技术领域Technical field
本发明涉及机器人技术领域，具体涉及一种基于快速扩展随机树和势场法的视觉伺服路径规划方法。The invention relates to the field of robot technology, and in particular to a visual servo path planning method based on rapidly expanding random trees and potential field methods.
背景技术Background technique
近几十年，机器人视觉伺服控制技术得到了快速发展，它通过视觉信息反馈帮助机器人感知外部环境的变化，引导机器人运动至期望位置，极大地提高了机器人智能化水平。但其仍然存在一些问题，如需对有用图像信息保持持续可视，需避免机器人与空间的障碍物或者目标物发生碰撞等。In recent decades, robot visual servo control technology has developed rapidly. It helps robots perceive changes in the external environment through visual information feedback, guides the robot to move to the desired position, and greatly improves the level of robot intelligence. However, there are still some problems. If you need to maintain continuous visibility of useful image information, you need to avoid collisions between the robot and obstacles or targets in space.
路径规划是机器人运动规划的重要组成部分，它可以很好地实现空间避障和限制机器人活动区域。因此，将路径规划引入视觉伺服中，为其提供可满足多空间条件约束的特征轨迹。势场法的基本思想是在障碍物处设置一个斥力势场,目标位置设置一个引力势场,以二者的合力决定机械臂的运动方向。快速扩展随机树法是基于数据结构——树的一种随机搜索算法，能快速搜索到有效无碰撞路径。将二者结合，用势场法的思想来构建成本函数，优化快速拓展随机树法得到基于快速扩展随机树和势场法的路径规划方法，它有效地结合快速扩展随机树法和势场法的优点，能快速有效地搜索高维空间，非常适合解决多自由度机器人在动态环境中的路径规划。Path planning is an important part of robot motion planning, which can effectively achieve spatial obstacle avoidance and limit the robot's activity area. Therefore, path planning is introduced into visual servoing to provide it with characteristic trajectories that can satisfy multiple spatial condition constraints. The basic idea of the potential field method is to set up a repulsive potential field at the obstacle and a gravitational potential field at the target position, and the combined force of the two determines the movement direction of the robotic arm. The rapid expansion random tree method is a random search algorithm based on the data structure tree, which can quickly search for effective collision-free paths. Combining the two, using the idea of the potential field method to construct the cost function, and optimizing the rapid expansion random tree method, a path planning method based on the rapid expansion random tree and potential field methods is obtained, which effectively combines the rapid expansion random tree method and the potential field method. The advantage is that it can search high-dimensional space quickly and effectively, and is very suitable for solving the path planning of multi-degree-of-freedom robots in dynamic environments.
发明内容Contents of the invention
本发明的目的在于针对机器人视觉伺服中出现的视野约束和碰撞问题，提出一种基于快速扩展随机树和势场法的视觉伺服路径规划方法，通过结合视觉伺服技术和路径规划技术实现满足多空间约束的控制任务。The purpose of this invention is to propose a visual servo path planning method based on rapidly expanding random trees and potential field methods in view of the field of view constraints and collision problems that occur in robot visual servoing. By combining visual servo technology and path planning technology, it can satisfy the needs of multiple spaces. Constrained control tasks.
本发明所述的路径规划方法涉及一种基于图像的眼在手机器人伺服控制系统，系统包括六自由度机器人本体、与机器人本体活动连接的末端执行器、以及安装在机器人末端执行器上的相机。The path planning method of the present invention relates to an image-based eye-in-hand robot servo control system. The system includes a six-degree-of-freedom robot body, an end effector movably connected with the robot body, and a camera installed on the robot end effector. .
为了实现上述的技术目的，本发明的技术方案是：In order to achieve the above technical objectives, the technical solution of the present invention is:
一种基于随机快速扩展树和势场法的视觉伺服路径规划方法，应用于包括六自由度机器人本体、与机器人本体活动连接的末端执行器和安装在机器人末端执行器上相机的工业机器人，其特征在于，所述方法包括下列步骤：A visual servo path planning method based on stochastic rapidly expanding trees and potential field methods, applied to industrial robots including a six-degree-of-freedom robot body, an end effector movablely connected to the robot body, and a camera installed on the robot end effector. Characteristically, the method includes the following steps:
S1：初始化，输入工业机器人的初始位姿和期望位姿/>其中(X0,Y0,Z0)为末端执行器的三维位置坐标，为末端执行器与各坐标轴的夹角弧度值，(X0,Y0,Z0)为末端执行器的期望三维位置坐标，/>为末端执行器与各坐标轴的期望夹角弧度值；S1: Initialization, input the initial pose of the industrial robot and desired pose/> Among them (X0 , Y0 , Z0 ) are the three-dimensional position coordinates of the end effector, is the arc value of the angle between the end effector and each coordinate axis, (X0 , Y0 , Z0 ) is the expected three-dimensional position coordinate of the end effector,/> is the expected arc value of the angle between the end effector and each coordinate axis;
S2：根据已知的作为控制参照物的目标物第j个特征点位置和相机参数矩阵K，其中/>为目标物第j个特征点的三维位置坐标，计算特征点在相机拍摄的图像中的像素坐标/>其中下标k表示参考坐标系，/>为像素的坐标值；S2: Based on the known j-th feature point position of the target as the control reference object and camera parameter matrix K, where/> For the three-dimensional position coordinates of the j-th feature point of the target, calculate the pixel coordinates of the feature point in the image captured by the camera/> The subscript k represents the reference coordinate system,/> is the coordinate value of the pixel;
S3：根据初始位姿T0和期望位姿T*构建中间位姿的成本函数Cost(Tk)；S3: Construct an intermediate pose based on the initial pose T0 and the desired pose T* The cost function Cost(Tk );
S4：根据工业机器人的初始位姿T0、期望位姿T*和成本函数Cost(Tk)构建搜索树，树的节点为具体构建搜索树的步骤为S5-S7；S4: Construct a search tree based on the industrial robot's initial pose T0 , expected pose T* and cost function Cost(Tk ). The nodes of the tree are The specific steps to build the search tree are S5-S7;
S5：在任务空间内随机生成一个位姿Trand，在搜索树中找到与其最近的节点Tnear，如二者之间的空间内无障碍物，则取二者的中点作为新的节点Tnew＝1/2(Trand+Tnear)；S5: Randomly generate a pose Trand in the task space, and find the node Tnear that is closest to it in the search tree. If there are no obstacles in the space between the two, take the midpoint of the two as the new node T.new =1/2(Trand +Tnear );
S6：根据Tnew求得相应的判断其是否满足视野约束和碰撞约束，即：S6: Obtain the corresponding value based on Tnew Determine whether it satisfies the field of view constraints and collision constraints, that is:
其中为Tnew包含的z轴坐标，umin、umax、vmin和vmax分别为视野约束的边界，如果为满足则进行下一步，否则舍弃该节点，返回S5；其中/>包含在Tnew中，具体求法与S2中步骤一致。in is the z-axis coordinate contained in Tnew , umin , umax , vmin and vmax are the boundaries of the visual field constraints respectively. If satisfied, proceed to the next step, otherwise discard the node and return to S5; where/> It is included in Tnew , and the specific calculation method is consistent with the steps in S2.
S7：判断新的节点是否符合要求，符合则添加到搜索树中并执行下一步，否则舍弃该节点，返回步骤S5；S7: Determine new nodes If it meets the requirements, add it to the search tree and perform the next step, otherwise discard the node and return to step S5;
S8：检查添加到搜索树中新的节点中的Tnew是否与目标位姿T*的距离小于阈值σ，是则认为找到合格路径，执行下一步骤，否则重复步骤S5至S8；S8: Check for new nodes added to the search tree Whether the distance between Tnew in and the target pose T* is less than the threshold σ, if so, it is considered that a qualified path has been found and the next step is performed. Otherwise, steps S5 to S8 are repeated;
S9：根据搜索到的合格路径的像素点映射轨迹利用基于图像的视觉伺服控制器进行跟踪控制使机器人实现初始位姿到期望位姿的避障并满足视野约束的运动。S9: Map the trajectory based on the pixel points of the searched qualified path The image-based visual servo controller is used for tracking control to enable the robot to avoid obstacles from the initial position to the desired position and move to meet the visual field constraints.
所述的基于快速扩展随机树和势场法的视觉伺服路径规划方法，所述步骤S2中求取像素坐标的方法为：The visual servo path planning method based on the rapid expansion random tree and potential field method, the pixel coordinates are obtained in step S2 The method is:
S201：根据初始位姿T0和中间位姿Tk并基于下式，求得用于描述它们之间相对旋转和平移的矩阵γk＝[0Rk|0tk]：S201: According to the initial pose T0 and the intermediate pose Tk and based on the following formula, obtain the matrix γk = [0 Rk |0 tk ] used to describe the relative rotation and translation between them:
T0＝0Rk·Tk+0tk；T0 =0 Rk ·Tk +0 tk ;
S202：根据旋转平移矩阵γk和以初始位姿为参考坐标系的目标物第j个特征点三维坐标求得以中间位姿为参考坐标系的目标物第j个特征点三维坐标S202: Based on the rotation and translation matrix γk and the three-dimensional coordinates of the j-th feature point of the target object with the initial pose as the reference coordinate system Find the three-dimensional coordinates of the j-th feature point of the target object with the intermediate pose as the reference coordinate system.
S203：根据相机参数构建参数矩阵K：S203: Construct parameter matrix K according to camera parameters:
其中f为相机焦距，pu和pv分别是相邻像素点u、v方向上的最小距离，(u0,v0)为主点的像素坐标，θ为成像点和光点连线与光轴的夹角；where f is the focal length of the camera, pu and pv are the minimum distances between adjacent pixel points in u and v directions respectively, (u0 , v0 ) are the pixel coordinates of the main point, θ is the line between the imaging point and the light point and the light The angle between the axes;
S204：根据相机的针孔模型，求得S204: According to the pinhole model of the camera, obtain
所述的基于快速扩展随机树和势场法的视觉伺服路径规划方法，所述步骤S3中构建成本函数的方法为：According to the visual servo path planning method based on the rapid expansion random tree and potential field method, the method of constructing the cost function in step S3 is:
基于势场法的思想，成本函数由两部分构成，引力部分和斥力部分：Based on the idea of potential field method, the cost function consists of two parts, the attraction part and the repulsion part:
Cost(Tk)＝C(Tk)+O(Tk)。Cost(Tk )=C(Tk )+O(Tk ).
在目标位姿处设置引力：Set gravity at the target pose:
C(Tk)＝Kc‖Tk-T*‖2，C(Tk )=Kc ‖Tk -T*‖2 ,
其中Kc为引力系数，其中‖Tk-T*‖2为：where Kc is the gravitational coefficient, where ‖Tk -T* ‖2 is:
在障碍物处设置斥力：Set repulsion at obstacles:
其中Ko为斥力系数，(Xob,Yob,Zob)为距离末端执行器最近的障碍物表面。Among them, Ko is the repulsion coefficient, and (Xob , Yob , Zob ) is the obstacle surface closest to the end effector.
中所述的基于快速扩展随机树和势场法的视觉伺服路径规划方法，所述步骤S7中判断新的节点是否符合要求的方法为：The visual servo path planning method based on the rapid expansion random tree and potential field method described in, the new node is determined in step S7 The methods to meet the requirements are:
S401：根据步骤S2中构建的成本函数Cost(Tk)，分别计算新的节点Tnew和最近节点Tnear的成本函数值Cost(Tnew)，Cost(Tnear)；S401: According to the cost function Cost(Tk ) constructed in step S2, calculate the cost function values Cost(Tnew ) and Cost(Tnear ) of the new node Tnew and the nearest node Tnear respectively;
S402：如果cost(Tnew)≤Cost(Tnear),则新的节点Tnew符合要求，否则计算ΔC：S402: If cost(Tnew )≤Cost(Tnear ), then the new node Tnew meets the requirements, otherwise calculate ΔC:
其中in
S403：根据ΔC计算接受概率TP：S403: Calculate the acceptance probability TP according to ΔC:
其中in
而t为循环次数改变的变量，设置其初值使得0＜TP≤1；And t is a variable that changes the number of cycles, and its initial value is set so that 0<TP≤1;
S404：取一个0到1之间的随机数rand，如果rand≤TP，则新的节点Tnew符合要求，使t＝t/a，其中a为调节参数，取值大于1，失败次数F置零，否则判断失败次数是否大于最大失败次数，即F≥Fmax，成立则t＝t·a，失败次数F置零，否则失败次数累加，即F＝F+1。S404: Take a random number rand between 0 and 1. If rand≤TP, then the new node Tnew meets the requirements, so that t=t/a, where a is the adjustment parameter, the value is greater than 1, and the number of failures F is set Zero, otherwise it is judged whether the number of failures is greater than the maximum number of failures, that is, F≥Fmax . If this is true, t=t·a, the number of failures F is set to zero, otherwise the number of failures is accumulated, that is, F=F+1.
本发明中所述的机器人系统包括六自由度机器人本体、与机器人本体活动连接的末端执行器、以及安装在机器人末端执行器上的相机。基于快速扩展随机树和势场法的路径规划方法有效地结合快速扩展随机树法和势场法的优点，能快速有效地搜索三维空间，非常适合解决多自由度机器人在动态环境中的路径规划。The robot system described in the present invention includes a six-degree-of-freedom robot body, an end effector movably connected to the robot body, and a camera installed on the robot end effector. The path planning method based on the rapidly expanding random tree and the potential field method effectively combines the advantages of the rapidly expanding random tree method and the potential field method. It can quickly and effectively search the three-dimensional space and is very suitable for solving the path planning of multi-degree-of-freedom robots in dynamic environments. .
本发明的技术效果在于，与现有视觉伺服路径规划方法相比，本发明提出结合快速扩展随机树法和势场法，快速有效地搜索三维任务空间，能很好地解决动态环境中的路径规划问题。另外，采用任务空间和图像空间交替搜索的方式，既满足任务空间防碰撞的问题，又满足图像空间的视野约束。The technical effect of the present invention is that, compared with the existing visual servo path planning method, the present invention proposes to combine the rapid expansion random tree method and the potential field method to quickly and effectively search the three-dimensional task space, which can well solve the path in the dynamic environment. planning issues. In addition, the alternate search method of task space and image space is adopted, which not only meets the problem of anti-collision in task space, but also meets the visual field constraints of image space.
附图说明Description of the drawings
图1为本发明所述路径规划方法的流程示意图。Figure 1 is a schematic flowchart of the path planning method according to the present invention.
图2为本发明具体实施方式中所述六自由度机器人手眼视觉伺服系统组成示意图。Figure 2 is a schematic diagram of the composition of the six-degree-of-freedom robot hand-eye visual servoing system in the specific embodiment of the present invention.
图3为本发明图像空间与任务空间映射关系示意图。Figure 3 is a schematic diagram of the mapping relationship between the image space and the task space of the present invention.
图4为本发明具体计算过程流程示意图。Figure 4 is a schematic flowchart of the specific calculation process of the present invention.
具体实施方式Detailed ways
下面结合具体实施例，并参照附图，对本发明作进一步详细说明。The present invention will be further described in detail below with reference to specific embodiments and the accompanying drawings.
本发明基于以下原理：势场法的基本思想是在障碍物处设置一个斥力势场,目标位置设置一个引力势场,以二者的合力决定机械臂的运动方向。快速扩展随机树法是基于数据结构——树的一种随机搜索算法，能快速搜索到有效无碰撞路径。将二者结合，用势场法的思想来构建成本函数，优化快速拓展随机树法。The invention is based on the following principles: the basic idea of the potential field method is to set up a repulsive potential field at the obstacle and a gravitational potential field at the target position, and the resultant force of the two determines the movement direction of the robotic arm. The rapid expansion random tree method is a random search algorithm based on the data structure tree, which can quickly search for effective collision-free paths. Combine the two, use the idea of potential field method to construct the cost function, and optimize and quickly expand the random tree method.
本实施例的应用场景如图2所示，包括基座固定的六自由度机器人本体，与机器人本体活动连接的作为末端执行器的机械手、安装在机器人末端执行器上的相机、任务空间内的长方体障碍物、以及处于相机视场范围内的方形目标物。本实施例旨在根据构建的视觉特征，对位于当前和期望系统状态的方形轮廓信息进行相关特征计算和匹配，用于组建视觉伺服控制中的特征误差向量，并推导图像信息与工作空间存在映射关系的雅克比矩阵，从而利用视觉特征引导手眼系统移动至期望位姿。The application scenario of this embodiment is shown in Figure 2, which includes a six-degree-of-freedom robot body with a fixed base, a manipulator as an end effector that is movablely connected to the robot body, a camera installed on the end effector of the robot, and a robot in the task space. Rectangular obstacles and square targets within the camera's field of view. This embodiment aims to perform relevant feature calculation and matching on the square outline information located in the current and desired system states based on the constructed visual features, to construct the feature error vector in visual servo control, and to derive the mapping between the image information and the work space. Jacobian matrix of the relationship, thereby using visual features to guide the hand-eye system to move to the desired posture.
基于以上所述的视觉伺服路径规划方法和应用场景，本发明方法采用的技术方案包括以下步骤：Based on the above-mentioned visual servo path planning method and application scenarios, the technical solution adopted by the method of the present invention includes the following steps:
S1:如图3所示，图中α为成像平面，β为目标物平面，FT为对应位姿的坐标系。求取像素坐标S1: As shown in Figure 3, α is the imaging plane, β is the target object plane, and FT is the coordinate system of the corresponding pose. Get pixel coordinates
根据初始位姿T0和中间位姿Tk求得旋转平移的矩阵γk＝[0Rk|0tk]，它们存在以下关系：According to the initial pose T0 and the intermediate pose Tk , the rotation and translation matrix γk = [0 Rk |0 tk ] is obtained. They have the following relationship:
T0＝0Rk·Tk+0tk；T0 =0 Rk ·Tk +0 tk ;
根据旋转平移矩阵γk和以初始位姿为参考坐标系的目标物第j个特征点三维坐标求得以中间位姿为参考坐标系的/>According to the rotation and translation matrix γk and the three-dimensional coordinates of the j-th feature point of the target object with the initial pose as the reference coordinate system Find/> with the intermediate pose as the reference coordinate system
根据相机参数构建参数矩阵K：Construct the parameter matrix K according to the camera parameters:
其中f为相机焦距，pu和pv分别是相邻像素点u、v方向上的最小距离，(u0,v0)为主点的像素坐标，θ为成像点和光点连线与光轴的夹角；where f is the focal length of the camera, pu and pv are the minimum distances between adjacent pixel points in u and v directions respectively, (u0 , v0 ) are the pixel coordinates of the main point, θ is the line between the imaging point and the light point and the light The angle between the axes;
根据相机的针孔模型，可求得According to the pinhole model of the camera, we can obtain
S2:构建成本函数：S2: Build cost function:
基于势场法的思想，成本函数由两部分构成，引力部分和斥力部分：Based on the idea of potential field method, the cost function consists of two parts, the attraction part and the repulsion part:
Cost(Tk)＝C(Tk)+O(Tk)。Cost(Tk )=C(Tk )+O(Tk ).
在目标位姿处设置引力：Set gravity at the target pose:
C(Tk)＝Kc‖Tk-T*‖2，C(Tk )=Kc ‖Tk -T* ‖2 ,
其中Kc为引力系数，其中‖Tk-T*‖2为：where Kc is the gravitational coefficient, where ‖Tk -T* ‖2 is:
在障碍物处设置斥力：Set repulsion at obstacles:
其中Ko为斥力系数，(Xob,Yob,Zob)为距离末端执行器最近的障碍物表面。Among them, Ko is the repulsion coefficient, and (Xob , Yob , Zob ) is the obstacle surface closest to the end effector.
S3:构建搜索树，树的节点为任务空间内随机生成一个位姿Trand，在搜索树中找到与其最近的节点Tnear，如二者之间的空间内无障碍物，则取二者的中点作为新的节点Tnew＝1/2(Trand+Tnear)，据Tnew求得相应的/>判断其是否满足视野约束和碰撞约束，即：S3: Construct a search tree, the nodes of the tree are Randomly generate a pose Trand in the task space, and find the node Tnear closest to it in the search tree. If there are no obstacles in the space between the two, take the midpoint of the two as the new node Tnew =1 /2(Trand +Tnear ), get the corresponding /> based on Tnew Determine whether it satisfies the field of view constraints and collision constraints, that is:
如果满足则进行下一步，否则舍弃该节点，重新生成；If satisfied, proceed to the next step, otherwise discard the node and regenerate it;
S4:进一步判断新的节点是否符合要求，符合则添加到搜索树中，否则舍弃该节点，重新生成；S4: Further determine the new node If it meets the requirements, it will be added to the search tree, otherwise the node will be discarded and regenerated;
S5：检查添加到搜索树中新的节点中的Tnew是否与目标位姿T*的距离小于阈值σ，是则找到合格路径，停止搜索，否则继续搜索；S5: Check for new nodes added to the search tree Whether the distance between Tnew in and the target pose T* is less than the threshold σ, if so, find a qualified path and stop the search, otherwise continue the search;
S6：根据搜索到的合格路径的像素点映射轨迹利用基于图像的视觉伺服(IBVS)进行跟踪控制使机器人实现初始位姿到期望位姿的避障并满足视野约束的运动。S6: Map the trajectory based on the pixel points of the searched qualified path Image-based visual servoing (IBVS) is used for tracking control to enable the robot to avoid obstacles from the initial position to the desired position and move to meet the visual field constraints.
所述步骤S4中中判断新的节点是否符合要求方法的流程图如图4所示，其具体方法为：Determine the new node in step S4 The flow chart of the method to determine whether it meets the requirements is shown in Figure 4. The specific method is:
S401：根据步骤S2中构建的成本函数Cost(Tk)，分别计算新的节点Tnew和最近节点Tnear的成本函数值Cost(Tnew)，Cost(Tnear)；S401: According to the cost function Cost(Tk ) constructed in step S2, calculate the cost function values Cost(Tnew ) and Cost(Tnear ) of the new node Tnew and the nearest node Tnear respectively;
S402：如果Cost(Tnew)≤Cost(Tnear),则新的节点Tnew符合要求，否则计算ΔC：S402: If Cost(Tnew )≤Cost(Tnear ), then the new node Tnew meets the requirements, otherwise calculate ΔC:
其中in
S403：根据ΔC计算接受概率TP：S403: Calculate the acceptance probability TP according to ΔC:
其中in
而t为循环次数改变的变量，设置其初值使得0＜TP≤1；And t is a variable that changes the number of cycles, and its initial value is set so that 0<TP≤1;
S404：取一个0到1之间的随机数rand，如果rand≤TP，则新的节点Tnew符合要求，使t＝t/a(a＞1)，失败次数F置零，否则判断失败次数是否大于最大失败次数，即F≥Fmax，成立则t＝t·a，失败次数F置零，否则失败次数累加，即F＝F+1。S404: Take a random number rand between 0 and 1. If rand≤TP, then the new node Tnew meets the requirements, so that t=t/a (a>1), the number of failures F is set to zero, otherwise the number of failures is determined. Is it greater than the maximum number of failures, that is, F≥Fmax ? If true, t=t·a, the number of failures F is set to zero, otherwise the number of failures is accumulated, that is, F=F+1.
至此，已经结合附图所示的具体实施方式描述了本发明的技术方案。在本实例中，利用基于随机快速扩展树和势场法的视觉伺服路径规划方法，位姿误差收敛到小于预设阈值，即本方法规划出从初始位姿到期望位姿的避障并满足视野约束的图像特征轨迹。So far, the technical solution of the present invention has been described with reference to the specific implementation modes shown in the drawings. In this example, using the visual servo path planning method based on random rapid expansion tree and potential field method, the pose error converges to less than the preset threshold, that is, this method plans obstacle avoidance from the initial pose to the desired pose and satisfies Field-of-view constrained image feature trajectories.
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