Design and Optimization of a Parallel Elastic Actuator Leg for Quadruped Robots

doi:10.12382/bgxb.2023.0897

Abstract

Abstract:

A parallel elastic actuator (PEA) leg is proposed to improve the motion performance of quadruped robots. By imitating the tendon-driven mechanism of quadruped animals, a tension spring is connected in parallel between the calf link and the thigh link to achieve parallel elastic effect at the knee joint. The PEA leg exhibits small size, low mass, and low inertia characteristics. A dynamics model of PEA knee joint is established. The proposed model is used for a multi-objective optimization of spring stiffness in considering peak torque, peak power, and energy efficiency in a predefined trajectory tracking task. The most optimal spring stiffness is determined to be 5510N/m. The performances of PEA joint and rigid actuator (RA) joint are compared through simulation and prototype experiments. A prismatic joint with stiffness is employed to simulate the effect of PEA tension spring in the Gazebo robot simulation environment. The output torque, power, and mechanical energy consumption of knee motor are obtained through physics engine simulation. A PEA knee joint experimental platform is constructed, and the prototype experiments are conducted to obtain the electrical parameters of the knee joint motor, such as input current, input power, and electrical energy consumption. The experimental results demonstrate that, compared to RA joint, the PEA joint achieves significant improvements. Specifically, within the trajectory period from 0.5s to 2.0s, the PEA joint reduces peak torque by 40% to 79%, peak power by 52% to 89%, and mechanical energy consumption by 40% to 89% in terms of motor output. Regarding motor input, the PEA joint reduces peak current by 46% to 77%, peak power by 43% to 76%, and electrical energy consumption by 62% to 73%.

Key words: quadruped robots, parallel elastic actuator, stiffness optimization, energy consumption

CLC Number:

TP242

LIU Siyu, LIAO Junbei, LEI Fei, WANG Zhirui, YAN Tong, DANG Ruina, GUO Zhao. Design and Optimization of a Parallel Elastic Actuator Leg for Quadruped Robots[J]. Acta Armamentarii, 2023, 44(S2): 71-83.

Figures/Tables 17

References 25

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名称	限位/(°)	长度/m	质量/kg
HAA	[-30, 30]
HFE	[-200, 40]
KFE	[25, 130]
髋			0.58
大腿		0.220	1.48
小腿		0.201	0.15
足底		0.025	0.03

名称	限位/(°)	长度/m	质量/kg
HAA	[-30, 30]
HFE	[-200, 40]
KFE	[25, 130]
髋			0.58
大腿		0.220	1.48
小腿		0.201	0.15
足底		0.025	0.03

参数	数值
输入输出连杆长度l_m/m	0.025
大腿长度l₁/m	0.220
小腿长度l₂/m	0.201
大腿质量m₁/kg	2.064
小腿质量m₂/kg	0.148
大腿转动惯量j₁/(kg·m²)	0.004
小腿转动惯量j₂/(kg·m²)	0.0003
大腿质心相对于大腿连杆长度的比例r₁	0.9
小腿质心相对于小腿连杆长度的比例r₂	0.2

参数	数值
输入输出连杆长度l_m/m	0.025
大腿长度l₁/m	0.220
小腿长度l₂/m	0.201
大腿质量m₁/kg	2.064
小腿质量m₂/kg	0.148
大腿转动惯量j₁/(kg·m²)	0.004
小腿转动惯量j₂/(kg·m²)	0.0003
大腿质心相对于大腿连杆长度的比例r₁	0.9
小腿质心相对于小腿连杆长度的比例r₂	0.2

T/s	理论模型			仿真结果
T/s	峰值力矩/(N·m)	峰值功率/W	能量损耗/J	峰值力矩/(N·m)	峰值功率/W	能量损耗/J
0.5	4.08 (41.08%)	19.39 (52.75%)	2.62 (38.41%)	4.02 (39.88%)	19.53 (51.59%)	2.74 (40.10%)
1.0	4.08 (79.59%)	10.67 (89.24%)	5.93 (89.18%)	4.13 (79.42%)	10.90 (89.13%)	6.10 (89.24%)
1.5	3.30 (77.83%)	6.35 (84.73%)	5.92 (88.96%)	3.36 (77.73%)	6.50 (84.54%)	6.11 (89.34%)
2.0	2.89 (73.64%)	4.54 (81.93%)	5.72 (85.91%)	2.97 (73.98%)	4.68 (82.01%)	5.93 (86.72%)