WO2023116129A1 - 一种协作机器人的柔顺力控制方法及系统 - Google Patents
一种协作机器人的柔顺力控制方法及系统 Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
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- the invention relates to the technical field of robot control, in particular to a compliance force control method and system of a collaborative robot.
- Collaborative robots have the advantages of good flexibility and flexible human-computer interaction, and have been widely used in industrial, medical and other fields.
- compliance force control is the core of collaborative robots to achieve complex tasks, high-quality operations and human-computer interaction.
- the existing force control methods for collaborative robots with redundant degrees of freedom are mainly based on the pseudo-inverse calculation of the robot Jacobian matrix. But this approach is difficult to deal with the physical constraints of the system.
- CN201911358551.4 proposes a pseudo-inverse of the Jacobian matrix without a machine, but this method of spatial decoupling is difficult to model and does not consider the problem of insufficient system stiffness.
- CN202010141357.7 proposes a robot stiffness optimization algorithm, which is completed by optimizing the body structure during the structural design process of the robot. On the premise that the robot body is solidified, this method cannot achieve the optimization of the system stiffness by adjusting the robot position.
- the existing robot force control method usually adopts the method based on the inversion of the Jacobian matrix, that is, for the terminal contact force, the inverse matrix operator of the Jacobian matrix is used to perform spatial changes, so as to calculate the joint control amount of the robot.
- this method is intuitive, it is usually difficult to deal with complex system constraints.
- stiffness optimization the current mainstream method generally adopts offline optimization. First, the trajectory of the robot is discretized, and then the stiffness optimization index of the system is established. Through Heuristic algorithm for global optimization. However, it is difficult to extend this method to the scene of force control. The main reason is that due to the unpredictability of the actual force, it is difficult to obtain the expected trajectory of the robot, so it is difficult to guarantee the force control accuracy of the robot.
- the purpose of the present invention is to overcome the deficiencies of the prior art.
- the present invention provides a method and system for controlling the compliant force of a collaborative robot, which can realize high-precision control of the contact force, and can increase the stiffness of the collaborative robot system in real time, thereby suppressing the Flutter; it can effectively avoid the system from falling into a singular position, and at the same time meet the joint angle and angular velocity limitations of the robot.
- an embodiment of the present invention provides a compliance force control method of a collaborative robot, the method comprising:
- a compliance force control process is performed on the collaborative robot based on the real-time control amount.
- the establishment of a stability control strategy model at the end of the collaborative robot includes:
- the relationship between the relative movement of the ends and the contact force is as follows:
- the stability control strategy model at the end of the collaborative robot is as follows:
- C m represents the group pit model
- G m represents the elastic coefficient
- F represents the contact force
- x represents the position of the end effector of the collaborative robot
- x d indicates the desired position of the end effector of the collaborative robot
- F d indicates the expected contact force
- t indicates the time
- k indicates the control parameter greater than 0.
- the establishment of the stiffness optimization strategy model of the collaborative robot includes:
- a stiffness index reconstruction process is performed based on the mapping relationship to obtain a stiffness optimization strategy model.
- mapping relationship is as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix.
- the stiffness index reconstruction process is performed based on the mapping relationship to obtain a stiffness optimization strategy model, as follows:
- det(JJ T ) is expanded to obtain the mapping relationship between stiffness optimization and robot joint motion, which is the stiffness optimization strategy model, as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that converts the matrix into a column vector.
- the establishment of the singular avoidance model of the collaborative robot includes:
- ⁇ and ⁇ both represent normal numbers; among them, ⁇ ⁇ F represents an operator for obtaining the Frobenoius norm of the matrix; Represents the pseudo-inverse of J; det represents the value of the determinant corresponding to the square matrix; trace represents the trace of the matrix.
- the real-time control quantity solution model is as follows:
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that transforms the matrix into a column vector
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers ; represent the lower bound and upper bound of ⁇ respectively; Respectively lower bound and upper bound.
- the solving of the real-time control quantity includes:
- ⁇ is a neural network parameter greater than 0;
- Proj represents a saturation function, which is defined as follows:
- J represents the Jacobian matrix of the collaborative robot
- T represents the transpose operator of the matrix
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers
- ⁇ - and ⁇ + represent ⁇
- a represents a positive control parameter; Indicates the joint angular acceleration of the collaborative robot; ⁇ indicates the joint angle of the collaborative robot; Indicates the feedback speed of the end effector of the collaborative robot; ⁇ 1 and ⁇ 2 both represent state variables.
- an embodiment of the present invention also provides a compliance force control system of a collaborative robot, the system comprising:
- the first establishment module used to establish the stability control strategy model at the end of the collaborative robot;
- the second establishment module used to establish the stiffness optimization strategy model of the collaborative robot
- the third building block used to build the singular avoidance model of the collaborative robot
- Solving module used to establish a real-time control quantity solution model based on the stability force control strategy model, the stiffness optimization strategy model and the singularity avoidance model, and perform real-time control quantity solution to obtain the real-time control quantity of the collaborative robot;
- a control module used to control the compliant force of the collaborative robot based on the real-time control amount.
- high-precision control of the contact force can be realized, and the stiffness of the collaborative robot system can be improved in real time, thereby suppressing flutter; when the stiffness of the collaborative robot system is good, the robot is usually close to the singular position, As a result, the flexibility of the system is greatly reduced, and the system can be effectively avoided from falling into a singular position, while satisfying the joint angle and angular velocity limitations of the robot.
- FIG. 1 is a schematic flow diagram of a compliance force control method of a collaborative robot in an embodiment of the present invention
- Fig. 2 is a schematic diagram of the structural composition of the compliance force control system of the collaborative robot in the embodiment of the present invention.
- FIG. 1 is a schematic flowchart of a compliance force control method for a collaborative robot in an embodiment of the present invention.
- a kind of compliant force control method of collaborative robot, described method comprises:
- the establishment of the stability control strategy model of the end of the collaborative robot includes: using the principle of group pit control to establish the relationship between the relative motion of the end of the collaborative robot and the contact force; The relationship between contact force and contact force establishes a stable force control strategy model at the end of the collaborative robot.
- the stability control strategy model at the end of the collaborative robot is as follows:
- C m represents the group pit model
- G m represents the elastic coefficient
- F represents the contact force
- x represents the position of the end effector of the collaborative robot
- x d indicates the desired position of the end effector of the collaborative robot
- F d indicates the expected contact force
- t indicates the time
- k indicates the control parameter greater than 0.
- the stabilization force control strategy model at the end of the noise-resistant collaborative robot is established as follows:
- C m represents the group pit model
- G m represents the elastic coefficient
- F represents the contact force
- x represents the position of the end effector of the collaborative robot
- x d indicates the desired position of the end effector of the collaborative robot
- F d indicates the expected contact force
- t indicates the time
- k indicates the control parameter greater than 0.
- the establishment of the stiffness optimization strategy model of the collaborative robot includes: establishing the stiffness index of the collaborative robot, and establishing the mapping relationship between the stiffness index and the decision-making quantity; based on the mapping relationship The stiffness index is reconstructed to obtain the stiffness optimization strategy model.
- mapping relationship is as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix.
- stiffness index reconstruction process is performed based on the mapping relationship to obtain a stiffness optimization strategy model, as follows:
- det(JJ T ) is expanded to obtain the mapping relationship between stiffness optimization and robot joint motion, which is the stiffness optimization strategy model, as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that converts the matrix into a column vector.
- the stiffness index of the robot is established, and the mapping relationship between it and the decision variable is established as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix.
- det(JJ T ) is expanded to obtain the mapping relationship between stiffness optimization and robot joint motion, which is the stiffness optimization strategy model, as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that converts the matrix into a column vector.
- the establishment of the singular avoidance model of the collaborative robot includes:
- ⁇ and ⁇ both represent normal numbers; among them, ⁇ ⁇ F represents an operator for obtaining the Frobenoius norm of the matrix; Represents the pseudo-inverse of J; det represents the value of the determinant corresponding to the square matrix; trace represents the trace of the matrix.
- ⁇ and ⁇ both represent normal numbers; among them, ⁇ ⁇ F represents an operator for obtaining the Frobenoius norm of the matrix; Represents the pseudo-inverse of J; det represents the value of the determinant corresponding to the square matrix; trace represents the trace of the matrix.
- S14 Establish a real-time control variable solution model based on the stability force control strategy model, the stiffness optimization strategy model, and the singularity avoidance model, and perform real-time control variable solution to obtain the real-time control variable of the collaborative robot;
- the real-time control quantity solution model is as follows:
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that transforms the matrix into a column vector
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers ; represent the lower bound and upper bound of ⁇ respectively; Respectively lower bound and upper bound.
- the real-time control variable solution includes:
- ⁇ is a neural network parameter greater than 0;
- Proj represents a saturation function, which is defined as follows:
- J represents the Jacobian matrix of the collaborative robot
- T represents the transpose operator of the matrix
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers
- ⁇ - and ⁇ + represent ⁇
- ⁇ represents the positive control parameter
- ⁇ indicates the joint angle of the collaborative robot
- ⁇ 1 and ⁇ 2 both represent state variables.
- the real-time control variable solution model is established according to the stability force control strategy model, the stiffness optimization strategy model and the singularity avoidance model as follows:
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that transforms the matrix into a column vector
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers ; represent the lower bound and upper bound of ⁇ respectively; Respectively lower bound and upper bound.
- ⁇ is a neural network parameter greater than 0;
- Proj represents a saturation function, which is defined as follows:
- J represents the Jacobian matrix of the collaborative robot
- T represents the transpose operator of the matrix
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers
- ⁇ - and ⁇ + represent ⁇
- ⁇ represents a positive control parameter
- ⁇ indicates the joint angle of the collaborative robot
- ⁇ 1 and ⁇ 2 both represent state variables.
- S15 Perform compliance force control processing on the collaborative robot based on the real-time control amount.
- the cooperative robot is controlled with compliance force.
- controller parameters k, ⁇ , ⁇ , ⁇ , joint angle limit ⁇ - , ⁇ + of the mechanical arm of the collaborative robot, angular velocity limit The initial state of the manipulator ⁇ (0), Desired trajectory x d (t), And the expected contact force F d , the task duration T, the position feedback x(t) performed by the end of the manipulator, the contact force F(t), and the joint feedback ⁇ .
- high-precision control of the contact force can be realized, and the stiffness of the collaborative robot system can be improved in real time, thereby suppressing flutter; when the stiffness of the collaborative robot system is good, the robot is usually close to the singular position, As a result, the flexibility of the system is greatly reduced, and the system can be effectively avoided from falling into a singular position, while satisfying the joint angle and angular velocity limitations of the robot.
- FIG. 2 is a schematic structural composition diagram of a compliance force control system of a collaborative robot in an embodiment of the present invention.
- a compliant force control system of a collaborative robot the system includes:
- the first establishment module 21 used to establish the stability control strategy model of the end of the collaborative robot
- the establishment of the stability control strategy model of the end of the collaborative robot includes: using the principle of group pit control to establish the relationship between the relative motion of the end of the collaborative robot and the contact force; The relationship between contact force and contact force establishes a stable force control strategy model at the end of the collaborative robot.
- the stability control strategy model at the end of the collaborative robot is as follows:
- C m represents the group pit model
- G m represents the elastic coefficient
- F represents the contact force
- x represents the position of the end effector of the collaborative robot
- x d indicates the desired position of the end effector of the collaborative robot
- F d indicates the expected contact force
- t indicates the time
- k indicates the control parameter greater than 0.
- the stabilization force control strategy model at the end of the noise-resistant collaborative robot is established as follows:
- C m represents the group pit model
- G m represents the elastic coefficient
- F represents the contact force
- x represents the position of the end effector of the collaborative robot
- x d indicates the desired position of the end effector of the collaborative robot
- F d indicates the expected contact force
- t indicates the time
- k indicates the control parameter greater than 0.
- the second establishment module 22 used to establish the stiffness optimization strategy model of the collaborative robot
- the establishment of the stiffness optimization strategy model of the collaborative robot includes: establishing the stiffness index of the collaborative robot, and establishing the mapping relationship between the stiffness index and the decision-making quantity; based on the mapping relationship The stiffness index is reconstructed to obtain the stiffness optimization strategy model.
- mapping relationship is as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix.
- stiffness index reconstruction process is performed based on the mapping relationship to obtain a stiffness optimization strategy model, as follows:
- det(JJ T ) is expanded to obtain the mapping relationship between stiffness optimization and robot joint motion, which is the stiffness optimization strategy model, as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that converts the matrix into a column vector.
- the stiffness index of the robot is established, and the mapping relationship between it and the decision variable is established as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix.
- det(JJ T ) is expanded to obtain the mapping relationship between stiffness optimization and robot joint motion, which is the stiffness optimization strategy model, as follows:
- det represents the value of the determinant corresponding to the square matrix
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that converts the matrix into a column vector.
- the third establishment module 23 used to establish the singular avoidance model of the collaborative robot
- the establishment of the singular avoidance model of the collaborative robot includes:
- ⁇ and ⁇ both represent normal numbers; among them, ⁇ ⁇ F represents an operator for obtaining the Frobenoius norm of the matrix; Represents the pseudo-inverse of J; det represents the value of the determinant corresponding to the square matrix; trace represents the trace of the matrix.
- ⁇ and ⁇ both represent normal numbers; among them, ⁇ ⁇ F represents an operator for obtaining the Frobenoius norm of the matrix; Represents the pseudo-inverse of J; det represents the value of the determinant corresponding to the square matrix; trace represents the trace of the matrix.
- Solving module 24 used to establish a real-time control variable solution model based on the stability force control strategy model, the stiffness optimization strategy model and the singularity avoidance model, and perform real-time control variable solution to obtain the real-time control variable of the collaborative robot ;
- the real-time control quantity solution model is as follows:
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that transforms the matrix into a column vector
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers ; represent the lower bound and upper bound of ⁇ respectively; Respectively lower bound and upper bound.
- the real-time control variable solution includes:
- ⁇ is a neural network parameter greater than 0;
- Proj represents a saturation function, which is defined as follows:
- J represents the Jacobian matrix of the collaborative robot
- T represents the transpose operator of the matrix
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers
- ⁇ - and ⁇ + represent ⁇
- ⁇ represents a positive control parameter
- ⁇ indicates the joint angle of the collaborative robot
- ⁇ 1 and ⁇ 2 both represent state variables.
- the real-time control variable solution model is established according to the stability force control strategy model, the stiffness optimization strategy model and the singularity avoidance model as follows:
- T represents the transpose operator of the matrix
- -1 represents the inverse operator of the matrix
- J represents the Jacobian matrix of the collaborative robot
- vec represents the operator that transforms the matrix into a column vector
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers ; represent the lower bound and upper bound of ⁇ respectively; Respectively lower bound and upper bound.
- ⁇ is a neural network parameter greater than 0;
- Proj represents a saturation function, which is defined as follows:
- J represents the Jacobian matrix of the collaborative robot
- T represents the transpose operator of the matrix
- ⁇ represents the flexibility index of the collaborative robot
- ⁇ and ⁇ represent normal numbers
- ⁇ - and ⁇ + represent ⁇
- the lower and upper bounds of Respectively The lower and upper bounds of ; + indicates positive control parameters; Indicates the joint angular acceleration of the collaborative robot; ⁇ indicates the joint angle of the collaborative robot; Indicates the feedback speed of the end effector of the collaborative robot; ⁇ 1 and ⁇ 2 both represent state variables.
- Control module 25 used to control the compliant force of the collaborative robot based on the real-time control amount.
- the cooperative robot is controlled with compliance force.
- controller parameters k, ⁇ , ⁇ , ⁇ , joint angle limit ⁇ - , ⁇ + of the mechanical arm of the collaborative robot, angular velocity limit The initial state of the manipulator ⁇ (0), Desired trajectory x d (t), And the expected contact force F d , the task duration T, the position feedback x(t) performed by the end of the manipulator, the contact force F(t), and the joint feedback ⁇ .
- high-precision control of the contact force can be realized, and the stiffness of the collaborative robot system can be improved in real time, thereby suppressing flutter; when the stiffness of the collaborative robot system is good, the robot is usually close to the singular position, As a result, the flexibility of the system is greatly reduced, and the system can be effectively avoided from falling into a singular position, while satisfying the joint angle and angular velocity limitations of the robot.
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Abstract
一种协作机器人的柔顺力控制方法及系统,方法包括:建立协作机器人末端的稳定力控制策略模型(S11);建立协作机器人的刚度优化策略模型(S12);建立协作机器人的奇异规避模型(S13);基于稳定力控制策略模型、刚度优化策略模型和奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得协作机器人的实时控制量(S14);基于实时控制量对协作机器人进行柔顺力的控制处理(S15)。该方法能够实现对接触力的高精度控制,并能够实时提升协作机器人系统的刚度,从而抑制颤振;能够有效规避系统陷入奇异位型,同时满足机器人的关节角度、角速度限制。
Description
本发明涉及机器人控制技术领域,尤其涉及一种协作机器人的柔顺力控制方法及系统。
协作机器人具备柔性好、人机交互灵活的优势,在工业、医疗等领域已取得了广泛的应用。其中柔顺力控制是协作机器人实现复杂任务高质量作业以及人机交互等的核心。通过对接触力的实时感知以及控制量的在线生成,可以实现机器人末端执行器按照预期的接触力施加于作用对象上。现有针对具有冗余自由度的协作机器人的力控制方法,主要是基于机器人雅克比矩阵的伪逆计算实现。但是这种方法难以处理系统的物理约束。CN201911358551.4提出了一种无需机器算雅克比矩阵的伪逆,但是这种空间解耦的方法建模困难,同时没有考虑系统刚度不足的问题。
然而,由于协作机器人自身结构的限制,系统的刚度较传统工业机器人有明显不足,使得机器人在机交互过程中能够容易出现颤振、误差较低等现象,使系统的稳定性显著下降。CN202010141357.7提出了一种机器人的刚度优化算法,该类方法是在机器人的结构设计过程中,通过对本体结构的优化完成的。在机器人本体固化的前提下,该方法无法通过调整机器人位型实现系统的刚度优化。
现有机器人力控制方法,通常采用基于雅克比矩阵求逆的方法,即针对末端接触力,采用雅克比矩阵的逆矩阵算子进行空间变化,从而计算机器人的关节控制量。这种方法虽然直观,但是这种方法通常难以处理复杂的系统约束;在刚度优化方面,目前的主流方法一般采用离线优化,首先将机器人的运动轨迹离散化,然后建立系统的刚度优化指标,通过启发式算法对进行全局寻优。但是这种方法难以扩展到力控制的场景,其主要原因是由于实际力相应的不可预知性,导致机器人的期望运动轨迹获取困难,从而难以保证机器人的力控制精度。
发明内容
本发明的目的在于克服现有技术的不足,本发明提供了一种协作机器人的柔顺力控制方法及系统,能够实现对接触力的高精度控制,并能够实时提升协作机器人系统的刚度,从而抑制颤振;能够有效规避系统陷入奇异位型,同时满足机器人的关节角度、角速度限制。
为了解决上述技术问题,本发明实施例提供了一种协作机器人的柔顺力控制方法,所述方法包括:
建立协作机器人末端的稳定力控制策略模型;
建立协作机器人的刚度优化策略模型;
建立协作机器人的奇异规避模型;
基于所述稳定力控制策略模型、所述刚度优化策略模型和所述奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得所述协作机器人的实时控制量;
基于所述实时控制量对所述协作机器人进行柔顺力的控制处理。
可选的,所述建立协作机器人末端的稳定力控制策略模型,包括:
利用组坑控制原理,建立所述协作机器人的末端相对运动与接触力之间的关系;
基于末端相对运动与接触力之间的关系建立协作机器人末端的稳定力控制策略模型。
可选的,所述端相对运动与接触力之间的关系如下:
所述协作机器人末端的稳定力控制策略模型如下:
其中,C
m表示组坑模型;G
m表示弹性系数;F表示接触力;x表示协作机器人末端执行器的位置;
表示协作机器人末端执行器的速度;x
d表示协作机器人末端执行器的期望位置;
表示协作机器人末端执行器的的期望速度;
表示协作机器人末端执行器的反馈速度;F
d表示期望接触力;t表示时间;k表示大于0的控制参数。
可选的,所述建立协作机器人的刚度优化策略模型,包括:
建立所述协作机器人的刚度指标,并建立所述刚度指标与决策量之间的映射关系;
基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型。
可选的,所述映射关系如下:
det((JJ
T)
-1);(3)
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子。
可选的,所述基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型,如下:
对所述映射关系的式子进行简化,将性能指标改写为:det(JJ
T),此时,所述协作机器人的刚度优化转为:
min det(JJ
T);(4)
根据所述协作机器人的关节角度θ对det(JJ
T)进行展开,得到刚度优化与机器人关节运动之间的映射关系即为刚度优化策略模型,如下:
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子。
可选的,所述建立协作机器人的奇异规避模型,包括:
建立协作机器人的灵活性约束如下:
根据决策变量对式(6)进行改写如下:
可选的,所述实时控制量求解模型如下:
θ
-≤θ≤θ
+
其中,T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界。
可选的,所述进行实时控制量求解,包括:
设置满足实时控制量求解模型的隐式解,对所述协作机器人的实时力控制与刚度优化如下:
其中,∈为大于0的神经网络参数;Proj表示一个饱和函数,定义如下:
其中,
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;T表示矩阵的转置算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界;a表示正控制参数;
表示协作机器人的关节角加速度;θ表示协作机器人的关节角度;
表示协作机器人末端执行器的反馈速度;λ
1和λ
2均表示状态变量。
另外,本发明实施例还提供了一种协作机器人的柔顺力控制系统,所述系统包括:
第一建立模块:用于建立协作机器人末端的稳定力控制策略模型;
第二建立模块:用于建立协作机器人的刚度优化策略模型;
第三建立模块:用于建立协作机器人的奇异规避模型;
求解模块:用于基于所述稳定力控制策略模型、所述刚度优化策略模型和所述奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得所述协作机器人的实时控制量;
控制模块:用于基于所述实时控制量对所述协作机器人进行柔顺力的控制处理。
在本发实施例中,能够实现对接触力的高精度控制,并能够实时提升协作机器人系统的刚度,从而抑制颤振;在协作机器人系统刚度较好时,通常会使机器人接近奇异位型,从而大大降低系统的灵活性,能够有效规避系统陷入奇异位型,同时满足机器人的关节角度、角速度限制。
为了更清楚地说明本发明实施例或现有技术中的技术方案,下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍,显而易见的,下面描述中的附图仅仅是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其它的附图。
图1是本发明实施例中的协作机器人的柔顺力控制方法的流程示意图;
图2是本发明实施例中的协作机器人的柔顺力控制系统的结构组成示意图。
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作出创造性劳动前提下所获得的所有其它实施例,都属于本发明保护的范围。
实施例一
请参阅图1,图1是本发明实施例中的协作机器人的柔顺力控制方法的流程示意图。
如图1所示,一种协作机器人的柔顺力控制方法,所述方法包括:
S11:建立协作机器人末端的稳定力控制策略模型;
在本发明具体实施过程中,所述建立协作机器人末端的稳定力控制策略模型,包括:利用组坑控制原理,建立所述协作机器人的末端相对运动与接触力之间的关系;基于末端相对运动与接触力之间的关系建立协作机器人末端的稳定力控制策略模型。
进一步的,所述端相对运动与接触力之间的关系如下:
所述协作机器人末端的稳定力控制策略模型如下:
其中,C
m表示组坑模型;G
m表示弹性系数;F表示接触力;x表示协作 机器人末端执行器的位置;
表示协作机器人末端执行器的速度;x
d表示协作机器人末端执行器的期望位置;
表示协作机器人末端执行器的的期望速度;
表示协作机器人末端执行器的反馈速度;F
d表示期望接触力;t表示时间;k表示大于0的控制参数。
具体的,利用阻抗控制原理,建立机器人末端相对运动与接触力之间的关系,如下:
建立抗噪的协作机器人末端的稳定力控制策略模型如下:
其中,C
m表示组坑模型;G
m表示弹性系数;F表示接触力;x表示协作机器人末端执行器的位置;
表示协作机器人末端执行器的速度;x
d表示协作机器人末端执行器的期望位置;
表示协作机器人末端执行器的的期望速度;
表示协作机器人末端执行器的反馈速度;F
d表示期望接触力;t表示时间;k表示大于0的控制参数。
S12:建立协作机器人的刚度优化策略模型;
在本发明具体实施过程中,所述建立协作机器人的刚度优化策略模型,包括:建立所述协作机器人的刚度指标,并建立所述刚度指标与决策量之间的映射关系;基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型。
进一步的,所述映射关系如下:
det((JJ
T)
-1);(3)
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子。
进一步的,所述基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型,如下:
对所述映射关系的式子进行简化,将性能指标改写为:det(JJ
T),此时,所述协作机器人的刚度优化转为:
min det(JJ
T);(4)
根据所述协作机器人的关节角度θ对det(JJ
T)进行展开,得到刚度优化 与机器人关节运动之间的映射关系即为刚度优化策略模型,如下:
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子。
具体的,建立机器人的刚度指标,并建立其与决策变量之间的映射关系如下:
det((JJ
T)
-1);(3)
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子。
对上述的式(3)进行简化,将性能指标改写为:det(JJ
T),此时,所述协作机器人的刚度优化转为:
min det(JJ
T);(4)
根据所述协作机器人的关节角度θ对det(JJ
T)进行展开,得到刚度优化与机器人关节运动之间的映射关系即为刚度优化策略模型,如下:
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子。
S13:建立协作机器人的奇异规避模型;
在本发明具体实施过程中,所述建立协作机器人的奇异规避模型,包括:
建立协作机器人的灵活性约束如下:
根据决策变量对式(6)进行改写如下:
建立协作机器人的灵活性约束如下:
根据决策变量对式(6)进行改写如下:
S14:基于所述稳定力控制策略模型、所述刚度优化策略模型和所述奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得所述协作机器人的实时控制量;
在本发明具体实时过程中,所述实时控制量求解模型如下:
θ
-≤θ≤θ
+
其中,T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界。
进一步的,所述进行实时控制量求解,包括:
设置满足实时控制量求解模型的隐式解,对所述协作机器人的实时力控制与刚度优化如下:
其中,∈为大于0的神经网络参数;Proj表示一个饱和函数,定义如下:
其中,
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;T表示矩阵的转置算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界; α表示正控制参数;
表示协作机器人的关节角加速度;θ表示协作机器人的关节角度;
表示协作机器人末端执行器的反馈速度;λ
1和λ
2均表示状态变量。
具体的,根据稳定力控制策略模型、刚度优化策略模型和奇异规避模型建立实时控制量求解模型如下:
θ
-≤θ≤θ
+
其中,T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界。
在对该实时控制量求解模型进行求解时,需要设计满足式(8)的隐式解,实现机器人的实时力控制与刚度优化如下:
其中,∈为大于0的神经网络参数;Proj表示一个饱和函数,定义如下:
其中,
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;T表示矩阵的转置算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界;α表示正控制参数;
表示协作机器人的关节角加速度;θ表示协作机器人的关节角度;
表示协作机器人末端执行器的反馈速度;λ
1和λ
2均表示状态变量。
S15:基于所述实时控制量对所述协作机器人进行柔顺力的控制处理。
在本发明具体实施过程中,最后根据该实时控制量对该协作机器人进行柔顺力的控制处理。
即,输入:控制器参数k、α、∈、β,协作机器人的机械臂的关节角限幅θ
-、θ
+,角速度限幅
机械臂初始状态θ(0)、
期望轨迹x
d(t),
以及期望接触力F
d,在任务时长T,机械臂末端执行的位置反馈x(t),接触力F(t),关节反馈θ。
1.初始化λ
1(0),λ
2(0);
Repeat
2.读取传感器测量值F,θ,x;
3.计算当前时刻的机器人雅克比矩阵J和H
i;
6.根据式(9b)(9c)更新状态变量λ
1、λ
2;
Until(t>T)。
在本发实施例中,能够实现对接触力的高精度控制,并能够实时提升协作机器人系统的刚度,从而抑制颤振;在协作机器人系统刚度较好时,通常会使机器人接近奇异位型,从而大大降低系统的灵活性,能够有效规避系统陷入奇异位型,同时满足机器人的关节角度、角速度限制。
实施例二
请参阅图2,图2是本发明实施例中的协作机器人的柔顺力控制系统的结构组成示意图。
如图2所示,一种协作机器人的柔顺力控制系统,所述系统包括:
第一建立模块21:用于建立协作机器人末端的稳定力控制策略模型;
在本发明具体实施过程中,所述建立协作机器人末端的稳定力控制策略模型,包括:利用组坑控制原理,建立所述协作机器人的末端相对运动与接触力之间的关系;基于末端相对运动与接触力之间的关系建立协作机器人末端的稳定力控制策略模型。
进一步的,所述端相对运动与接触力之间的关系如下:
所述协作机器人末端的稳定力控制策略模型如下:
其中,C
m表示组坑模型;G
m表示弹性系数;F表示接触力;x表示协作机器人末端执行器的位置;
表示协作机器人末端执行器的速度;x
d表示协作机器人末端执行器的期望位置;
表示协作机器人末端执行器的的期望速度;
表示协作机器人末端执行器的反馈速度;F
d表示期望接触力;t表示时间;k表示大于0的控制参数。
具体的,利用阻抗控制原理,建立机器人末端相对运动与接触力之间的关系,如下:
建立抗噪的协作机器人末端的稳定力控制策略模型如下:
其中,C
m表示组坑模型;G
m表示弹性系数;F表示接触力;x表示协作机器人末端执行器的位置;
表示协作机器人末端执行器的速度;x
d表示协作机器人末端执行器的期望位置;
表示协作机器人末端执行器的的期望速度;
表示协作机器人末端执行器的反馈速度;F
d表示期望接触力;t表示时间;k表示大于0的控制参数。
第二建立模块22:用于建立协作机器人的刚度优化策略模型;
在本发明具体实施过程中,所述建立协作机器人的刚度优化策略模型,包括:建立所述协作机器人的刚度指标,并建立所述刚度指标与决策量之间的映射关系;基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型。
进一步的,所述映射关系如下:
det((JJ
T)
-1);(3)
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子。
进一步的,所述基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型,如下:
对所述映射关系的式子进行简化,将性能指标改写为:det(JJ
T),此时,所述协作机器人的刚度优化转为:
min det(JJ
T);(4)
根据所述协作机器人的关节角度θ对det(JJ
T)进行展开,得到刚度优化与机器人关节运动之间的映射关系即为刚度优化策略模型,如下:
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子。
具体的,建立机器人的刚度指标,并建立其与决策变量之间的映射关系如下:
det((JJ
T)
-1);(3)
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子。
对上述的式(3)进行简化,将性能指标改写为:det(JJ
T),此时,所述协作机器人的刚度优化转为:
min det(JJ
T);(4)
根据所述协作机器人的关节角度θ对det(JJ
T)进行展开,得到刚度优化与机器人关节运动之间的映射关系即为刚度优化策略模型,如下:
其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子。
第三建立模块23:用于建立协作机器人的奇异规避模型;
在本发明具体实施过程中,所述建立协作机器人的奇异规避模型,包括:
建立协作机器人的灵活性约束如下:
根据决策变量对式(6)进行改写如下:
建立协作机器人的灵活性约束如下:
根据决策变量对式(6)进行改写如下:
求解模块24:用于基于所述稳定力控制策略模型、所述刚度优化策略模型和所述奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得所述协作机器人的实时控制量;
在本发明具体实时过程中,所述实时控制量求解模型如下:
θ
-≤θ≤θ
+
其中,T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界。
进一步的,所述进行实时控制量求解,包括:
设置满足实时控制量求解模型的隐式解,对所述协作机器人的实时力控制与刚度优化如下:
其中,∈为大于0的神经网络参数;Proj表示一个饱和函数,定义如下:
其中,
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;T表示矩阵的转置算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界;α表示正控制参数;
表示协作机器人的关节角加速度;θ表示协作机器人的关节角度;
表示协作机器人末端执行器的反馈速度;λ
1和λ
2均表示状态变量。
具体的,根据稳定力控制策略模型、刚度优化策略模型和奇异规避模型建立实时控制量求解模型如下:
θ
-≤θ≤θ
+
其中,T表示矩阵的转置算子;-1表示矩阵的求逆算子;
θ
i表示θ的第i个值,i=1,2,3,…,n;
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;vec表示将矩阵转化为列向量的算子;κ表示协 作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界。
在对该实时控制量求解模型进行求解时,需要设计满足式(8)的隐式解,实现机器人的实时力控制与刚度优化如下:
其中,∈为大于0的神经网络参数;Proj表示一个饱和函数,定义如下:
其中,
表示协作机器人的关节角速度;J表示协作机器人的雅克比矩阵;T表示矩阵的转置算子;κ表示协作机器人的灵活性指标;β、η均表示正常数;θ
-、θ
+分别表示θ的下界与上界;
分别表示
的下界与上界;+表示正控制参数;
表示协作机器人的关节角加速度;θ表示协作机器人的关节角度;
表示协作机器人末端执行器的反馈速度;λ
1和λ
2均表示状态变量。
控制模块25:用于基于所述实时控制量对所述协作机器人进行柔顺力的控制处理。
在本发明具体实施过程中,最后根据该实时控制量对该协作机器人进行柔顺力的控制处理。
即,输入:控制器参数k、α、∈、β,协作机器人的机械臂的关节角限幅θ
-、θ
+,角速度限幅
机械臂初始状态θ(0)、
期望轨迹x
d(t),
以及期望接触力F
d,在任务时长T,机械臂末端执行的位置反馈x(t),接触力F(t),关节反馈θ。
1.初始化λ
1(0),λ
2(0);
Repeat
2.读取传感器测量值F,θ,x;
3.计算当前时刻的机器人雅克比矩阵J和H
i;
6.根据式(9b)(9c)更新状态变量λ
1、λ
2;
Until(t>T)。
在本发实施例中,能够实现对接触力的高精度控制,并能够实时提升协作机器人系统的刚度,从而抑制颤振;在协作机器人系统刚度较好时,通常会使机器人接近奇异位型,从而大大降低系统的灵活性,能够有效规避系统陷入奇异位型,同时满足机器人的关节角度、角速度限制。
本领域普通技术人员可以理解上述实施例的各种方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成,该程序可以存储于一计算机可读存储介质中,存储介质可以包括:只读存储器(ROM,ReadOnly Memory)、随机存取存储器(RAM,Random Access Memory)、磁盘或光盘等。
另外,以上对本发明实施例所提供的一种协作机器人的柔顺力控制方法及系统进行了详细介绍,本文中应采用了具体个例对本发明的原理及实施方式进行了阐述,以上实施例的说明只是用于帮助理解本发明的方法及其核心思想;同时,对于本领域的一般技术人员,依据本发明的思想,在具体实施方式及应用范围上均会有改变之处,综上所述,本说明书内容不应理解为对本发明的限制。
Claims (10)
- 一种协作机器人的柔顺力控制方法,其特征在于,所述方法包括:建立协作机器人末端的稳定力控制策略模型;建立协作机器人的刚度优化策略模型;建立协作机器人的奇异规避模型;基于所述稳定力控制策略模型、所述刚度优化策略模型和所述奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得所述协作机器人的实时控制量;基于所述实时控制量对所述协作机器人进行柔顺力的控制处理。
- 根据权利要求1所述的柔顺力控制方法,其特征在于,所述建立协作机器人末端的稳定力控制策略模型,包括:利用组坑控制原理,建立所述协作机器人的末端相对运动与接触力之间的关系;基于末端相对运动与接触力之间的关系建立协作机器人末端的稳定力控制策略模型。
- 根据权利要求1所述的柔顺力控制方法,其特征在于,所述建立协作机器人的刚度优化策略模型,包括:建立所述协作机器人的刚度指标,并建立所述刚度指标与决策量之间的映射关系;基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型。
- 根据权利要求4所述的柔顺力控制方法,其特征在于,所述映射关系如下:det((JJ T) -1); (3)其中,det表示方阵对应的行列式的值;T表示矩阵的转置算子;-1表示矩阵的求逆算子。
- 根据权利要求4所述的柔顺力控制方法,其特征在于,所述基于所述映射关系进行刚度指标重构处理,获得刚度优化策略模型,如下:对所述映射关系的式子进行简化,将性能指标改写为:det(JJ T),此时,所述协作机器人的刚度优化转为:min det(JJ T); (4)根据所述协作机器人的关节角度θ对det(JJ T)进行展开,得到刚度优化与机器人关节运动之间的映射关系即为刚度优化策略模型,如下:
- 根据权利要求1所述的柔顺力控制方法,其特征在于,所述进行实时控制量求解,包括:设置满足实时控制量求解模型的隐式解,对所述协作机器人的实时力控制与刚度优化如下:其中,ε为大于0的神经网络参数;Proj表示一个饱和函数,定义如下:
- 一种协作机器人的柔顺力控制系统,其特征在于,所述系统包括:第一建立模块:用于建立协作机器人末端的稳定力控制策略模型;第二建立模块:用于建立协作机器人的刚度优化策略模型;第三建立模块:用于建立协作机器人的奇异规避模型;求解模块:用于基于所述稳定力控制策略模型、所述刚度优化策略模 型和所述奇异规避模型建立实时控制量求解模型,并进行实时控制量求解,获得所述协作机器人的实时控制量;控制模块:用于基于所述实时控制量对所述协作机器人进行柔顺力的控制处理。
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