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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (10): 1843-1851    DOI: 10.3785/j.issn.1008-973X.2019.10.001
机械与能源工程     
基于模型预测控制的仿人机器人实时步态优化
丁加涛(),何杰,李林芷,肖晓晖*()
武汉大学 动力与机械学院，湖北 武汉 430072
Real-time walking pattern optimization for humanoid robot based on model predictive control
Jia-tao DING(),Jie HE,Lin-zhi LI,Xiao-hui XIAO*()
School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China
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摘要：

为了提高仿人机器人在行走过程中的抗干扰能力，提出基于模型预测控制（MPC）的步态生成与优化策略. 基于飞轮倒立摆模型（IPFM），建立系统状态空间模型. 给定落脚点参考位置和躯干旋转参考角度，提出包含质心（CoM）轨迹生成、落脚点调整和躯干旋转角度优化的多目标惩罚函数；考虑足部支撑范围、落脚点变动范围等可行性约束，建立二次规划（QP）求解模型. 利用开源求解器，实现最优质心轨迹、足部落脚点和躯干旋转角度的在线生成. 通过仿真验证了该算法的可行性和有效性. 结果表明，每个控制循环在2 ms内完成，满足实时控制需求；该方法能够利用躯干旋转以实现更大范围变步行参数的稳定行走；与只调整落脚点相比，机器人对各个方向外力的抵抗能力都有提高.
关键词： 模型预测控制（MPC）;  飞轮倒立摆模型（IPFM）;  落脚点调整;  躯干转动;  双足步行;  仿人机器人    
Abstract:

A model predictive control (MPC) strategy was proposed for walking pattern generation and optimization in order to compensate for the dynamic disturbances during the walking process of a humanoid robot. The state equation of the locomotion system was established based on the inverted pendulum plus flywheel model (IPFM). Given the reference step locations and reference body rotation angles, the multi-objective cost function was proposed, where the center of mass (CoM) trajectory generation, step locations adjustment and trunk rotation optimization were addressed simultaneously. The quadratic programming (QP) problem was formulated by considering the feasibility constraints including the constraints of maximal support region, limits of step location variation and others. The optimal CoM trajectory, step locations and trunk rotation angles were computed online by using the open-sourced solver. The simulation results demonstrated the feasibility and effectiveness of the proposed method. Results show that each control loop is solved within 2 ms so that it can be used in real time. The proposed method endows humanoids with the ability of walking stably with larger variation of step parameters by exploiting reactive trunk rotation. The robot can recover from severer external pushes from different directions by using the proposed method, compared with other strategies which merely adjust the step locations.
Key words: model predictive control (MPC)    inverted pendulum plus flywheel model (IPFM)    step locations adaptation    trunk rotation    bipedal walking    humanoid robot
收稿日期: 2019-02-01 出版日期: 2019-09-30
CLC:  TP 242  
通讯作者: 肖晓晖     E-mail: jtdingx@163.com;xhxiao@whu.edu.cn
作者简介: 丁加涛（1993—），男，博士生，从事双足步行研究. orcid.org/0000-0002-2396-9688. E-mail： jtdingx@163.com
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引用本文:

丁加涛,何杰,李林芷,肖晓晖. 基于模型预测控制的仿人机器人实时步态优化[J]. 浙江大学学报(工学版), 2019, 53(10): 1843-1851.

Jia-tao DING,Jie HE,Lin-zhi LI,Xiao-hui XIAO. Real-time walking pattern optimization for humanoid robot based on model predictive control. Journal of ZheJiang University (Engineering Science), 2019, 53(10): 1843-1851.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.10.001    或    http://www.zjujournals.com/eng/CN/Y2019/V53/I10/1843

图 1  双足步行飞轮倒立摆模型
图 2  双足步行足部支撑多边形与ZMP、CoM轨迹
图 3  COMAN机器人虚拟样机与ODE仿真环境
参数 数值 参数 数值
${\alpha _{{{{C}}_{{x}}}}}$ 2×105 ${\alpha _{{{{C}}_{{y}}}}}$ 105
${\alpha _{{{{\varTheta }}_{\rm{r}}}}}$ 5×109 ${\alpha _{{{{\varTheta }}_{\rm{p}}}}}$ 106
${\beta _{{{{C}}_{{x}}}}}$ 10 ${\beta _{{{{C}}_{{y}}}}}$ 10
${\beta _{{{{\varTheta }}_{\rm{r}}}}}$ 105 ${\beta _{{{{\varTheta }}_{\rm{p}}}}}$ 103
${\gamma _{{{{C}}_{{x}}}}}$ 1 ${\gamma _{{{{C}}_{{y}}}}}$ 1
${\gamma _{{{{\varTheta }}_{\rm{r}}}}}$ 10 ${\gamma _{{{{\varTheta }}_{\rm{p}}}}}$ 10
${\delta _{{{{D}}_{{x}}}}}$ 5×107 ${\delta _{{{{D}}_{{y}}}}}$ 5×107
Nh 31 Nf 2
Nc 415 dt/s 0.05
T/s 0.8 m/kg 30
Ix（Iy）/（kg·m2） 0.3 g/（m·s?2） 9.8
表 1  机器人与控制器的模型参数设置
参数 数值 参数 数值
$p_{{x}}^{\min }$/m ?0.03 $p_{{x}}^{\max }$/m 0.07
$p_{{y}}^{\min }$/m ?0.05 $p_{{y}}^{\max }$/m 0.05
$s_{{x}}^{\min }$/m ?0.2 $s_{{x}}^{\max }$/m 0.3
$s_{{y}}^{\min }$/m ?0.1 $s_{{y}}^{\max }$/m 0.2
$\dot d_{{x}}^{\min }$/（m·s?1） ?2 $\dot d_{{x}}^{\max }$/（m·s?1） 3
$\dot d_{{y}}^{\min }$/（m·s?1） ?2 $\dot d_{{y}}^{\max }$/（m·s?1） 2
$\theta _{\rm{r}}^{\min }$/（o） ?5 $\theta _{\rm{r}}^{\max }$/（o） 10
$\theta _{\rm{p}}^{\min }$/（o） ?10 $\theta _{\rm{p}}^{\max }$/（o） 10
$\tau _{\rm{r}}^{\min }$/（N·m） ?60 $\tau _{\rm{r}}^{\max }$/（N·m） 80
$\tau _{\rm{p}}^{\min }$/（N·m） ?80 $\tau _{\rm{p}}^{\max }$/（N·m） 80
表 2  二次规划约束条件参数设置
周期 步长/cm 步宽/cm 周期 步长/cm 步宽/cm
5 5 ? 9 ?5 14
6 15 ? 10 0 14
7 5 16 11 ?5 0
8 15 16 12 5 0
表 3  变步行参数设置
图 4  变步行参数行走躯干转动角度
图 5  变步行参数行走前向足部支撑区域和ZMP、CoM轨迹
图 6  变步行参数行走侧向足部支撑区域和ZMP、CoM轨迹
图 7  变步行参数行走CoM轨迹
图 8  沿y轴负方向25 N外力作用下不同策略对应的实际落脚点和实际CoM轨迹
图 9  沿y轴负方向25 N外力作用下不同策略生成的横滚角度和实际横滚角度
N
策略 x轴正向 x轴负向 y轴正向 y轴负向
仅落脚点调整 240 165 167 30
落脚点调整+躯干转动 308 185 202 65
表 4  不同方向的最大抵抗外力
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