WO2021184655A1 - 一种超冗余机械臂末端轨迹运动规划方法 - Google Patents
一种超冗余机械臂末端轨迹运动规划方法 Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
- B25J9/1666—Avoiding collision or forbidden zones
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- the invention belongs to the technical field of computer-aided manufacturing and robotic processing.
- Hyper-redundant robots refer to robots with far more degrees of freedom than the minimum degrees of freedom required to complete the task. Hyper-redundant robots have good environmental adaptability due to their strong flexibility and high degree of freedom.
- hyper-redundant robots have been extensively researched and applied in the fields of aerospace manufacturing, nuclear power equipment maintenance, and hazardous materials handling. Realizing obstacle avoidance movement is one of the main goals of hyper-redundant manipulator motion planning.
- scholars have proposed a variety of effective obstacle avoidance planning methods, such as artificial potential energy field method, neural network algorithm and so on.
- the above-mentioned obstacle avoidance algorithm only emphasizes the end work ability, and does not impose strict constraints on the joint motion.
- a motion method that follows the end trajectory is proposed. This method strictly avoids obstacles by ensuring that the ends and joints of the hyper-redundant manipulator are as close as possible to the planned path curve.
- most of the currently designed super-redundant manipulators are in series, with low rigidity and poor carrying capacity. And there is no guarantee that the joints are on the path curve, and the accuracy is low. At the same time, the solution is complicated and inefficient.
- the present invention provides a method for planning the trajectory motion of the end of a super-redundant manipulator.
- a method for planning the end trajectory of a hyper-redundant manipulator which includes the following steps:
- step (3) includes the following sub-steps:
- the motion mechanism is composed of two parts: a super-redundant manipulator and a feed base; among them, the manipulator is composed of 8 UCR parallel joints in series, and two adjacent UCR parallel joints share a platform, that is, each UCR The moving platform of the parallel joint is also the fixed platform of the next UCR parallel joint; each UCR parallel joint fixed platform and the moving platform have a phase difference of 60° along the joint axis, and the robot UCR parallel joints are sequenced from the base Serial number, recorded as 1 ⁇ 8;
- the UCR (Universal-Cylindrical-Revolute) parallel joint is a three-degree-of-freedom parallel mechanism with rotation around the X and Y axes and movement around the Z axis (two rotations and one movement).
- the organization consists of a fixed platform, three branch chains and a moving platform.
- the branch chain is composed of Universal, Cylindrical and Revolute from bottom to top.
- the universal pair of the branch chain is connected with the fixed platform, and the rotating pair is connected with the moving platform.
- the initial state of each branch chain of the UCR parallel joint is kept the same, that is, the expansion and contraction amount of the cylinder pair (the length of the three branch chains) is the same, and the posture of the moving platform and the fixed platform are the same.
- step (4) includes the following sub-steps:
- the Z axis of the discrete data point in the B-spline path curve is along the tangential direction at the point. Assume that the parameters corresponding to two adjacent discrete points are divided with , The corresponding discrete points are: with . but with Tangent vector with Unit vector of
- step (5) includes the following sub-steps:
- the robotic arm is formed by 8 UCR parallel joints interlaced 60 o in series, and the three branches of UCR parallel joints are symmetrically distributed at 120 o . Therefore, the drive equations of UCR parallel joints numbered in odd and even digits (mechanism drive output And the functional relationship between poses).
- the above technical solutions conceived by the present invention can achieve the following beneficial effects: (1)
- the super-redundant manipulator has compact structure, high rigidity, strong bearing capacity and high reliability; (2) ) The method can strictly ensure that the end of the manipulator is on the cubic B-spline path curve, with high accuracy, and the cubic B-spline trajectory G2 is continuous, ensuring smooth motion; (3) The method is solved by the UCR parallel joint drive equation with high accuracy. , Fast efficiency.
- Figure 1 is a schematic diagram of the robotic arm and the base;
- Figure 2 is the UCR parallel joint configuration diagram;
- Figure 3 is the branch chain configuration diagram;
- Figure 4 is the flow chart of the robot arm end trajectory motion planning method;
- Figure 5 is the super redundant mechanical arm
- Figure 6 is a coordinate transformation diagram based on quaternion rotation;
- Figure 7 is a pose diagram of each UCR parallel joint of the manipulator.
- the motion mechanism has 25 degrees of freedom, and is composed of two parts, a super-redundant mechanical arm 1 and a feed base 2.
- the structure diagram is shown in FIG. 1.
- the robotic arm 1 is composed of 8 UCR parallel joints in series, with a total of 24 degrees of freedom. Two adjacent UCR parallel joints share the same platform, that is, the moving platform of each UCR parallel joint is also the fixed platform of the next UCR parallel joint. Each UCR parallel joint fixed platform 4 and the movable platform 5 have a phase difference of 60° along the joint axis.
- the feed base 2 provides a degree of freedom for feeding, which greatly improves the working space of the robotic arm 1.
- the UCR parallel joints of the robotic arm are numbered starting from the base 1, which are recorded as 1 ⁇ 8.
- the UCR (Universal-Cylindrical-Revolute) parallel joint is a three-degree-of-freedom parallel mechanism with rotation around the X and Y axes and movement around the Z axis (two rotations and one movement).
- the mechanism consists of a fixed platform 4, three branch chains and a moving platform 5.
- the universal pair of the branch chain is connected with the fixed platform, and the rotating pair is connected with the moving platform.
- the branch chain is composed of Universal, Cylindrical and Revolute from bottom to top.
- the initial state of each branch chain of the UCR parallel joint is consistent, that is, the amount of expansion and contraction of the cylinder pair is the same, so the initial state of the movable platform and the fixed platform are the same.
- the cylinder pair in this embodiment is a drive pair, and this embodiment uses a motor to drive.
- O 0 -X 0 Y 0 Z 0 and O 1 -X 1 Y 1 Z 1 are established respectively on the fixed platform and moving platform of the first UCR parallel joint.
- O 0 and O 1 are the centers of the fixed platform and the movable platform, respectively.
- the homogeneous transformation matrix of the coordinate system O 1 -X 1 Y 1 Z 1 relative to the coordinate system O 0 -X 0 Y 0 Z 0 is: ;
- the rotation matrix is ,
- the translation matrix is
- the coordinates of P 1_1 , P 1_2 , P 1_3 in the coordinate system O 0 -X 0 Y 0 Z 0 are: ;
- the coordinates of Q 1_1 , Q 1_2 , Q 1_3 in the coordinate system O 1 -X 1 Y 1 Z 1 are: ; Among them, Indicates the radius of the fixed platform and the movable platform.
- the coordinate systems O 1 -X 1 Y 1 Z 1 and O 2 -X 2 Y 2 Z 2 are established on the second UCR parallel joint fixed platform and moving platform respectively.
- O 1 and O 2 are the centers of the fixed platform and the moving platform, respectively.
- the homogeneous transformation matrix of the coordinate system O 2 -X 2 Y 2 Z 2 relative to the coordinate system O 1 -X 1 Y 1 Z 1 is:
- the rotation matrix is ,
- the translation matrix is The coordinates of P 2_1 , P 2_2 , P 2_3 in the coordinate system O 1 -X 1 Y 1 Z 1 are:
- the realization of following the B-spline trajectory at the end of the continuous path includes five parts: (1) According to the working environment, obtain the mark points that need to be passed in the work space; (2) Use the cubic B-spline curve to fit the mark points, Generate a path curve; (3) Obtain the working status of each UCR parallel joint of the manipulator according to the base feed; (4) Adjust the position of the UCR parallel joint in the working state in real time, so that the manipulator follows the three-time B-spline path curve Movement; (5) According to the posture and driving equation of each UCR parallel joint, the rod length of each joint branch is solved and output.
- the method flow chart is shown in Figure 4.
- the B-spline curve is widely used in trajectory fitting due to its versatility and easy realization.
- the B-spline curve can be defined by the control points and node vectors, which can reduce the amount of data storage by expressing the path trajectory.
- the B-spline curve itself has high continuity, and the cubic B-spline curve is continuous with G2.
- the fitted trajectory has better smoothness, and the original data points are used to strictly ensure the trajectory accuracy.
- each UCR parallel joint of the robot arm is the starting point of the cubic B-spline path curve.
- the initial length of each UCR parallel joint is equal, and is .
- the base provides the feed amount when the robot arm performs end-following motion .
- Each UCR parallel joint of the robot arm enters the working area in turn (in working state), and records its corresponding number.
- the Z axis of the discrete data points in the B-spline path curve is along the tangential direction at that point. Assume that the parameters corresponding to two adjacent discrete points are divided with , The corresponding discrete points are: with . but with Tangent vector with Unit vector of
- the manipulator is composed of 8 UCR parallel joints interlaced 60 o in series, and the internal three branches of the UCR parallel joint are symmetrically distributed at 120 o , so the driving equations of the UCR parallel joints with odd and even numbers are different.
- the center position and coordinate system of each platform are shown in Figure 7.
- the UCR joints in the working state will adjust the pose, and the UCR parallel joints that have not entered the working range will remain in the initial state; when the pose adjustment is performed, first, determine the UCR parallel joints According to the parity of the number, the corresponding driving equation is called to solve the UCR joint, and the length of the corresponding three branch chains is obtained and output.
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Abstract
本发明公开了一种超冗余机械臂末端轨迹运动规划方法,包括以下步骤:(1)根据工作环境,获得工作空间中需要通过的标记点;(2)利用三次B-spline曲线,对标记点进行拟合,生成路径曲线;(3)根据基座进给量,获得机械臂各UCR并联关节的工作状态;(4)实时调整工作状态UCR并联关节的位姿,使得机械臂沿着三次B-spline路径曲线运动;(5)根据各UCR并联关节的位姿和驱动方程,求解出各关节支链的杆长并输出。本发明优点:机械臂结构紧凑,刚度大,承载能力强,可靠性高;严格保证机械臂末端处于三次B-spline路径曲线上,精度高;通过UCR并联关节驱动方程求解,求解精度高,效率快。
Description
本发明属于计算机辅助制造及机器人加工技术领域。
随着工作环境的复杂化和狭窄化,超冗余机器人得到了广泛的研究和应用。超冗余机器人是指自由度数远多于完成作业任务所需要最少自由度的机器人。超冗余机器人因其灵活性强,自由度高等特点,使其具备良好的环境适应性。目前,超冗余机器人在航空航天制造、核电设备检修、危险材料处理等领域得到了广泛的研究和应用。实现避障运动是超冗余机械臂运动规划的主要目标之一。目前学者们提出了多种有效的避障规划方法,如人工势能场法、神经网络算法等。但是,上述避障算法只强调末端作业能力,而未对关节运动进行严格的约束。为了进一步提高超冗余机械臂避障的能力,跟随末端轨迹的运动方法被提出。该方法通过保证超冗余机械臂的末端和关节尽可能逼近规划的路径曲线,来严格进行避障。但是,目前设计的超冗余机械臂多为串联结构,刚度低,承载能力差。且不能保证关节在路径曲线上,精度低。同时,求解复杂,效率低。
针对现有技术的以上缺陷或改进需求,本发明提供了一种超冗余机械臂末端轨迹运动规划方法。
为实现上述目的,按照本发明的一个方面,提供了一种超冗余机械臂末端轨迹运动规划方法,包括如下步骤:
(1)根据工作环境,获得工作空间中超冗余机械臂需要通过的标记点;
(2)利用三次B-spline曲线,对标记点进行拟合,生成路径曲线;
(3)根据基座进给量,获得机械臂各UCR并联关节的工作状态;
(4)实时调整工作状态UCR并联关节的位姿,使得机械臂沿着三次B-spline路径曲线运动;
(5)根据各UCR并联关节的位姿和驱动方程,求解出各关节支链的杆长,并输出。
优选地,其步骤(3)包括如下子步骤:
S11、所述运动机构由超冗余机械臂与进给基座两部分组成;其中,机械臂由8个UCR并联关节串联而成,相邻2个UCR并联关节共用一个平台,即每个UCR并联关节的动平台也是下一个UCR并联关节的定平台;每个UCR并联关节定平台和动平台之间存在沿关节轴线60°的相位差,并从基座开始对机械臂UCR并联关节进行顺序编号,分别记为1~8;
S12、假设机械臂末端动平台中心为三次B-spline路径曲线的起点,每个UCR并联关节的初始长度相等,且为
;机械臂在进行末端跟随运动时,基座提供进给量
,机械臂各UCR并联关节依次进入工作区域,并记录其对应的编号。
对本发明技术方案的优选,UCR(Universal-Cylindrical-Revolute)并联关节为具有绕X,Y轴转动和绕Z轴移动(两转一移)的三自由度并联机构。该机构由定平台、三个支链和动平台组成。支链从下至上由万向副(Universal)、圆柱副(Cylindrical)和转动副(Revolute)组成。支链的万向副与定平台相连,转动副与动平台相连。
对本发明技术方案的优选,UCR并联关节各支链的初始状态保持一致,即圆柱副的伸缩量(三个支链的长度)一致,动平台与定平台姿态相同。通过调整三个支链的长度,可以对UCR并联关节中动平台相对于定平台的位姿进行调节。
优选地,其步骤(4)包括如下子步骤:
S21、计算各工作状态UCR并联关节在B-spline路径曲线上的离散点;首先在工作状态UCR并联关节最大编号的定平台处建立基坐标系为:
, 坐标原点:
。则第一个坐标系
已知,然后通过在[0,1]区间的二分法,在B-spline路径曲线上找到离散点,对应参数为
,使得通过位姿矩阵
反算出的UCR杆长处于行程范围,并记录参数
处对应的坐标系
。然后通过在[
,1]区间的二分法,在B-spline路径曲线上找到第二个离散点,对应参数
。依次类推,可以找到每个工作状态UCR并联关节动平台在B-spline路径曲线上对应的离散数据点;
优选地,其步骤(5)包括如下子步骤:
S31、机械臂由8个UCR并联关节交错60
o串联而成,而UCR并联关节内部三支链成120
o对称分布,所以编号为奇数位和偶数位的UCR并联关节的驱动方程(机构驱动输出与位姿之间的函数关系)不同。
S32、机械臂沿B-spline路径曲线运动时,处于工作状态的UCR关节才进行位姿调整,未进入工作区间的UCR并联关节保持初始状态不变;在进行位姿调整时,首先,判断UCR并联机构编号的奇偶性,根据奇偶性,分别调用对应的驱动方程对UCR关节进行求解,得到对应三个支链的长度,并输出。
总体而言,通过本发明所构思的以上技术方案与现有技术相比,能够取得下列有益效果:(1)超冗余机械臂结构紧凑,刚度大,承载能力强,可靠性高;(2)方法能严格保证机械臂末端处于三次B-spline路径曲线上,精度高,且三次B-spline轨迹G2连续,保证了运动的平顺;(3)方法通过UCR并联关节驱动方程求解,求解精度高,效率快。
图1是机械臂和基座示意图;图2是UCR并联关节构型图;图3是支链构型图;图4是机械臂末端轨迹运动规划方法流程图;图5是超冗余机械臂的典型工作情况;图6是基于四元数旋转的坐标变换图;图7是机械臂各UCR并联关节位姿图。
实施例1
本实施例中运动机构有25个自由度,且由超冗余机械臂1与进给基座2两部分组成,结构图如图1所示。
如图1所示,机械臂1由8个UCR并联关节串联而成,共有24个自由度。相邻2个UCR并联关节共用一个平台,即每个UCR并联关节的动平台也是下一个UCR并联关节的定平台。每个UCR并联关节定平台4和动平台5之间存在沿关节轴线60°的相位差。进给基座2提供一个进给自由度,极大提高了机械臂1的工作空间,并从基座1开始对机械臂UCR并联关节进行编号,分别记为1~8。
如图2所示,UCR(Universal-Cylindrical-Revolute)并联关节为具有绕X,Y轴转动和绕Z轴移动(两转一移)的三自由度并联机构。该机构由定平台4、三个支链和动平台5组成。支链的万向副与定平台相连,转动副与动平台相连。
如图3所示,支链从下至上由万向副(Universal)、圆柱副(Cylindrical)和转动副(Revolute)组成。UCR并联关节各支链的初始状态保持一致,即圆柱副的伸缩量一致,所以初始状态动平台与定平台姿态相同。通过调整三个支链的长度,可以对UCR并联关节中动平台相对于定平台的位姿进行调节。
本实施例的圆柱副为驱动副,本实施例采用电机驱动。
在第一个UCR并联关节定平台和动平台分别建立坐标系O
0-X
0Y
0Z
0和O
1-X
1Y
1Z
1。O
0和O
1分别为定平台和动平台圆心。三个支链与定平台和动平台的连接点分别为P
1_i, Q
1_i
(
i=1,2,3),其坐标均为O
0-X
0Y
0Z
0下的值。假设坐标系O
1-X
1Y
1Z
1相对于坐标系O
0-X
0Y
0Z
0的齐次变换矩阵为:
;旋转矩阵为
,平移矩阵为
P
1_1,P
1_2,P
1_3在坐标系O
0-X
0Y
0Z
0下的坐标为:
;Q
1_1,Q
1_2,Q
1_3在坐标系O
1-X
1Y
1Z
1下的坐标为:
;其中,
表示定平台和动平台半径。
则处于奇数位的UCR并联关节的驱动方程(即动平台相对于定平台的位姿与支链杆长之间的函数关系)为:
在第二个UCR并联关节定平台和动平台分别建立坐标系O
1-X
1Y
1Z
1和O
2-X
2Y
2Z
2。O
1和O
2分别为定平台和动平台圆心。三个支链与定平台和动平台的连接点分别为P
2_i,Q
2_i (
i=1,2,3),其坐标均为O
1-X
1Y
1Z
1下的值。假设坐标系O
2-X
2Y
2Z
2相对于坐标系O
1-X
1Y
1Z
1的齐次变换矩阵为:
Q
2_1,Q
2_2,Q
2_3在坐标系O
2-X
2Y
2Z
2下的坐标为:
则处于偶数位的UCR并联关节的驱动方程(即动平台相对于定平台的位姿与支链杆长之间的函数关系)为:
连续路径下跟随末段B样条轨迹运动实现包括五部分:(1)根据工作环境,获得工作空间中需要通过的标记点;(2)利用三次B-spline曲线,对标记点进行拟合,生成路径曲线;(3)根据基座进给量,获得机械臂各UCR并联关节的工作状态;(4)实时调整工作状态UCR并联关节的位姿,使得机械臂沿着三次B-spline路径曲线运动;(5)根据各UCR并联关节的位姿和驱动方程,求解出各关节支链的杆长,并输出。方法流程图如图4所示。
B-spline曲线以其通用性和易实现的特性被广泛应用在轨迹拟合中。B-spline曲线由控制点和节点矢量即可定义,以其表示路径轨迹可以减少数据存储量。此外B-spline曲线本身具备较高的连续性,三次B-spline曲线就G2连续,拟合后的轨迹有更好的光顺性,且经过原有数据点,严格保证轨迹精度。
其中,
为控制点,
称为
次B-spline曲线的基函数,本文中
。节点矢量
。图5中的标记点
通过三次B-spline曲线。根据标记点生成三次B-spline路径曲线具体细节参见非专利文献《三次B样条反算的一种简便算法》。
假设机械臂末端动平台(编号为8的UCR并联关节)中心为三次B-spline路径曲线的起点。每个UCR并联关节的初始长度相等,且为
。机械臂在进行末端跟随运动时,基座提供进给量
,机械臂各UCR并联关节依次进入工作区域(处于工作状态),并记录其对应的编号。
计算各工作状态UCR并联关节在B-spline路径曲线上的离散点;首先在工作状态UCR并联关节最大编号的定平台处建立基坐标系为:
,坐标原点:
。则第一个坐标系
已知,首先通过在[0,1]区间的二分法,在B-spline路径曲线上找到离散点,对应参数为
,使得通过位姿矩阵
反算出的UCR杆长处于行程范围,并记录参数
处对应的坐标系
。然后通过在[
,1]区间的二分法,在B-spline路径曲线上找到第二个离散点,对应参数
。依次类推,可以找到每个工作状态UCR并联关节动平台在B-spline路径曲线上对应的离散数据点。
机械臂由8个UCR并联关节交错60
o串联而成,而UCR并联关节内部三支链成120
o对称分布,所以编号为奇数位和偶数位的UCR并联关节的驱动方程不同。当机械臂所有UCR并联关节均处于工作状态时,每个平台中心位置和坐标系如图7所示。
机械臂沿B-spline路径曲线运动时,处于工作状态的UCR关节才进行位姿调整,未进入工作区间的UCR并联关节保持初始状态不变;在进行位姿调整时,首先,判断UCR并联关节编号的奇偶性,根据奇偶性,分别调用对应的驱动方程对UCR关节进行求解,得到对应三个支链的长度,并输出。
Claims (4)
- 一种超冗余机械臂末端轨迹运动规划方法,其特征在于,包括以下步骤:(1)根据工作环境,获得工作空间中超冗余机械臂需要通过的标记点;(2)利用三次B-spline曲线,对标记点进行拟合,生成路径曲线;(3)根据基座进给量,获得机械臂各UCR并联关节的工作状态;(4)实时调整工作状态UCR并联关节的位姿,使得机械臂沿着三次B-spline路径曲线运动;(5)根据各UCR并联关节的位姿和驱动方程,求解出各关节支链的杆长,并输出。
- 根据权利要求1所述的超冗余机械臂末端轨迹运动规划方法,其特征在于,步骤(3)包括如下子步骤:S11、所述运动机构由超冗余机械臂与进给基座两部分组成;其中,机械臂由8个UCR并联关节串联而成,相邻2个UCR并联关节共用一个平台,即每个UCR并联关节的动平台也是下一个UCR并联关节的定平台;每个UCR并联关节定平台和动平台之间存在沿关节轴线60°的相位差,并从基座开始对机械臂UCR并联关节进行顺序编号,分别记为1~8;
- 根据权利要求2所述的超冗余机械臂末端轨迹运动规划方法,其特征在于,UCR并联关节为具有绕X,Y轴转动和绕Z轴移动的三自由度并联机构,该机构由定平台、三个支链和动平台组成,支链从下至上由万向副(Universal)、圆柱副(Cylindrical)和转动副(Revolute)组成,支链的万向副与定平台相连,转动副与动平台相连。
- 根据权利要求2所述的超冗余机械臂末端轨迹运动规划方法,其特征在于,UCR并联关节各支链的初始状态保持一致,即圆柱副的伸缩量一致,动平台与定平台姿态相同。5. 如权利要求1所述的超冗余机械臂末端轨迹运动规划方法,其特征在于,步骤(4)包括如下子步骤:S21、计算各工作状态UCR并联关节在B-spline路径曲线上的离散点;首先在工作状态UCR并联关节最大编号的定平台处建立基坐标系为: ,坐标原点: 。则第一个坐标系 已知,然后通过在[0,1]区间的二分法,在B-spline路径曲线上找到离散点,对应参数为 ,使得通过位姿矩阵 反算出的UCR杆长处于行程范围,并记录参数 处对应的坐标系 。然后通过在[ ,1]区间的二分法,在B-spline路径曲线上找到第二个离散点,对应参数 。依次类推,可以找到每个工作状态UCR并联关节动平台在B-spline路径曲线上对应的离散数据点;6. 如权利要求1所述的超冗余机械臂末端轨迹运动规划方法,其特征在于,步骤(5)包括如下子步骤:S31、机械臂由8个UCR并联关节交错60°串联而成,而UCR并联关节内部三支链成120°对称分布,UCR并联关节编号为奇数位和偶数位的关节的驱动方程不同;S32、机械臂沿B-spline路径曲线运动时,处于工作状态的UCR关节才进行位姿调整,未进入工作区间的UCR并联关节保持初始状态不变;在进行位姿调整时,首先,判断UCR并联关节编号的奇偶性;其次,根据奇偶性,分别调用对应的驱动方程对UCR并联关节进行求解,得到UCR并联关节对应三个支链的长度,并输出。
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