that achieves hemispherical movements of the coupler. Each leg, distinguished by a specific color, consists of a motor unit, a non-linear elastic transmission, and a kinematic chain of four revolute joints. Panel (b) displays the CAD of the VS-Wrist equipping a robotic prosthetic hand and highlights its DoFs. Panel (c) shows a close-up picture of the prototype.
• Figure 3: Definition of the local reference coordinate frames of a generic leg according to the Denavit Hartenberg convention. d, $\eta$, and $\alpha$ are fixed design parameters.
• Figure 4: Schematic representation of the PS transmission. Each UJ is represented with two perpendicular and incident revolute joints, positioned at the center of either the fixed base frame or the coupler. Note that the two UJs are 90° out of phase to counteract the changing angular velocity of the driving shaft introduced by the lower UJ. The table on the right summarizes the Denavit Hartenberg parametrization of the kinematic chain. $L = d \sqrt{2(1-\cos(\alpha)} = 37.5$ mm is a fixed design parameter.
• Figure 5: The various panels depict the nominal range of motion of the 2 DoFs VS joint, illustrating the kinematic behavior of the system using the inverse kinematic model. Panels (a) to (e) represent motion around the $Y_b$-axis, while panels (f) to (j) showcase a revolution around the $Z_b$-axis (from $\frac{\pi}{2}$ to $-\frac{\pi}{2}$).