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CN116834013A - Double-arm robot layout optimization method based on teaching learning - Google Patents

Double-arm robot layout optimization method based on teaching learning
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CN116834013A
CN116834013ACN202310934311.4ACN202310934311ACN116834013ACN 116834013 ACN116834013 ACN 116834013ACN 202310934311 ACN202310934311 ACN 202310934311ACN 116834013 ACN116834013 ACN 116834013A
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李秦川
王梓浩
史东豪
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Zhejiang Sci Tech University ZSTU
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Abstract

The application relates to the technical field of double-arm base optimization, in particular to a double-arm robot layout optimization method based on teaching learning, which comprises the following steps: step 1: teaching record; step 2: DMP learning; step 3: selecting and generalizing a track by a common track end point; step 4: selecting an expected layout mode; step 5: designing a robot layout measurement index; step 6: optimizing the pending layout according to the index; step 7: adjusting learning algorithm parameters to generalize and execute a faster task track; step 8: the layout determining method can accelerate the optimized selection of the layout of the double-arm robot platform, can improve the execution efficiency of the task for the given task, and is used for constructing the double-arm platform for the given task.

Description

Translated fromChinese
一种基于示教学习的双臂机器人布局优化方法A teaching-based learning-based layout optimization method for dual-arm robots

技术领域Technical field

本发明涉及双臂基座优化技术领域,具体领域为一种基于示教学习的双臂机器人布局优化方法。The invention relates to the technical field of dual-arm base optimization, and the specific field is a method for optimizing the layout of a dual-arm robot based on teaching and learning.

背景技术Background technique

双臂基座布置问题是双臂操作的基础,当前的发明和论文主要关注双臂布局的位置标定问题,对于布局本身选取的关注较少。现有的方法采取公共工作空间和双臂各自工作空间乘积,旋转角度范围,运动性能和操作度等指标进行优化,这往往需要对工作空间全局进行计算和搜索,耗费大量时间和算力。而实际上双臂机器人在生产中的应用往往只是运行有限的轨迹,如双臂咖啡拉花等,全局性能并不能影响其工作。The problem of double-arm base layout is the basis of double-arm operation. Current inventions and papers mainly focus on the position calibration problem of the double-arm layout, and less attention is paid to the selection of the layout itself. Existing methods optimize indicators such as the product of the common workspace and the respective workspaces of both arms, the range of rotation angles, motion performance, and operability. This often requires calculation and search of the global workspace, which consumes a lot of time and computing power. In fact, the application of dual-arm robots in production often only runs limited trajectories, such as dual-arm coffee latte art, and the overall performance does not affect its work.

发明内容Contents of the invention

针对现有技术存在的不足,本发明的目的在于提供一种基于示教学习的双臂机器人布局优化方法。In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a method for optimizing the layout of a two-arm robot based on teaching learning.

为实现上述目的,本发明提供如下技术方案:一种基于示教学习的双臂机器人布局优化方法,其特征在于:其步骤为:In order to achieve the above object, the present invention provides the following technical solution: a teaching learning-based layout optimization method for a two-arm robot, which is characterized in that the steps are:

步骤1:示教记录:使用视觉系统读取专家在工作空间内执行任务的双手轨迹;Step 1: Teaching record: Use the vision system to read the trajectory of the expert's hands performing tasks in the workspace;

步骤2:DMP学习:使用DMP学习双手轨迹;Step 2: DMP learning: Use DMP to learn the trajectory of both hands;

步骤3:常见轨迹终点选取并泛化轨迹:选取工作空间中轨迹的目标点,泛化得出空间内常用轨迹,减少专家工作量;Step 3: Select common trajectory end points and generalize the trajectory: select the target point of the trajectory in the work space, and generalize to obtain common trajectories in the space, reducing the workload of experts;

步骤4:选取预期布局方式:根据机器人特性和任务布局限制,确定机械臂布局待定集合;Step 4: Select the expected layout method: Based on the robot characteristics and task layout restrictions, determine the undetermined set of robot arm layouts;

步骤5:设计机器人布局衡量指标:根据现有指标,建立综合考虑机器人操作性能,公共工作空间占比的综合指标;Step 5: Design robot layout measurement indicators: Based on existing indicators, establish a comprehensive indicator that comprehensively considers robot operating performance and the proportion of public work space;

步骤6:根据指标优选待定布局:根据指标在待定布局集合中优选性能较优集合;Step 6: Select the pending layout based on the indicators: Select the set with better performance among the pending layout sets based on the indicators;

步骤7:调节学习算法参数泛化执行更快的任务轨迹:调节DMP参数加快泛化轨迹的演化,获得能更快完成任务的轨迹,由于机器人的关节限制,对机器人布局提出新的要求;Step 7: Adjust the parameters of the learning algorithm to generalize and execute faster task trajectories: Adjust the DMP parameters to speed up the evolution of the generalized trajectory and obtain a trajectory that can complete the task faster. Due to the joint limitations of the robot, new requirements are put forward for the robot layout;

步骤8:确定布局方法,最后得到新布局方法。。Step 8: Determine the layout method, and finally get the new layout method. .

在其中一些实施例中,根据步骤2,建立DMP模型为:In some of these embodiments, according to step 2, the DMP model is established as:

αz,为正βz常数,x为变量,g为目标,v为速度,为加速度,τ>0为时间常数,s时间无关阶段数,初值为1,αs为收敛常数,f(s)为强制项。αz , is the positive βz constant, x is the variable, g is the target, v is the speed, is the acceleration, τ>0 is the time constant, s is the number of time-independent stages, the initial value is 1, αs is the convergence constant, and f(s) is the mandatory term.

在其中一些实施例中,强制项f(s)为:In some of these embodiments, the mandatory term f(s) is:

强制项包括N高斯基元,确保轨迹的相似,y0是起始点,wi是权重,ψi是高斯核。The mandatory terms include N Gaussian primitives to ensure the similarity of trajectories, y0 is the starting point, wi is the weight, and ψi is the Gaussian kernel.

在其中一些实施例中,高斯核ψi为:ψi(s)=exp(-hi(s-ci)2),wi通过LWR进行学习。In some embodiments, the Gaussian kernel ψi is: ψi (s) = exp (-hi (sci )2 ), wi is learned by LWR.

在其中一些实施例中,根据步骤3-7,计算过程通过最小化目标函数获取:In some of these embodiments, according to steps 3-7, the calculation process is obtained by minimizing the objective function:

min{ft(s)-f(s)}min{ft (s)-f(s)}

f(s)是示教轨迹,ft(s)表达如下:f(s) is the teaching trajectory, ft (s) is expressed as follows:

通过设计不同的初始和结束位型,获取该双臂机器人任务的可能轨迹,为双臂基座的优化提供参考轨迹。By designing different initial and end positions, the possible trajectory of the dual-arm robot mission is obtained, which provides a reference trajectory for the optimization of the dual-arm base.

在其中一些实施例中,对不同基座参数采用多指标综合评估进行分析,具体指标如下:In some of the embodiments, different base parameters are analyzed using multi-index comprehensive evaluation. The specific indexes are as follows:

可操纵性指数、关节极限和扩展可操纵性;Maneuverability index, joint limits and extended maneuverability;

可操纵性指数:机器人末端执行器无条件改变其位置和方向的能力信息,该信息固有地包含在雅可比矩阵中,特别是其奇异值,表示为,Maneuverability index: information about the ability of the robot end effector to unconditionally change its position and orientation. This information is inherently contained in the Jacobian matrix, especially its singular values, expressed as,

关节极限:成本函数当一个关节变量接近其极限时,关节极限的接近度必须趋于无穷大,采用以下函数,Joint limit: cost function When a joint variable approaches its limit, the proximity of the joint limit must tend to infinity, using the following function,

扩展可操纵性:为了建立一个包含关节极限和自碰撞信息的可操纵性度量,必须计算权重矩阵,这些矩阵将有助于建立给出扩展可操作性测度的增广雅可比矩阵,使用由学习生成的轨迹避免在运动所有方向的探索和尝试,Extended Maneuverability: In order to build a maneuverability measure that includes joint limits and self-collision information, weight matrices must be calculated that will help build an augmented Jacobian matrix that gives an extended maneuverability measure, using the learned Generated trajectories avoid exploration and attempts in all directions of motion,

在其中一些实施例中,增广雅可比计算为,In some of these embodiments, the augmented Jacobian is calculated as,

在其中一些实施例中,评价指标设为,In some of these embodiments, the evaluation index is set to,

与现有技术相比,本发明的有益效果是:基于示教学习,学习并泛化机器人在工作空间需要运行的轨迹,综合末端轨迹的运行效率和操作性能等指标,完成对双臂机器人基座的布局优化。Compared with the existing technology, the beneficial effects of the present invention are: based on teaching learning, it learns and generalizes the trajectory that the robot needs to run in the work space, comprehensively integrates the operating efficiency and operating performance of the end trajectory and other indicators, and completes the basic analysis of the dual-arm robot. Seat layout optimization.

本申请的一个或多个实施例的细节在以下附图和描述中提出,以使本申请的其他特征、目的和优点更加简明易懂,通过本申请的实施例对本申请进行详尽说明和了解。Details of one or more embodiments of the present application are set forth in the following drawings and descriptions to make other features, objects, and advantages of the present application more concise and understandable, and the present application will be described and understood in detail through the embodiments of the present application.

附图说明Description of the drawings

图1为本发明的方案流程图。Figure 1 is a flow chart of the solution of the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

请参阅图1,本发明提供一种技术方案:一种基于示教的双臂基座优化布局方法,其具体实施方案为:Please refer to Figure 1. The present invention provides a technical solution: a method for optimizing the layout of a double-arm base based on teaching. The specific implementation is:

步骤1:示教记录;Step 1: Teaching record;

使用视觉系统读取专家在工作空间内执行任务的双手轨迹。Use a vision system to read the trajectory of an expert's hands as they perform tasks within the workspace.

步骤2:DMP学习;Step 2: DMP learning;

使用DMP学习双手轨迹。Learning bimanual trajectories using DMP.

步骤3:常见轨迹终点选取并泛化轨迹;Step 3: Select common trajectory end points and generalize the trajectory;

选取工作空间中轨迹的目标点,泛化得出空间内常用轨迹,减少专家工作量。Select the target point of the trajectory in the work space and generalize it to obtain commonly used trajectories in the space, reducing the workload of experts.

步骤4:选取预期布局方式;Step 4: Select the desired layout method;

根据机器人特性和任务布局限制,确定机械臂布局待定集合。According to the robot characteristics and task layout constraints, the undetermined set of robot arm layouts is determined.

步骤5:设计机器人布局衡量指标;Step 5: Design robot layout metrics;

根据现有指标,建立综合考虑机器人操作性能,公共工作空间占比的综合指标。Based on the existing indicators, establish a comprehensive indicator that comprehensively considers the robot's operating performance and the proportion of public work space.

步骤6:根据指标优选待定布局;Step 6: Optimize the pending layout based on indicators;

根据指标在待定布局集合中优选性能较优集合。Based on the indicators, the set with better performance is selected among the pending layout sets.

步骤7:调节学习算法参数泛化执行更快的任务轨迹;Step 7: Adjust the parameters of the learning algorithm to generalize and execute faster task trajectories;

调节DMP参数加快泛化轨迹的演化,获得能更快完成任务的轨迹,由于机器人的关节限制,对机器人布局提出新的要求。Adjusting DMP parameters speeds up the evolution of generalized trajectories and obtains trajectories that can complete tasks faster. Due to the joint limitations of the robot, new requirements are put forward for the robot layout.

步骤8:确定布局方法。Step 8: Determine the layout method.

最后得到新布局方法。Finally get the new layout method.

具体方法DMPs模型可以建立为:The specific method DMPs model can be established as:

αz,为正βz常数,x为变量,g为目标,v为速度,为加速度,τ>0为时间常数,s时间无关阶段数,初值为1,αs为收敛常数αz , is the positive βz constant, x is the variable, g is the target, v is the speed, is the acceleration, τ>0 is the time constant, s is time independent of the number of stages, the initial value is 1, αs is the convergence constant

强制项f(s)为:The mandatory term f(s) is:

强制项包括N高斯基元,确保轨迹的相似,y0是起始点,wi是权重,ψi是高斯核,ψi(s)=exp(-hi(s-ci)2),wi可以通过LWR进行学习.The mandatory term includes N Gaussian basic elements to ensure the similarity of trajectories, y0 is the starting point, wi is the weight, ψi is the Gaussian kernel, ψi (s) = exp (-hi (sci )2 ), wi Learning can be done through LWR.

计算过程通过最小化如下目标函数获取:The calculation process is obtained by minimizing the following objective function:

min{ft(s)-f(s)}min{ft (s)-f(s)}

f(s)是示教轨迹,ft(s)如下:f(s) is the teaching trajectory, ft (s) is as follows:

通过设计不同的初始和结束位型,可以获取该双臂机器人任务的可能轨迹,为双臂基座的优化提供参考轨迹。By designing different initial and end positions, the possible trajectory of the dual-arm robot mission can be obtained, providing a reference trajectory for the optimization of the dual-arm base.

和在整个空间的位型优化类似,我们对不同基座参数采用多指标综合评估进行分析,具体指标如下:Similar to position optimization in the entire space, we use multi-index comprehensive evaluation to analyze different base parameters. The specific indicators are as follows:

可操纵性指数,机器人末端执行器无条件改变其位置和方向的能力信息。该信息固有地包含在雅可比矩阵中,特别是其奇异值,表示为Maneuverability index, information about the ability of a robot end effector to unconditionally change its position and orientation. This information is inherently contained in the Jacobian matrix, specifically its singular values, expressed as

关节极限:成本函数当一个关节变量接近其极限时,关节极限的接近度必须趋于无穷大。我们采用以下函数Joint Limits: Cost Function As a joint variable approaches its limit, the approach to the joint limit must approach infinity. We use the following function

扩展可操纵性:为了建立一个包含关节极限和自碰撞信息的可操纵性度量,必须计算权重矩阵。这些矩阵将有助于建立给出扩展可操作性测度的增广雅可比矩阵。它本质上取决于指定的运动,这里使用由学习生成的轨迹避免在运动所有方向的探索和尝试。Extended maneuverability: In order to establish a maneuverability metric that includes joint limit and self-collision information, a weight matrix must be calculated. These matrices will help to build augmented Jacobian matrices that give extended operability measures. It essentially depends on the specified motion, and here using trajectories generated by learning avoids exploration and attempts in all directions of motion.

最后,增广雅可比可以计算为Finally, the augmented Jacobian can be calculated as

评价指标可以设为The evaluation index can be set to

通过本技术方案,提出使用示教学习的方法进行布局优化,提高布局效率,且通过对示教学习方法中参数的调节获得不同运行速度的执行方案,提高任务执行效率;Through this technical solution, it is proposed to use the teaching and learning method to optimize the layout and improve the layout efficiency. By adjusting the parameters in the teaching and learning method, we can obtain execution plans with different running speeds and improve the task execution efficiency;

现有的方法采取多指标对工作空间全局进行分析进而优化布局,耗费大量时间和算力。而实际上双臂机器人在生产中的应用往往任务单一近似,全局性能并不能影响其工作,本发明基于示教学习,只需优化任务和任务相关区域性能,不仅能更快完成布局优化,还能应对任务效率提升的需求。Existing methods use multiple indicators to analyze the overall workspace and optimize the layout, which consumes a lot of time and computing power. In fact, the application of dual-arm robots in production often has a single task, and the global performance does not affect its work. This invention is based on teaching learning and only needs to optimize the performance of tasks and task-related areas. It can not only complete layout optimization faster, but also Able to cope with the need to improve task efficiency.

以上实施例仅表达了本申请的几种实施方式,其描述较为具体和详细,但并不能因此而理解为对发明专利范围的限制。应当指出的是,对于本领域的普通技术人员来说,在不脱离本申请构思的前提下,还可以做出若干变形和改进,这些都属于本申请的保护范围。因此,本申请专利的保护范围应以所附权利要求为准。The above embodiments only express several implementation modes of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all fall within the protection scope of the present application. Therefore, the protection scope of this patent application should be determined by the appended claims.

尽管已经示出和描述了本发明的实施例,对于本领域的普通技术人员而言,可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型,本发明的范围由所附权利要求及其等同物限定。Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art will understand that various changes, modifications, and substitutions can be made to these embodiments without departing from the principles and spirit of the invention. and modifications, the scope of the invention is defined by the appended claims and their equivalents.

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
CN118809556A (en)*2024-07-172024-10-22华中科技大学 A dual-manipulator teaching processing method and system for complex parts in narrow space
CN118809556B (en)*2024-07-172025-10-17华中科技大学Teaching processing method and system for double mechanical arms in narrow space of complex part

Citations (7)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
US6526373B1 (en)*1999-10-082003-02-25Dassault SystemesOptimization tool for robot placement
CN101998895A (en)*2008-02-202011-03-30Abb研究有限公司Method and system for optimizing the layout of a robot work cell
CN105676642A (en)*2016-02-262016-06-15同济大学Station layout and motion time cooperative optimization method for six-freedom-degree robot
US20180036882A1 (en)*2016-08-042018-02-08Canon Kabushiki KaishaLayout setting method and layout setting apparatus
CN112207835A (en)*2020-09-182021-01-12浙江大学Method for realizing double-arm cooperative work task based on teaching learning
CN112621754A (en)*2020-12-112021-04-09中国科学院沈阳计算技术研究所有限公司Design method for multi-robot-cooperated assembly line safety layout
CN115097816A (en)*2022-05-202022-09-23深圳市大族机器人有限公司Modularized multi-robot cooperation control method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
US6526373B1 (en)*1999-10-082003-02-25Dassault SystemesOptimization tool for robot placement
CN101998895A (en)*2008-02-202011-03-30Abb研究有限公司Method and system for optimizing the layout of a robot work cell
CN105676642A (en)*2016-02-262016-06-15同济大学Station layout and motion time cooperative optimization method for six-freedom-degree robot
US20180036882A1 (en)*2016-08-042018-02-08Canon Kabushiki KaishaLayout setting method and layout setting apparatus
CN112207835A (en)*2020-09-182021-01-12浙江大学Method for realizing double-arm cooperative work task based on teaching learning
CN112621754A (en)*2020-12-112021-04-09中国科学院沈阳计算技术研究所有限公司Design method for multi-robot-cooperated assembly line safety layout
CN115097816A (en)*2022-05-202022-09-23深圳市大族机器人有限公司Modularized multi-robot cooperation control method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
徐永吉;: "汽车门槛焊接总成机器人工作站规划", 金属加工(热加工), no. 16, 20 August 2017 (2017-08-20)*

Cited By (2)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
CN118809556A (en)*2024-07-172024-10-22华中科技大学 A dual-manipulator teaching processing method and system for complex parts in narrow space
CN118809556B (en)*2024-07-172025-10-17华中科技大学Teaching processing method and system for double mechanical arms in narrow space of complex part

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