技术领域technical field
本发明涉及机器人领域，尤其是一种柔性机器人逆运动学求解方法、系统、设备、存储介质。The invention relates to the field of robots, in particular to a flexible robot inverse kinematics solution method, system, equipment and storage medium.
背景技术Background technique
柔性机器人相对于传统机械臂有纤细的躯干，冗余的自由度，在复杂多障碍的环境中体现出了极强的灵活性，因此被广泛应用于核电领域、航天领域大型设备的检修、维护、装配等作业任务。这些特殊的狭小空间环境中，很多情况，只需要柔性机器人的末端位置可达(即在指定的位置(姿态)的情况下，能有对应的关节角度解。)，而姿态范围内可达即可。然而目前所有研发的柔性机器人中，它们的关节大多数由万向节结构组成，因此每个关节处只有俯仰和偏航两个方向的自由度，整体上柔性机器人的自由度配置为P-Y-Y-P-P…，缺少了滚转的自由度，这样将会导致其姿态空间有限而出现以下的问题：Compared with traditional manipulators, flexible robots have a slender torso and redundant degrees of freedom, which shows great flexibility in complex and multi-obstacle environments. Therefore, they are widely used in the overhaul and maintenance of large-scale equipment in the field of nuclear power and aerospace. , assembly and other tasks. In these special narrow space environments, in many cases, only the end position of the flexible robot needs to be reachable (that is, in the case of a specified position (posture), the corresponding joint angle solution can be obtained.), and the reachable range of the posture can be Can. However, in all currently developed flexible robots, most of their joints are composed of gimbal structures, so each joint has only two degrees of freedom in pitch and yaw directions. The overall degree of freedom of the flexible robot is configured as P-Y-Y-P-P..., The lack of roll degree of freedom will lead to the limited attitude space and the following problems:
(1)柔性机器人在自由度的配置上缺少滚转的自由度，在柔性机器人的整体上的自由度有限的情况下，难以通过其它的关节的运动等效成末端的滚转运动。(1) The flexible robot lacks the rolling degree of freedom in the configuration of the degrees of freedom. When the overall degree of freedom of the flexible robot is limited, it is difficult to convert the movement of other joints into a rolling motion of the end.
(2)在柔性机器人自由度冗余情况下，虽然可以通过其余的关节的运动，能够等效成末端的滚转运动，在一些给定的末端位置和姿态的情况下，其还是可能不存在有效解。(2) In the case of redundant degrees of freedom of the flexible robot, although the movement of the remaining joints can be equivalent to the rolling motion of the end, it may not exist in the case of some given end positions and postures effective solution.
(3)通过其它关节的运动，等效成末端的滚转运动，在一定程度上，不可避免地减少了柔性机器人操作有效长度。(3) Through the movement of other joints, it is equivalent to the rolling movement of the end, which inevitably reduces the effective length of the flexible robot operation to a certain extent.
另外，在目前的柔性机器人的逆运动学的求解方法中，具有位置可达，但姿态只有部分可达的特点，即在一些特殊狭小空间环境中特定的目标末端位置和姿态情况下，利用传统的机器人逆运动学数值迭代法难以找到有效的关节角的解。In addition, in the current solution method of inverse kinematics of flexible robots, the position is reachable, but the attitude is only partially reachable. The numerical iterative method of the inverse kinematics of the robot is difficult to find an efficient solution for the joint angles.
发明内容SUMMARY OF THE INVENTION
本发明旨在至少在一定程度上解决相关技术中的技术问题之一。为此，本发明的一个目的是提供一种柔性机器人逆运动学求解方法、系统、设备、存储介质，用于提高柔性机器人逆运动学求解有解的可能性。The present invention aims to solve one of the technical problems in the related art at least to a certain extent. To this end, an object of the present invention is to provide a method, system, device, and storage medium for solving the inverse kinematics of a flexible robot, so as to improve the possibility of solving the inverse kinematics of a flexible robot.
本发明所采用的技术方案是：一种柔性机器人逆运动学求解方法，包括以下步骤：The technical solution adopted in the present invention is: a flexible robot inverse kinematics solution method, comprising the following steps:
在柔性机器人原有自由度的基础上，增加末端虚拟自由度；On the basis of the original degree of freedom of the flexible robot, the virtual degree of freedom of the end is increased;
获取增加所述末端虚拟自由度后的柔性机器人的正运动学方程；obtaining the forward kinematics equation of the flexible robot after adding the virtual degree of freedom of the end;
根据所述正运动学方程获取柔性机器人的雅克比矩阵；Obtain the Jacobian matrix of the flexible robot according to the forward kinematics equation;
根据所述雅克比矩阵进行柔性机器人逆运动学求解。According to the Jacobian matrix, the inverse kinematics of the flexible robot is solved.
进一步地，根据所述雅克比矩阵和数值迭代法进行柔性机器人逆运动学求解。Further, the inverse kinematics solution of the flexible robot is performed according to the Jacobian matrix and the numerical iterative method.
进一步地，所述末端虚拟自由度为末端虚拟移动自由度和/或末端虚拟旋转自由度。Further, the terminal virtual degree of freedom is the terminal virtual movement degree of freedom and/or the terminal virtual rotation degree of freedom.
本发明所采用的另一技术方案是：一种柔性机器人逆运动学求解系统，包括：Another technical solution adopted by the present invention is: a flexible robot inverse kinematics solution system, comprising:
末端虚拟自由度增加单元，用于在柔性机器人原有自由度的基础上，增加末端虚拟自由度；The end virtual degree of freedom increasing unit is used to increase the end virtual degree of freedom on the basis of the original degree of freedom of the flexible robot;
正运动学方程获取单元，用于获取增加所述末端虚拟自由度后的柔性机器人的正运动学方程；a forward kinematics equation acquiring unit, used for acquiring the forward kinematics equation of the flexible robot after adding the virtual degree of freedom of the end;
雅克比矩阵获取单元，用于根据所述正运动学方程获取柔性机器人的雅克比矩阵；a Jacobian matrix acquiring unit, configured to acquire the Jacobian matrix of the flexible robot according to the forward kinematic equation;
逆运动学求解单元，用于根据所述雅克比矩阵进行柔性机器人逆运动学求解。The inverse kinematics solving unit is used for solving the inverse kinematics of the flexible robot according to the Jacobian matrix.
进一步地，所述逆运动学求解单元根据所述雅克比矩阵和数值迭代法进行柔性机器人逆运动学求解。Further, the inverse kinematics solving unit performs the inverse kinematics solution of the flexible robot according to the Jacobian matrix and the numerical iterative method.
进一步地，所述末端虚拟自由度为末端虚拟移动自由度和/或末端虚拟旋转自由度。Further, the terminal virtual degree of freedom is the terminal virtual movement degree of freedom and/or the terminal virtual rotation degree of freedom.
本发明所采用的另一技术方案是：一种柔性机器人逆运动学求解设备，包括：Another technical solution adopted by the present invention is: a flexible robot inverse kinematics solution device, comprising:
至少一个处理器；以及，at least one processor; and,
与所述至少一个处理器通信连接的存储器；其中，a memory communicatively coupled to the at least one processor; wherein,
所述存储器存储有可被所述至少一个处理器执行的指令，所述指令被所述至少一个处理器执行，以使所述至少一个处理器能够执行所述的柔性机器人逆运动学求解方法。The memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the flexible robot inverse kinematics solution method.
本发明所采用的另一技术方案是：一种计算机可读存储介质，所述计算机可读存储介质存储有计算机可执行指令，所述计算机可执行指令用于使计算机执行所述的柔性机器人逆运动学求解方法。Another technical solution adopted in the present invention is: a computer-readable storage medium, where the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to make the computer execute the reverse operation of the flexible robot. Kinematic solution method.
本发明的有益效果是：The beneficial effects of the present invention are:
本发明一种柔性机器人逆运动学求解方法、系统、设备、存储介质，通过增加末端虚拟自由度，克服传统的逆运动学求解方法中，经常无有效解的缺点，提高了柔性机器人逆运动学求解有解的可能性。The invention provides a method, system, equipment and storage medium for solving the inverse kinematics of a flexible robot. By increasing the virtual degree of freedom at the end, the traditional inverse kinematics solving method overcomes the shortcoming that there is often no effective solution, and improves the inverse kinematics of the flexible robot. Solve for the possibility of a solution.
附图说明Description of drawings
图1是本发明中一种柔性机器人逆运动学求解方法的柔性机器人的末端虚拟自由度的一具体实施例示意图；1 is a schematic diagram of a specific embodiment of the virtual degree of freedom of the end of a flexible robot according to a method for solving the inverse kinematics of a flexible robot in the present invention;
图2是本发明中一种柔性机器人逆运动学求解方法的柔性机械臂DH坐标系的一具体实施例示意图；2 is a schematic diagram of a specific embodiment of the DH coordinate system of the flexible robotic arm of a flexible robot inverse kinematics solution method in the present invention;
图3是本发明中一种柔性机器人逆运动学求解方法的一具体实施例方法流程图。FIG. 3 is a flow chart of a specific embodiment of a method for solving the inverse kinematics of a flexible robot in the present invention.
具体实施方式Detailed ways
需要说明的是，在不冲突的情况下，本申请中的实施例及实施例中的特征可以相互组合。It should be noted that the embodiments in the present application and the features of the embodiments may be combined with each other in the case of no conflict.
实施例1Example 1
本实施例中，为了解决柔性机器人的自由度配置上缺少滚转的自由度，存在用传统迭代方法在给定末端位置姿态时难以求出有效解的问题；提供一种柔性机器人逆运动学求解方法，包括以下步骤：In this embodiment, in order to solve the lack of rolling degrees of freedom in the configuration of the degrees of freedom of the flexible robot, there is a problem that it is difficult to obtain an effective solution with the traditional iterative method when the end position and attitude are given; an inverse kinematics solution of the flexible robot is provided. method, including the following steps:
在柔性机器人原有自由度的基础上，增加末端虚拟自由度；On the basis of the original degree of freedom of the flexible robot, the virtual degree of freedom of the end is increased;
获取增加末端虚拟自由度后的柔性机器人的正运动学方程；Obtain the forward kinematics equation of the flexible robot after adding the virtual degrees of freedom at the end;
根据正运动学方程获取柔性机器人的雅克比矩阵；Obtain the Jacobian matrix of the flexible robot according to the forward kinematics equation;
根据雅克比矩阵进行柔性机器人逆运动学求解。The inverse kinematics of the flexible robot is solved according to the Jacobian matrix.
可知，在柔性臂机器人本身带有的自由度的基础上，将其末端功能如相机视角或任务约束(如抓取东西的任务)等虚拟成额外的自由度，关节的极限则是这个相机视角或者任务的约束范围，从而增加柔性机器人的在任意给定的末端位置姿态的情况下的有解可能性。与柔性机器人传统逆运动学求解方法相比，该方法相当于减低了柔性机器人的末端约束的维数，扩大了柔性机器人的求解搜索范围，具有有解数量多，迭代效率高特点，可广泛应用于柔性机器人的逆运动学求解中。参考图1，图1是本发明中一种柔性机器人逆运动学求解方法的柔性机器人的末端虚拟自由度的一具体实施例示意图；利用图1所示的柔性机器人用于抓取物品；本实施例中，柔性机器人具有2n个自由度，属于冗余机器人，由n关节组成，每个关节具有2个互相垂直的自由度(如图1中的Y轴和Z轴)，增加了X方向的自由度作为末端虚拟自由度。It can be seen that on the basis of the degrees of freedom of the flexible arm robot itself, its end functions such as camera perspective or task constraints (such as the task of grabbing things) are virtualized into additional degrees of freedom, and the limit of the joint is the camera perspective. Or the constraint range of the task, thereby increasing the solution possibility of the flexible robot at any given end position and pose. Compared with the traditional inverse kinematics solution method of the flexible robot, this method is equivalent to reducing the dimension of the end constraint of the flexible robot and expanding the solution search range of the flexible robot. It has the characteristics of large number of solutions and high iterative efficiency, and can be widely used. In the inverse kinematics solution of flexible robots. Referring to FIG. 1, FIG. 1 is a schematic diagram of a specific embodiment of the virtual degree of freedom at the end of a flexible robot according to a method for solving the inverse kinematics of a flexible robot in the present invention; the flexible robot shown in FIG. 1 is used for grabbing items; this implementation In the example, the flexible robot has 2n degrees of freedom, belongs to redundant robots, and consists of n joints, each joint has 2 mutually perpendicular degrees of freedom (Y axis and Z axis in Figure 1), adding the degrees of freedom as end virtual degrees of freedom.
作为技术方案的进一步改进，根据雅克比矩阵和数值迭代法进行柔性机器人逆运动学求解。给柔性机器人增加虚拟的自由度，满足任务的约束，提高有解的可能性和迭代的效率。与传统的运动学逆解方法相比，该方法具有有解的可能性高，迭代的效率高，更贴合柔性机器人的任务环境等优点，比较适用于对柔性机器人的逆运动学求解。As a further improvement of the technical scheme, the inverse kinematics of the flexible robot is solved according to the Jacobian matrix and numerical iterative method. Add virtual degrees of freedom to the flexible robot, meet the constraints of the task, and improve the possibility of a solution and the efficiency of iteration. Compared with the traditional inverse kinematics solution method, this method has the advantages of high possibility of a solution, high iterative efficiency, and is more suitable for the task environment of flexible robots. It is more suitable for the inverse kinematics solution of flexible robots.
下面对柔性机器人逆运动学求解方法做具体说明：The following is a detailed description of the inverse kinematics solution method of the flexible robot:
首先，为了对柔性机械臂进行运动学分析与求解，需要建立D-H坐标系。D-H坐标法虽然是机器人学中通用方法，但当前D-H坐标系的建立规则不一，且没有形成统一的标准，大多根据个人习惯建立。本实施例按照改善后的D-H坐标系规则建立D-H坐标系(如图2所示)，并得到D-H参数表如表1所示。D-H坐标系建立规则如下：Zi轴沿第i关节的轴线方向，Xi轴垂直于Zi轴，并指向离开Zi轴的方向；Yi轴按右手坐标系的规则建立。First, in order to analyze and solve the kinematics of the flexible manipulator, it is necessary to establish a DH coordinate system. Although the DH coordinate method is a common method in robotics, the current rules for establishing the DH coordinate system are different, and there is no unified standard. Most of them are established according to personal habits. In this embodiment, a DH coordinate system is established according to the improved DH coordinate system rule (as shown in FIG. 2 ), and a DH parameter table is obtained as shown in Table 1. The rules for establishing the DH coordinate system are as follows: the Zi axis is along the axis direction of the i-th joint, the Xi axis is perpendicular to the Zi axis, and points to the direction away from the Zi axis; the Yi axis is established according to the rules of the right-handed coordinate system.
表1-柔性机械臂DH参数表Table 1 - DH parameter table of flexible manipulator
根据D-H坐标系建立规则以及前面的D-H参数表，可以依次得到齐次变换矩阵：According to the D-H coordinate system establishment rules and the previous D-H parameter table, the homogeneous transformation matrix can be obtained in turn:
将上述齐次变换矩阵依次连乘即可得到21号坐标系在1号坐标系中的表示，亦即机械臂的正运动学求解：Multiplying the above homogeneous transformation matrices in turn can get the representation of the No. 21 coordinate system in the No. 1 coordinate system, that is, the forward kinematics solution of the robotic arm:
1T21＝1T2·2T3…20T21＝f(θ1,θ2,…,θ20)，1 T21 =1 T2 ·2 T3 ...20 T21 =f(θ1 ,θ2 ,...,θ20 ),
其中，T为末端位姿X对应的齐次变换矩阵。Among them, T is the homogeneous transformation matrix corresponding to the end pose X.
接着，在柔性机器人原有自由度的基础上，根据末端相机或任务的约束范围特点等，增加若干末端虚拟自由度，末端虚拟自由度为末端虚拟移动自由度或末端虚拟旋转自由度，末端虚拟自由度可以对应一个虚拟的移动关节，或者一个旋转关节。末端虚拟自由度至少有一个，更优选地，末端虚拟自由度可以为2个或者2个以上的末端虚拟移动自由度或末端虚拟旋转自由度或者两者的混合，使得逆运动学的求解更能与其自身特征或者任务约束范围更加匹配。此时其正运动学方程可以表示为：Then, on the basis of the original degrees of freedom of the flexible robot, according to the constraints of the end camera or the task, a number of virtual degrees of freedom of the end are added. A degree of freedom can correspond to a virtual movement joint, or a rotation joint. There is at least one virtual degree of freedom at the end, and more preferably, the virtual degree of freedom at the end can be two or more virtual degrees of freedom of movement at the end or virtual rotation at the end or a mixture of the two, so that the inverse kinematics can be solved more efficiently. It better matches its own characteristics or task constraints. At this time, its positive kinematic equation can be expressed as:
其中，为增加末端虚拟自由度后的关节总变量；θ和f1(θ)分别代表为柔性机器人原关节变量和原正运动学方程；和分别为末端虚拟自由度对应的关节变量和正运动学方程，该末端虚拟自由度变量的极限约束则对应了相机视角或者任务的约束范围，即末端虚拟自由度参与了柔性机器人的逆运动学求解的过程，并没有参与柔性机器人的实际运动控制中。根据末端虚拟自由度、柔性机器人的运动学方程、雅克比矩阵，增加末端虚拟自由度之后的柔性机器人的正运动学方程可以表示为：in, is the total joint variable after adding the virtual degree of freedom at the end; θ and f1 (θ) represent the original joint variable and original positive kinematic equation of the flexible robot respectively; and are the joint variables and forward kinematic equations corresponding to the virtual degrees of freedom at the end, respectively, and the limit constraints of the virtual degrees of freedom at the end correspond to the camera angle of view or the constraint range of the task, namely The end virtual degrees of freedom participate in the process of solving the inverse kinematics of the flexible robot, and do not participate in the actual motion control of the flexible robot. According to the virtual degrees of freedom at the end, the kinematics equation of the flexible robot, and the Jacobian matrix, the forward kinematics equation of the flexible robot after adding the virtual degrees of freedom at the end can be expressed as:
X＝f(Θ)；X=f(Θ);
由正运动学方程，两边微分可以得到：From the forward kinematics equation, the differential on both sides can be obtained:
其中J(Θ)为柔性机器人的新雅克比矩阵，其进一步地可以表示为：where J(Θ) is the new Jacobian matrix of the flexible robot, which can be further expressed as:
其中，J(θ)为柔性机器人的原雅克比矩阵，为末端虚拟自由度部分对应的雅克比矩阵。ei为关节旋转轴的单位矢量，ri为关节旋转轴中心到臂末端的矢量。Among them, J(θ) is the original Jacobian matrix of the flexible robot, is the Jacobian matrix corresponding to the end virtual degrees of freedom part. ei is the unit vector of the joint rotation axis, andri is the vector from the center of the joint rotation axis to the end of the arm.
通过给柔性机器人增加末端虚拟自由度，增加了柔性机器人的逆运动学求解有解的可能性，有助于快速找到一组满足于任务约束情况下的逆解，参考图3，图3是本发明中一种柔性机器人逆运动学求解方法的一具体实施例方法流程图；其中，θi为柔性机器人自身各个关节对应的关节角度，为柔性机器人的末端虚拟自由度(关节)对应的关节变量，具体的求解过程包括：By adding virtual degrees of freedom at the end of the flexible robot, the possibility of solving the inverse kinematics of the flexible robot is increased, which helps to quickly find a set of inverse solutions that satisfy the task constraints. A method flow chart of a specific embodiment of a flexible robot inverse kinematics solution method in the invention; wherein, θi is the joint angle corresponding to each joint of the flexible robot itself, is the joint variable corresponding to the virtual degree of freedom (joint) at the end of the flexible robot. The specific solution process includes:
(1)给定迭代的初始关节角度Θ0，期望的末端位姿Xd(位置姿态简称位姿)。(1) Given the initial joint angle Θ0 of the iteration, the desired end pose Xd (position pose is referred to as pose).
(2)设定当前循环迭代的次数i＝0。(2) Set the number of iterations of the current loop i=0.
(3)由正运动学方程计算初始的柔性机器人末端位姿X0，进一步得到当前条件下的末端位姿与期望的末端位姿的位姿差值为：ΔX0＝Xd-X0＝Xd-f(Θ0)。(3) By the forward kinematic equation Calculate the initial flexible robot end pose X0 , and further obtain the pose difference between the end pose under the current conditions and the expected end pose: ΔX0 =Xd -X0 =Xd -f(Θ0 ) .
(4)根据当前的关节角度，由上述的雅克比矩阵公式，计算当前的雅克比矩阵J(Θ)。(4) According to the current joint angle, the current Jacobian matrix J(Θ) is calculated by the above Jacobian matrix formula.
(5)由末端的位姿误差，通过雅克比矩阵映射到关节角度的误差，进一步地得到：ΔΘi＝J+(Θi)ΔXi，其中J+(Θi)是雅克比矩阵J(Θ)的伪逆。(5) From the pose error of the end, the error of the joint angle mapped by the Jacobian matrix is further obtained: ΔΘi =J+ (Θi )ΔXi , where J+ (Θi ) is the Jacobian matrix J ( The pseudo-inverse of Θ).
(6)更新关节角度Θi+1＝Θi+ΔΘi。(6) Update the joint angle Θi+1 =Θi +ΔΘi .
(7)在更新的新的关节角度的情况下,更新末端的位姿Xi+1＝f(Θi+1)以及与期望的位姿的位姿差ΔXi+1。(7) In the case of the updated new joint angle, update the pose Xi+1 =f(Θi+1 ) of the end and the pose difference ΔXi+1 with the desired pose.
(8)判断末端位姿差是否小于设定值，即norm(ΔXi+1)≤ε，如条件满足，迭代结束，Θi+1为最终的关节角的解；否则进行下一步。(8) Determine whether the end pose difference is less than the set value, that is, norm(ΔXi+1 )≤ε, if the condition is satisfied, the iteration ends, and Θi+1 is the solution of the final joint angle; otherwise, go to the next step.
(9)比较i的值，如果i≤imax，则进行下一步，否则，迭代结束，方程没有合适的解。(9) Compare the value of i, if i≤imax , proceed to the next step, otherwise, the iteration ends and the equation has no suitable solution.
(10)迭代次数i＝i+1。(10) The number of iterations i=i+1.
(11)重复(4)-(10)，直到迭代结束。(11) Repeat (4)-(10) until the iteration ends.
实施例2Example 2
一种柔性机器人逆运动学求解系统，包括：An inverse kinematics solution system for a flexible robot, comprising:
末端虚拟自由度增加单元，用于在柔性机器人原有自由度的基础上，增加末端虚拟自由度；The end virtual degree of freedom increasing unit is used to increase the end virtual degree of freedom on the basis of the original degree of freedom of the flexible robot;
正运动学方程获取单元，用于获取增加末端虚拟自由度后的柔性机器人的正运动学方程；The forward kinematic equation acquisition unit is used to obtain the forward kinematic equation of the flexible robot after adding the virtual degree of freedom at the end;
雅克比矩阵获取单元，用于根据正运动学方程获取柔性机器人的雅克比矩阵；The Jacobian matrix acquisition unit is used to acquire the Jacobian matrix of the flexible robot according to the forward kinematic equation;
逆运动学求解单元，用于根据雅克比矩阵进行柔性机器人逆运动学求解。The inverse kinematics solving unit is used to solve the inverse kinematics of the flexible robot according to the Jacobian matrix.
进一步地，逆运动学求解单元根据雅克比矩阵和数值迭代法进行柔性机器人逆运动学求解。末端虚拟自由度为末端虚拟移动自由度和/或末端虚拟旋转自由度。Further, the inverse kinematics solving unit performs the inverse kinematics solution of the flexible robot according to the Jacobian matrix and the numerical iterative method. The end virtual degrees of freedom are the end virtual movement degrees of freedom and/or the end virtual rotational degrees of freedom.
一种柔性机器人逆运动学求解系统的具体工作过程参照实施例1的描述，不再赘述。For the specific working process of a flexible robot inverse kinematics solution system, refer to the description in Embodiment 1, and will not be repeated here.
实施例3Example 3
一种柔性机器人逆运动学求解设备，包括：A flexible robot inverse kinematics solution device, comprising:
至少一个处理器；以及，at least one processor; and,
与所述至少一个处理器通信连接的存储器；其中，a memory communicatively coupled to the at least one processor; wherein,
所述存储器存储有可被所述至少一个处理器执行的指令，所述指令被所述至少一个处理器执行，以使所述至少一个处理器能够执行所述的柔性机器人逆运动学求解方法。The memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the flexible robot inverse kinematics solution method.
柔性机器人逆运动学求解方法的具体描述参照实施例1的描述，不再赘述。For the specific description of the method for solving the inverse kinematics of the flexible robot, refer to the description in Embodiment 1, and will not be repeated here.
实施例4Example 4
一种计算机可读存储介质，所述计算机可读存储介质存储有计算机可执行指令，所述计算机可执行指令用于使计算机执行所述的柔性机器人逆运动学求解方法。A computer-readable storage medium storing computer-executable instructions for causing a computer to execute the inverse kinematics solution method for a flexible robot.
柔性机器人逆运动学求解方法的具体描述参照实施例1的描述，不再赘述。For the specific description of the method for solving the inverse kinematics of the flexible robot, refer to the description in Embodiment 1, and will not be repeated here.
以上是对本发明的较佳实施进行了具体说明，但本发明创造并不限于所述实施例，熟悉本领域的技术人员在不违背本发明精神的前提下还可做出种种的等同变形或替换，这些等同的变形或替换均包含在本申请权利要求所限定的范围内。The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the described embodiments, and those skilled in the art can also make various equivalent deformations or replacements on the premise that does not violate the spirit of the present invention , these equivalent modifications or substitutions are all included within the scope defined by the claims of the present application.
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811137249.1ACN109366486B (en) | 2018-09-28 | 2018-09-28 | Flexible robot inverse kinematics solving method, system, equipment and storage medium |
| Application Number | Priority Date | Filing Date | Title |
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| CN201811137249.1ACN109366486B (en) | 2018-09-28 | 2018-09-28 | Flexible robot inverse kinematics solving method, system, equipment and storage medium |
| Publication Number | Publication Date |
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| CN109366486Atrue CN109366486A (en) | 2019-02-22 |
| CN109366486B CN109366486B (en) | 2021-12-07 |
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811137249.1AActiveCN109366486B (en) | 2018-09-28 | 2018-09-28 | Flexible robot inverse kinematics solving method, system, equipment and storage medium |
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| CN (1) | CN109366486B (en) |
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