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中北大学学位论文
双平台错动型混联六足机器人“旋龟”的构型设计与运动规划
摘要
城市中存在大量狭窄危险复杂的地下空间是人类不宜进入或无法进入的,例如年久
失修的防空洞、发生事故的煤矿井下、军事工程、暗挖隧道等。对这类狭窄危险复杂地
下空间的开发再利用意义重大,涉及国防安全和国计民生等诸多领域,是智慧城市的重
要标志。本文设计了一种基于混联机构的六足机器人“旋龟”,该六足机器人依靠并联机
构上、下平台的交替错动进行移动。由 R&(2-UPU/2-RPR)混联机构作为旋龟六足机器人
的机身,可以满足旋龟六足机器人进入地下空间执行搬运、巡检、维护等任务的要求。
首先,对旋龟六足机器人进行整体的构型设计,其中包括旋龟六足机器人机身机构
的设计以及固连于平台的腿部结构设计,并对旋龟六足机器人的关键零部件的尺寸、传
感器的安装位置等方面进行了设计。
其次,对 2-UPU/2-RPR 冗余并联机构进行了运动学分析。利用螺旋理论建立 2-
UPU/2-RPR 冗余并联机构的坐标系并验证了该机构的自由度数目;通过对机构特征的分
析,在保证机构约束关系的前提下,利用闭环矢量法求得机构的逆解方程;通过粒子群
优化算法的收敛特性构建机构的正解方程,根据给定的输入参数得到机构的正解算例,
并利用 Matlab 软件获得机构正解的适应度曲线;然后在得到机构位置逆解方程的基础
上求得该机构的速度 Jacobian 矩阵;随后利用 Jacobian 矩阵分析了 2-UPU/2-RPR 冗余
并联机构的奇异性;通过极限位置探索法得到了机构的工作空间,其形状规则且较为连
续,可知该机构有着良好的运动性能。
再次,对旋龟六足机器人进行了静力学及动力学分析。对于机器人的静力学分析采
用了拆杆法得到其力和力矩的平衡方程,随后通过静力学仿真,表明该六足机器人有着
较大的负载能力。接着对旋龟六足机器人进行动力学分析得到了其动力学方程,并进行
了模态分析,得到旋龟六足机器人分别在两组六条腿支撑以及各组三条腿支撑下的一到
六阶模态振型,并在此基础上对旋龟六足机器人谐响应进行了分析,得到了旋龟六足机
器人的频率-位移曲线,得到旋龟六足机器人的敏感频率,对于机器人共振的避免和机器
中北大学学位论文
人故障的诊断具有指导意义。
然后,对旋龟六足机器人进行了稳定性分析及步态规划。采用重心投影法分析旋龟
六足机器人的运动稳定性,并综合考虑旋龟六足机器人的稳定性以及腿部的干涉,得到
了旋龟六足机器人的运动极限参数,包括最大移动步幅以及在一个间歇周期中单次转动
的最大零半径转角;分析了旋龟六足机器人固连于两平台上两组腿的占空系数、运动顺
序、运动步幅以及各分支链在旋龟六足机器人运动过程中的杆长变化情况,并利用无冲
击复合摆线对旋龟六足机器人的足端运动轨迹进行了规划,极大的避免了旋龟六足机器
人在腿部与地面接触时产生的冲击。
最后,对旋龟六足机器人进行建模并对其在不同地形环境下的越障性能力进行了分
析。通过 SolidWorks 软件内置的 Motion 模块,对基于 R&(2-UPU/2-RPR)混联机构的双
平台错动型六足机器人“旋龟”在平地行走、攀越凸台、跨越沟壑以及零半径转弯四种
工况进行了模拟仿真,获得了旋龟六足机器人的位置、步态以及重心等一系列参数。并
通过仿真结果与理论轨迹的对比,得出旋龟六足机器人相互错动的两平台质心在竖直方
向上的变化规律是类似的,从而对建立的运动学模型进行了验证。
基于 R&(2-UPU/2-RPR)混联机构的双平台错动型六足机器人“旋龟”由于其适应地
形能力以及在狭窄环境下的零半径转弯能力等优越性能,在地下空间的开发再利用方面
具有广泛的应用前景。
关键词:旋龟六足机器人,R&(2-UPU/2-RPR)混联机构,构形设计,运动学,静
力学,步态规划,轨迹规划
中北大学学位论文
Configuration Design and Motion Planning of the Dual-platform
Staggered Hybrid Hexapod Robot “Xuangui”
ABSTRACT
There are a large number of narrow, dangerous and complex underground spaces in cities
that are not suitable or inaccessible for humans to enter, such as air-raid shelters in disrepair,
underground coal mines where accidents have occurred, military projects, and concealed
tunnels. The development and reuse of such narrow, dangerous and complex underground
spaces is of great significance, involving many fields such as national defense security, and the
national economy and the people’s livelihood, and is an important symbol of smart cities. In
this paper, we design a hexapod robot “Xuangui” based on the hybrid mechanism, which relies
on the alternate staggering of the upper and lower platforms of the parallel mechanism to move.
The R&(2-UPU/2-RPR) hybrid mechanism is used as the body of the hexapod robot Xuangui,
which can satisfy the requirements of the hexapod robot Xuangui to enter the underground
space to perform its tasks such as transportation, inspection, and maintenance.
Firstly, the overall configuration design of the hexapod robot Xuangui is carried out,
including the design of the body mechanism of the hexapod robot Xuangui and the design of
the leg structure fixed to the platform. The dimensions of the key components of the hexapod
robot Xuangui and the installation position of the sensors are also designed.
Secondly, the kinematics of 2-UPU/2-RPR redundant parallel mechanism is analyzed. The
coordinate systems of 2-UPU/2-RPR redundant parallel mechanism is established by screw
theory and the number of degrees of freedom of the mechanism is verified. By the analyzing of
the characteristics of the mechanism and ensuring the constraint relationship of mechanism, the
inverse solution equation of the mechanism is obtained using closed-loop vector method. The
positive solution equation of the mechanism is constructed by the convergence characteristics
of the particle swarm optimization algorithm. According to the given input parameters, the
中北大学学位论文
positive solution example of the mechanism is obtained, and the fitness curve of the positive
solution of the mechanism is obtained using Matlab software. Then the velocity Jacobian matrix
of the mechanism is obtained based on the inverse solution equation of the mechanism position.
Then, the singularity of 2-UPU/2-RPR redundant parallel mechanism is analyzed by Jacobian
matrix. The workspace of the mechanism is obtained usinglimit position exploration method,
and its shape is regular and continuous, indicatingthat the mechanism has good kinematic
performance.
Thirdly, the statics and dynamics of the hexapod robot Xuangui are analyzed. The
equilibrium equations of forces and moments are obtained by the rod removel method. The
statics simulation shows that the hexapod robot has a large loading capacity. Then, the dynamics
analysis of the hexapod robot Xuangui are carried out to obtain its dynamics equations, and
modal analysis is performed to obtain the first- order to sixth-order modal vibration patterns of
the hexapod robot Xuangui supported by two groups of six legs and each group of three legs,
and the harmonic response of the hexapod robot Xuangui is analyzed on this basis to obtain the
frequency-displacement curve and the sensitivity frequency of the hexapod robot Xuangui are
obtained, which is of guidance for the avoidance of robot resonance and the diagnosis of robot
faults.
Then, the stability analysis and gait planning of the hexapod robot Xuangui are carried out.
The center of gravity projection method is used to analyze the motion stability of the hexapod
robot Xuangui. Considering the stability of the hexapod robot Xuangui and the interference of
the legs, the motion limit parameters of the hexapod robot Xuangui are obtained, including the
maximum moving stride and the maximum zero radius angle of a single rotation in an
intermittent cycle. The space-occupying coefficient, movement order, movement stride and the
variation of rod length of each branch chain of the two groups of legs fixed on the two platforms
of the hexapod robot Xuangui during the movement of the hexapod robot Xuangui are studied.
The foot-end trajectory of the hexapod robot Xuangui is planned by using the non-impact
composite cycloid, which greatly avoids the impact of the hexapod robot Xuangui when the leg
is in contact with the ground.
中北大学学位论文
Finally, the hexapod robot Xuangui is modeled and its obstacle surmounting performance
in different terrain environments is analyzed. Through the Motion module built in SolidWorks
software, the simulation of the dual-platform staggered hexapod robot Xuangui based on R&(2-
UPU/2-RPR) hybrid mechanism is carried out in four working conditions: walking on the flat
ground, climbing the convex platform, crossing the gully and turning with zero radius. A series
of parameters such as the position, gait and center of gravity of the hexapod robot Xuangui are
obtained. By comparing the simulation results with the theoretical trajectory, it is concluded
that the two-platform centroids of the hexapod robot Xuangui are similar in the vertical
direction.
The dual-platform staggered hexapod robot “Xuangui” based on R&(2-UPU/2-RPR)
hybrid mechanism has a wide application prospect in the development and reuse of
underground space due to its superior performance such as adaptability to terrain and zero
radius turning ability in narrow environment.
Keywords: Hexapod robot Xuangui, R&(2-UPU/2-RPR) hybrid mechanism,
Configuration design, Kinematics, Statics, Gait planning, Trajectory planning
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