﻿ 四足机器人静-动步态平滑切换算法
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 山东大学学报(工学版)  2018, Vol. 48 Issue (4): 42-49  DOI: 10.6040/j.issn.1672-3961.0.2017.364 0

### 引用本文

XIN Yaxian, LI Yibin, LI Bin, RONG Xuewen. Smooth walk-to-trot gait transition algorithm for quadruped robot[J]. Journal of Shandong University (Engineering Science), 2018, 48(4): 42-49. DOI: 10.6040/j.issn.1672-3961.0.2017.364.

### 文章历史

1. 山东大学控制科学与工程学院, 山东 济南 250061;
2. 齐鲁工业大学(山东省科学院)理学院, 山东 济南 250353

Smooth walk-to-trot gait transition algorithm for quadruped robot
XIN Yaxian1, LI Yibin1, LI Bin2, RONG Xuewen1
1. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China;
2. School of Science, Qilu University of Technology(Shandong Academy of Sciences), Jinan 250353, Shandong, China)
Abstract: In order to improve the adaptability of quadruped robot for various terrains, different cases that could occur when robot changed its gaits from walk to trot were analyzed and the optimal transition algorithms which could let gait transition more smooth and waste least time when robot kept stability were proposed. In order to ensure the smoothness of transition sequence, the speed formula of time was given to keep the center of gravity constant acceleration. An algorithm named modified wide stability margin method (MWSM) was proposed to offset the stand back influenced by inertial force and caused by the acceleration through adjust the relative position of the trunk and four feet. The model of quadruped robot was constructed based on the robot simulator Webots, and simulation results showed the validity and effectiveness of the algorithm. The approach could be applied in six points of one static walk circle and switched to trot smoothly and steadily.
Key words: quadruped robot    static walk    trot    smooth gait transition
0 引言

1 间歇静步态分析

 图 1 间歇静步态一个步态周期的六阶段 Figure 1 Six stages of the static walk of one gait period

walk步态向trot步态切换过程中, 若不考虑切换点时机器人的状态, 给定一个统一或简化的机器人切换规则, 有时会导致机器人失稳或等待切换时间过长, 不利于提高步态切换效率。因此, 本研究根据walk步态切换点xh的不同进行细分, 当切换条件触发时, 利用状态机进行机器人当前状态的判定, 对每一个切换点给出一个切换规则, 在保证平稳切换的基础上, 实现机器人在最短切换时间下的平滑步态变换。

2 对角小跑步态分析

 图 2 对角小跑步态 Figure 2 The trotting gait

 \left\{ \begin{align} &{{x}_{\text{RFh}}}={{x}_{\text{LHh}}}=-L\prime /2 \\ &\text{ }{{x}_{\text{LFh}}}={{x}_{\text{RHh}}}=L\prime /2 \\ \end{align} \right., (1)

 \left\{ \begin{align} &{{x}_{\text{RFh}}}={{x}_{\text{LHh}}}=L\prime /2 \\ &{{x}_{\text{LFh}}}={{x}_{\text{RHh}}}=-L\prime /2 \\ \end{align} \right.。 (2)
3 间歇静步态向对角小跑步态切换

3.1 节律控制

(1) 获取xRFhxRHhxLFhxLHh作为输入。

(2) 定义变量(d, f, h)。d=1, 右侧足xh值非零; d=0, 左侧足xh值非0。针对xh非零一侧, f=1, 前腿xh值大于0; f=0, 前腿xh小于0; h=1, 后腿xh大于0; h=0, 后腿xh等于0。

(3) 若f+h < 2, 执行(4);若f+h=2, 执行(5)。

(4) 若d=1, 重心向右侧移动s; 若d=0, 重心向左侧移动s。结束切换队列1。转(6)。

(5) 若d=1, 重心向右向前移动, 解耦为向右移动s, 向前移动L/2;d=0, 重心移动解耦为向左移动s, 向前移动L/2。

(6) 若d=1且h=1, 或d=0且h=0, 队列2中的摆动足为RH足所在的DL1, 支撑足为DL2; 否则摆动足为LH足所在的DL2, 支撑足为DL1; 支撑足支撑身体前移L′, 摆动足落足点在自身髋关节前方L′/2处。切换队列2结束。

(7) 切换队列2中的支撑足作为切换队列3中的摆动足, 摆动足作为支撑足, 仍使支撑足支撑身体前移L′, 摆动足落足在自身髋关节前方L′/2处。切换队列3结束。

3.2 模式控制

walk-to-trot步态切换中, 除了要改变节律之外, 其步长S、周期T、重心移动速度v都需要进行相应调整。三者关系为v=S/T。但是, 间歇静步态的重心前移不是均匀分布在整个周期中, 而是集中在1/3个周期。因此, 将间歇静步态重心的实际移动速度记为vwalk=3L/Twalk, 其中Twalk为walk步态的周期。而对trot步态一个周期的两个阶段, 重心不断前移, 速度记为vtrot=2L′/Ttrot, 其中Ttrot为trot步态的周期。

 ${{L}_{t}}={{v}_{\text{walk}}}t+0.5a{{t}^{2}},$ (3)
 ${{v}_{t}}={{v}_{\text{walk}}}+at。$ (4)

 ${{v}_{t}}={{v}_{\text{walk}}}+\frac{v_{\text{trot}}^{2}-v_{\text{walk}}^{2}}{2{{L}_{\text{sum}}}}t。$ (5)

 $\frac{ma}{mg}=\frac{l}{\text{high}},$ (6)

 图 3 改进的泛稳定裕量判据法 Figure 3 Criteria method of modified wide stability margin
4 仿真试验与结果分析

 图 4 四足机器人仿真模型 Figure 4 Simulation model of the quadruped robot

 图 5 walk-to-trot步态序列切换情况1示意图 Figure 5 Schematic diagram of the status during the case 1 of walk-to-trot gait sequence transition

 图 6 walk-to-trot步态序列切换情况1仿真截图 Figure 6 Simulation snapshots of the status during the case 1 of walk-to-trot gait sequence transition

 图 7 四足足端位置数据曲线图 Figure 7 The data graph of the four feet′ position
 图 8 躯干质心沿z轴位置数据曲线图 Figure 8 The data graph of the body′ position on z axis
 图 9 稳定裕量数据曲线图 Figure 9 The data graph of the stability value
 图 10 步态序列切换速度曲线 Figure 10 The data graph of gait sequence transition′s speed

 图 11 WSM和MWSM方法稳定裕度比较曲线图 Figure 11 Comparison curve of the stability margin between WSM and MWSM method

5 结语