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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (2): 244-250    DOI: 10.3785/j.issn.1008-973X.2021.02.004
    
Gait planning of quadruped robot based on divergence component of motion
Ming-min LIU1,2,3(),Dao-kui QU1,2,4,Fang XU1,2,4,*(),Feng-shan ZOU1,2,4,Kai JIA1,2,4,Ji-lai SONG4
1. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
2. Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, China
3. University of Chinese Academy of Sciences, Beijing 100049, China
4. Shenyang SIASUN Robot and Automation Co. Ltd, Shenyang 110168, China
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Abstract  

An online gait planning method based on the divergence component of motion (DCM) was proposed in order to make the quadruped robot move stably when a large trajectory tracking error occurs. The quadruped robot was simplified into a 3D linear inverted pendulum model (LIPM). The DCM methodology was used to calculate the reference trajectory that keeps the DCM bounded according to the footprint of offline planning. Gait planning applied loose initial state model predictive control to optimize the footprint and desired state trajectory that can quickly converge to the reference trajectory online, under the condition of satisfying the stride constraints and zero moment point (ZMP) constraints. The whole body control was used to optimize the torque to track the trajectory of the desired state under the conditions of motion constraints, dynamic constraints, and friction constraints by constructing a quadratic program. The above algorithm was verified by simulation and results show that loose initial state model predictive control can tolerate larger trajectory tracking errors compared with traditional model predictive control and the quadruped robot can move steadily in troting gait and converge to the reference trajectory as soon as possible when a large trajectory tracking error of DCM occurs.

Key words： quadruped robot      gait planning      divergent component of motion (DCM)      linear inverted pendulum model (LIPM)      zero moment point (ZMP)     
Received: 17 March 2020      Published: 09 March 2021
CLC:  TP 242  
Fund:  国家重点研发计划资助项目（2017YFC0806700）；山东省重大科技创新工程资助项目（2019JZZY010128）
Corresponding Authors: Fang XU     E-mail: liumingmin@siasun.com;xufang@sia.cn
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Ming-min LIU
Dao-kui QU
Fang XU
Feng-shan ZOU
Kai JIA
Ji-lai SONG
Cite this article:

Ming-min LIU,Dao-kui QU,Fang XU,Feng-shan ZOU,Kai JIA,Ji-lai SONG. Gait planning of quadruped robot based on divergence component of motion. Journal of ZheJiang University (Engineering Science), 2021, 55(2): 244-250.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.02.004     OR     http://www.zjujournals.com/eng/Y2021/V55/I2/244


基于运动发散分量的四足机器人步态规划

为了使四足机器人在出现较大的轨迹跟踪误差时仍然可以稳定运动，提出基于运动发散分量（DCM）的在线步态规划方法. 将四足机器人抽象成三维线性倒立摆模型（LIPM），根据离线规划的落脚点，应用DCM方法论递推出保持DCM有界的参考轨迹；在满足步幅约束、零力矩点（ZMP）约束的条件下，步态规划运用宽松初始状态模型预测控制在线优化出可快速收敛到参考轨迹上的落脚点以及期望状态轨迹；全身运动控制器通过构建二次规划优化出满足运动约束、动力学约束、摩擦力约束等条件下跟踪期望状态轨迹的力矩. 通过仿真验证以上算法，仿真结果表明：与经典模型预测控制相比，宽松初始状态模型预测控制可以承受较大的轨迹跟踪误差，四足机器人可以在出现较大的轨迹跟踪误差时以troting步态稳定运动并尽快收敛到离线规划的轨迹上.


关键词： 四足机器人,  步态规划,  运动发散分量（DCM）,  线性倒立摆模型（LIPM）,  零力矩点（ZMP） 
Fig.1 Simplification of quadruped robot into a 3D linear inverted pendulum
Fig.2 Reference trajectory of state and input variables
Fig.3 ZMP boundary of quadruped robot
Fig.4 Block diagram of quadruped robot motion control architecture
Fig.5 Comparison of standard and loose initial state MPC
Fig.6 Robot physical prototype and virtual prototype
Fig.7 Sequence diagram of gait
参数 数值 参数 数值
${z_0}/{\rm{m}}$ 0.32 $\mu $ 0.4
$T /{\rm{s}}$ 0.25 $\alpha $ 20
$\lambda/{\rm{m}}$ 0.1 ${\tau _{ {\rm{min} } } }/({\rm{N}}\cdot {\rm{m}})$ ?35
$N$ 4 ${\tau _{ {\rm{max} } } }/({\rm{N}}\cdot {\rm{m}})$ 35
${{ Q}}$ ${\rm{diag}}\;[100,\;100,\;1,\;1]$ ${k_{\rm{\xi }}}$ 300
${{R}}$ ${\rm{diag}}\;[100,\;100]$ ${{S}}$ ${\rm{diag}}\;[70,\;0,\;100,\;80,\;80,\;80]$
${{V}}$ ${\rm{diag}}\;[10,\;10]$ ${{W}}$ $10{{I}}$
${{{p}}_{{\rm{cur}}}}$ ${\left[ \!\!\!{\begin{array}{*{20}{c}} 0,&0 \end{array}} \!\!\!\right]^{\rm{T}}}$ ${{{\delta }}_{{\rm{cur}}}}$ ${\left[ \!\!\!\!\!\!\!\!\!\!{\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 0,\!\!\!&\!\!\!0 ,\end{array}}\!\!\!{\begin{array}{*{20}{c}} 0,\!\!\!&\!\!\!0 \end{array}} \end{array}}\!\!\! \!\!\!\!\!\!\!\right]^{\rm{T}}}$
Tab.1 Parameter settings in quadruped robot simulation
Fig.8 Simulation results of trotting gait trajectory tracking
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