A Compact Variable Stiffness Actuator for Agile Legged Locomotion

TL;DR

This work introduces the Variable-Length Leaf-Spring Actuator (VLLSA), a compact, leaf-spring-based VSA designed for agile legged locomotion. By decoupling stiffness modulation from robot configuration and employing a gear-assisted, slider-driven leaf-spring, the VLLSA achieves a wide stiffness range with fast modulation and low energy consumption, while enabling accurate open-loop stiffness models. A real-time hopping controller based on Virtual Model Control integrates online stiffness variation, and hardware experiments (in-place and forward hopping) demonstrate improved hopping height, reduced instantaneous knee power, and overall energy efficiency compared with fixed-stiffness and direct-drive modes. The results suggest that VLLSA can enhance the agility and energy efficiency of legged robots in dynamic tasks, with potential for further optimization toward continuous stiffness control and larger stiffness ranges.

Abstract

The legged robots with variable stiffness actuators (VSAs) can achieve energy-efficient and versatile locomotion. However, equipping legged robots with VSAs in real-world application is usually restricted by (i) the redundant mechanical structure design, (ii) limited stiffness variation range and speed, (iii) high energy consumption in stiffness modulation, and (iv) the lack of online stiffness control structure with high performance. In this paper, we present a novel Variable-Length Leaf-Spring Actuator (VLLSA) designed for legged robots that aims to address the aforementioned limitations. The design is based on leaf-spring mechanism and we improve the structural design to make the proposed VSA (i) compact and lightweight in mechanical structure, (ii) precise in theoretical modeling, and (iii) capable of modulating stiffness with wide range, fast speed, low energy consumption and high control performance. Hardware experiments including in-place and forward hopping validate advantages of the proposed VLLSA.

Figures (7)

• Figure 1: (a) Overview of VLLSA-leg. (b) Cross section of VLLSA-leg. (c) The installation size of VLLSA. The leg is controlled by the DJI Development Board Type C and the embedded brushless-FOC drivers on the joint motors. The controller board communicates with the motor drivers and broadcasts commands through CAN at 1KHz. The hip and knee joints are respectively driven by 8016 motor with 1:6 planetary reducer. The stiffness motor is Maxon EC 22L(24V).
• Figure 2: Modeling of VLLSA. (a) The bending part of leaf-spring within the two pairs of roller-bearing. (b) The slider and linear guide maintain a zero slope of the undeflected part. (c) The modeling mechanism of VLLSA-leg.
• Figure 3: The experimental platform to test VLLSA.
• Figure 4: Experiment results. (a) Output stiffness with respect to slider position. Two fixed deformation angles of leaf spring $q= \{12^{\circ}, 20^{\circ}\}$ are selected for demonstration. The red star and blue triangles denote the data with $q=12^{\circ}$ and $q=20^{\circ}$ respectively. (b) Output torque with respect to deformation angle. The red square and blue circle denote the data with $x=35$mm and $x=70$mm respectively. (c) Speed of output stiffness modulation. The red star and blue dot denote the data with variation of Low Stiffness (LS, $x=35$ mm) to High Stiffness (HS, $x=70$ mm) and HS to LS respectively. (d) The average power to change the output stiffness, the legend is the same as in (c).
• Figure 5: Hopping control strategy. (a) Parameters of the VMC designed for VLLSA-leg; (b) Hopping control strategy. The red arrow shows slider switches from high stiffness to low stiffness, and the blue arrow shows slider switches from low stiffness to high stiffness.

Theorems & Definitions (1)

• Remark 1: Spring selection