漂浮基机械臂系统耦合动力学与解耦控制方法

陈正仓; 贾峰

doi:10.13433/j.cnki.1003-8728.20220175

漂浮基机械臂系统耦合动力学与解耦控制方法

doi: 10.13433/j.cnki.1003-8728.20220175

陈正仓,
贾峰^,

长安大学工程机械学院，西安　710064

基金项目: 国家自然科学基金项目(52275005，52105085)与陕西省自然科学基金项目(2022JQ-342)

详细信息

作者简介:
陈正仓（1989−），工程师，博士研究生，研究方向为移动机器人耦合动力学与控制技术，chenzhc8905@chd.edu.cn

通讯作者:
贾峰，讲师，博士研究生，jiafeng@chd.edu.cn

中图分类号: TH24
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- 文章访问数: 132
- HTML全文浏览量: 46
- PDF下载量: 26
- 被引次数: 0
出版历程
- 收稿日期: 2021-11-04
- 刊出日期: 2023-12-25

Coupling Dynamics and Coordinated Control Method of Space Floating Manipulator System

CHEN Zhengcang,
JIA Feng^,

School of Construction Machinery, Chang'an University, Xi'an 710064, China

摘要

摘要: 在执行空间任务过程中，漂浮基机械臂系统内部的动力学耦合现象使得基体姿态调整和机械臂末端定位与控制问题变得更加复杂。综合考虑多种空间漂浮基机械臂系统共性特征，关注机械臂与基体耦合规律，建立统一的耦合动力学模型，并利用整个系统的非完整性特征和耦合特点，对特定系统设计解耦控制规律。通过控制机械臂关节主动运动实现基体位姿可控和机械臂末端任务不受制约的目的。结果表明，通过合理设置控制参数，在解空间存在的情况下，能够达到漂浮基体与机械臂末端协调运动的目的。
- 耦合动力学 /
- 漂浮基体 /
- 机械臂 /
- 控制 /
- 仿真
Abstract: In the process of space task, the dynamic coupling phenomenon in the floating base manipulator system makes the adjustment of the base posture and the positioning and control of the end of the manipulator more complex. In this paper, considering the common characteristics of various space-based manipulator systems, we focus on the coupling law between the manipulator and the floating base, establish a unified coupling dynamic model, and utilize the non-integrity and coupling characteristics of the whole system to design the coordinated control law for a specific system. Then, by controlling the active motion of the joint of the manipulator, the pose of the base can be controlled and the task at the end of the manipulator can be free. Finally, a simulation experiment is set up to verify the effectiveness of the proposed method. The results show that the coordinated motion of the floating base and the end of the manipulator can be achieved by reasonably setting the control parameters in the presence of solution space.
- coupling dynamics /
- floating base /
- manipulator /
- cooperative control /
- simulation

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图 1 可移动基机械臂系统的多种类型^{[12, 21]}

Figure 1. Various types of mobile base manipulator system

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图 2 系统简化示意图

Figure 2. Simplified diagram of a manipulator system

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图 3 控制流程图设计

Figure 3. Control design procedure

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图 4 单臂浮动基空间机械臂模型

Figure 4. Model of single arm floating base space manipulator

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图 5 漂浮基6-DOF机械臂系统关节零位构型

Figure 5. Initial configuration of a 6-DOF SBMS

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图 7 关节角轨迹跟踪曲线

Figure 7. Joint angle trajectory tracking curve

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图 8 跟踪误差曲线

Figure 8. Tracking error curve

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图 9 广义惯量变化趋势图

Figure 9. Generalized inertia variation

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图 6 系统仿真流程

Figure 6. The simulation procedures flowchart of the system

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图 10 系统解耦仿真流程图

Figure 10. Decoupling process simulation flow chart

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图 11 关节空间轨迹曲线

Figure 11. The joint paths

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图 12 关节力矩曲线

Figure 12. The torque curves of joints

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图 13 耦合度变化曲线

Figure 13. Coupled force curves

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图 14 系统构型与姿态变化简图

Figure 14. Configuration and attitude change

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表 1 运动学参数及定义

Table 1. Kinematic parameters and their definitions

参数	定义
N	N=kn（n为机械臂关节，k为机械臂个数）
${\boldsymbol{\phi }}\in {\Re ^n}$	关节角变量
${{\boldsymbol{r}}_i} \in {\Re ^3}$	连杆i位置矢量
${{\boldsymbol{a}}_i},{{\boldsymbol{b}}_i} \in {\Re ^3}$	质心i指向关节i的方向向量
${{\boldsymbol{k}}_i} \in {\Re ^3}$	关节i的单位方向向量
${{\boldsymbol{v}}_i},{{\boldsymbol{\omega}}_i} \in {\Re ^3}$	连杆i的质心速度和角速度
${{\boldsymbol{V}}_i} = {\left[ {\dot {\boldsymbol{r}}_i^{\rm{T}},{\boldsymbol{\omega}}_i^{\rm{T}}} \right]^{\rm{T}}} \in {\Re ^{{\text{6}} \times {\text{1}}}}$	连杆i的速度旋量

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表 2 动力学相关参数及定义

Table 2. Notations of dynamic parameters and their definitions

参数	定义
${m_i},{I_i}$	连杆i的质量和惯性张量
${{\boldsymbol{X}}_P} \in {\Re ^{{\text{6}} \times {\text{1}}}}$	浮动基体位姿旋量
${\dot {\boldsymbol{x}}_P} = {\left[ {{\boldsymbol{v}}_0^{\text{T}},{\boldsymbol{\omega}}_0^{\text{T}}} \right]^{\rm{T}}} \in {\Re ^{6 \times 1}}$	浮动基体速度旋量
${{\boldsymbol{H}}_P} \in {\Re ^{{{6 \times 6}}}}$	基体参照自身的惯性张量
${{\boldsymbol{H}}_\phi } \in {\Re ^{n \times n}}$	机械臂参照自身的惯性张量
${{\boldsymbol{H}}_{P\phi }} \in {\Re ^{{\text{6}} \times n}}$	基体参照机械臂的耦合惯性张量
${{\boldsymbol{c}}_P} \in {\Re ^{{{6 \times 6}}}}$	基体的非线性速度相关项
${{\boldsymbol{c}}_\phi } \in {\Re ^{n \times n}}$	机械臂的非线性速度相关项
${{\boldsymbol{c}}_{P\phi }} \in {\Re ^{{\text{6}} \times n}}$	基体与机械臂之间的非线性耦合速度相关项
${{\boldsymbol{F}}_P} \in {R^{ {\text{6} } \times {\text{1} } } }$	作用于基体上的广义外部力项
${{\boldsymbol{F}}_E} \in {R^{ {\text{6} } \times {\text{1} } } }$	作用于机械臂末端的广义外部力项
${\boldsymbol{\tau}} \in {R^{n \times {\text{1}}}}$	关节力矩项
${{\boldsymbol{J}}_b} \in {\Re ^{ {\text{6} } \times {\text{6} } } }$	基体参照自身的雅可比矩阵
${{\boldsymbol{J}}_\phi } \in {\Re ^{ {6} \times n} }$	机械臂参照基体的雅可比矩阵

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表 3 漂浮基6-DOF机械臂系统几何惯性参数

Table 3. Geometric and inertia parameters of a floating-base

名称	Base	L₁	L₂	L₃	L₄	L₅	L₆
质量/kg	13350	49.4	82307	56.59	21443	9.11	4.51
${\boldsymbol{a}}/{\rm{m} }$	–	0	−0.52	−0.16	0	−0.026	0
	–	0	0	0	0	0	0
	–	−0.205	0	0	−0.4	0	−0.025
${\boldsymbol{ b}}/{\rm{m} }$	0	0	1.88	0.25	0	0.105	0
	0	0	0	0	0	0	0
	0.996	0.105	0	0	1.1	0
${\boldsymbol{ I}}/\left(\mathrm{ ~ kg} \cdot \mathrm{m}^{2}\right)$	6168.5	3.338	1967	0.605	2945	6.9 × 10⁻²	3.7 × 10⁻²
	6168.3	2.236	38063	0.62	2947	6.24 × 10⁻²	3.07 × 10⁻²
	9738.4	3.088	38627	0.69	152.9	8.65 × 10⁻²	2.12 × 10⁻²
	0.05	9 × 10⁻⁴	0.331	3.13 × 10⁻²	2.18 × 10⁻⁴	1.9 × 10⁻²	8 × 10⁻⁵
	1.1 × 10⁻³	6.70 × 10⁻⁵	4.23 × 10⁻²	1.17 × 10⁻⁴	0.279	1.09 × 10⁻³	4 × 10⁻³
	0.103	−7.7 × 10⁻⁶	6.65	2.08 × 10⁻⁴	−5.76 × 10⁻³	7.8 × 10⁻⁴	3.6 × 10⁻⁶

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