用于四足机器人的并联弹性腿足关节设计与优化

doi:10.12382/bgxb.2023.0897

摘要/Abstract

摘要：

为了提升四足机器人腿足的运动性能,设计一种具有并联弹性驱动器(Parallel Elastic Actuator,PEA)的腿足关节,通过模仿四足动物的肌腱作用原理,将拉簧并联在小腿连杆和大腿连杆之间,在膝关节处实现了并联弹性驱动,具有尺寸小、质量和惯量低的特点。建立了PEA膝关节的动力学模型,并借助该模型,在预设跟踪任务轨迹下,综合考虑峰值力矩、峰值功率和能量利用率,对拉簧的刚度系数进行多目标优化,得到全局最优的拉簧刚度为5510N/m。为了对比本PEA关节与电机直驱关节的性能,从仿真和实验两个方面进行验证。利用Gazebo机器人仿真环境,使用带有刚度的滑动副来实现PEA拉簧的效果,通过物理引擎模拟获取关节电机的输出力矩、输出功率、机械能耗;搭建PEA膝关节实验平台开展样机实验,获取膝关节电机的电源输入参数,如输入电流、输入功率、电源能耗。实验结果表明:PEA对比电机直驱关节,在0.5~2.0s的轨迹周期下,电机输出方面可以减少峰值力矩40%~79%、峰值功率52%~89%和机械能损耗40%~89%,电机输入方面可以减少峰值电流46%~77%、峰值电功率43%~76%和电能损耗62%~73%。

关键词: 四足机器人, 并联弹性驱动器, 刚度优化, 能量损耗

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

中图分类号:

TP242

刘思宇, 廖峻北, 雷飞, 王志瑞, 闫曈, 党睿娜, 郭朝. 用于四足机器人的并联弹性腿足关节设计与优化[J]. 兵工学报, 2023, 44(S2): 71-83.

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.

图/表 17

图1 四足机器人用并联弹性腿

Fig.1 Quadruped robot with PEA leg

图2 并联弹性腿爆炸图

Fig.2 Exploded view of PEA leg

表1 并联弹性腿机械参数

Table 1 Mechanical parameters of PEA leg

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

图3 拉簧布置

Fig.3 Layout of tension spring

图4 PEA膝关节的动力学模型

Fig.4 Dynamics model of knee joint driven by PEA

表2 并联弹性腿动力学参数

Table 2 Dynamics parameters of PEA leg

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

图5 PEA拉簧刚度优化过程

Fig.5 Optimization process of PEA’s tension spring stiffness

图6 峰值力矩、峰值功率、能量损耗和优化目标函数的热力图

Fig.6 Heatmaps of peak torque, peak power, energy consumption and target optimization function

图7 Gazebo环境下机器人描述

Fig.7 Robot description in Gazebo environment

图8 虚拟拉簧与虚拟拉簧工作原理

Fig.8 Virtual tension spring and its working principle

图9 从电机输出特性层面验证理论和仿真下并联弹性腿的有效性

Fig.9 Effectiveness of PEA leg validated from the perspective of motor output characteristics in theory and simulation

表3 理论模型与仿真实验,验证峰值力矩、峰值功率和能量损耗减少量与减少百分比

Table 3 Reduction in quantity and percentage of peak torque, peak power and energy consumption validated by dynamics model and simulation

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%)

图10 前跃轨迹实验

Fig.10 Experiments of forward jumping

表4 前跃轨迹实验,有PEA对比无PEA在峰值力矩、峰值功率、能量损耗方面的减少

Table 4 Reduction in peak torque, peak power, and energy consumption with and without PEA in the experiments of forward jumping

l_x/m	峰值力矩/(N·m)	峰值功率/W	能量损耗/J
0.00	4.14 (42.50%)	18.86 (54.66%)	3.91 (50.34%)
0.08	4.01 (38.11%)	11.65 (34.88%)	2.34 (30.50%)
0.16	3.94 (21.87%)	7.76 (29.28%)	1.92 (12.52%)
0.24	3.55 (15.65%)	4.63 (18.31%)	0.95 (5.27%)

图11 并联弹性腿样机测试

Fig.11 Prototype experiment setup of PEA leg

图12 从电机电源输入层面验证并联弹性腿有效性

Fig.12 Effectiveness of PEA leg validated from the perspective of electricity input

表5 样机实验,验证峰值电流、峰值电功率和电能损耗减少量与减少百分比

Table 5 Reduction in quantity and percentage of peak current, peak electrical power and electrical energy consumption for validating PEA’s improvements

周期/s	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%)
1.0	4.08 (79.59%)	10.67 (89.24%)	5.93 (89.18%)
1.5	3.30 (77.83%)	6.35 (84.73%)	5.92 (88.96%)
2.0	2.89 (73.64%)	4.54 (81.93%)	5.72 (85.91%)

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