CN112828359B - Robot milling attitude planning method and system based on multiple constraints of potential field method - Google Patents

Abstract

The invention discloses a multi-constraint robot milling processing attitude planning method and system based on a potential field method, and belongs to the field of milling processing and manufacturing. The invention transforms the geometrical physical constraints into virtual potential fields, so that the constrained quantity is far away from the constraint boundary under the action of the repulsive moment generated by the virtual potential field, so that the generated attitude trajectory satisfies the geometrical physical constraints. The present invention comprehensively considers the redundant angle of the robot and the forward inclination angle of the end effector, and further improves the processing quality. After considering this factor, the generated trajectory is used for milling, and the machining accuracy is significantly improved. The present invention proposes a new potential field function, which calculates the virtual dynamic equation through numerical integration to solve the attitude trajectory, and the obtained solution is a numerical value in the continuous domain, so that the robot trajectory always guarantees the joint motion C3 to be continuous during the movement process, thereby The smoothness of the generated pose trajectory is guaranteed.

Description

Multi-constraint robot milling attitude planning method and system based on potential field method

technical field

The invention belongs to the field of milling processing and manufacturing, and more particularly relates to a robot milling processing attitude planning method and system based on the potential field method with multiple constraints.

Background technique

Industrial robots are widely used in various types of automated production due to their high flexibility, programmability, and competitive cost. Trajectory planning in the face of different production task requirements has become a rigid requirement for robot operations. For robotic milling, it has higher requirements on machining trajectory accuracy and machining mechanical properties, which poses greater challenges than other tasks such as palletizing and handling; compared with traditional five-axis machining, robot milling In addition to the inclination angle and the roll angle, there are also redundant angles that have an impact on the machining mechanical properties, which has a higher planning difficulty. Therefore, it is necessary to develop attitude trajectory planning technology suitable for multi-axis milling of robots.

In the current field of machine tool and robot attitude planning, algorithms based on sampling and graph theory are mainly used to discretize the reachable space of the entire robot, and perform traversal calculations on indicators such as machining performance and operational performance, which are expensive. And due to the discrete reachable space, the planning result needs to be smoothed. Khatib and other scholars from Stanford University in the United States published an article Real-Time Obstacle Avoidance for Manipulators and Mobile Robots on Autonomous Robot Vehicles, and proposed a robot obstacle avoidance trajectory planning algorithm based on the potential field method. Set the attraction, and realize the non-interference trajectory planning of the robot from the initial point to the end point through the action of the two forces. Since it is only necessary to calculate the force at the position of the robot, the traversal of the entire reachable space is avoided; and the smoothness of the generated trajectory is guaranteed through continuous calculation. Cho and other scholars from Seoul National University in South Korea published an article in the International Journal of Advanced ManufacturingTechnology. The International Journal of Advanced ManufacturingTechnology introduced the potential field method into the attitude trajectory planning of the milling tool of the machine tool. Scholars such as Lacharnay of the University of Paris in France published an article on Computer-Aided Design. A physically-based model for global collision avoidance in 5-axis point milling has improved this method. By giving the global interference obstacles a virtual repulsive force field, The pre-planned tool attitude trajectory is given an attractive field, and virtual modal parameters are given to the tool, so that the tool can achieve an efficient, no global interference, and smooth tool through the action of attractive and repulsive forces during the movement of the tool along the planned path. Attitude planning. Related research only applies the potential field method to robot obstacle avoidance and machine tool attitude planning, and there are currently few corresponding planning algorithms for the application of robot multi-axis milling attitude trajectory planning.

SUMMARY OF THE INVENTION

In view of the defects and improvement needs of the prior art, the present invention provides a multi-constraint robot milling attitude planning method and system based on the potential field method, the purpose of which is to comprehensively consider the influence of the tool attitude and redundant angles on the machining accuracy during the milling process , which can efficiently generate a smooth robot attitude trajectory along the tool path, which is beneficial to improve the machining accuracy of the workpiece.

In order to achieve the above object, according to the first aspect of the present invention, a multi-constraint robot milling attitude planning method based on the potential field method is provided, and the method includes the following steps:

S1. Get the tool path;

S2. Initialize the virtual moment of inertia M of the robot end effector, the virtual rotational damping C of the robot end effector, initialize the posture of the robot end effector at the first tool position point, and initialize the constraint value θ _lim and threshold θ of each joint angle of the robot. ₀ , the tool rake angle constraint value l _lim and the threshold value l ₀ , the roll angle constraint value t _lim and the threshold value t ₀ , and the error index constraint value δ _lim and the threshold value δ ₀ ;

S3. For each tool position point in the tool path, perform the following processing until the robot end effector pose planning on the tool position point on the entire tool path is completed:

(1) Take the tool position point in the tool path as the coordinate origin, take the normal vector direction of the workpiece design surface as the Z _ECS axis, take the tangent vector direction of the tool path as the X _ECS axis, and establish the Y _ECS axis through the right-hand rule to establish the ECS coordinates Tie;

(2) Calculate the joint angle θ of the robot based on the relationship between the TCS and BCS coordinate systems and the kinematics of the robot; calculate the tool rake angle l and roll angle t based on the relationship between the TCS and ECS coordinate systems; The relationship between the robot stiffness and milling mechanics, and the machining error index δ is calculated;

(3) Calculate the absolute value of the difference between the actual value and the constraint value, respectively, to obtain θ′, l′, t′, δ′;

(4) Substitute the calculated θ', l', t', and δ' into the repulsive moment function respectively and sum up the calculated repulsive moments, and calculate the total repulsive moment received by the end effector on the tool position, The repulsive moment function is obtained by taking the partial derivative of the potential field function, and the potential field function must satisfy the following constraints at the same time:

1) When any of θ′, l′, t′, and δ′ tends to 0, the potential field tends to infinity;

2) When any of θ′, l′, t′, and δ′ is greater than the corresponding threshold, the potential field is always equal to 0;

3) At least the second-order partial derivatives are guaranteed to be continuous;

(5) Substitute the obtained total repulsive moment into the virtual dynamic equation, and solve to obtain the robot end effector attitude at the next tool position. The virtual dynamic equation is as follows:

是总排斥力矩，ω(t)是机器人末端执行器对应的TCS在BCS坐标系下的旋转速度，

是机器人末端执行器对应的TCS在BCS坐标系下的旋转加速度。Among them, M is the virtual moment of inertia of the robot end effector, C is the virtual rotational damping, P(t) is the total potential field function, α _i is the euclidean of the TCS coordinate system rotating around the X-axis, Y-axis or Z-axis of the BCS in turn pull angle,

is the total repulsive moment, ω(t) is the rotation speed of the TCS corresponding to the robot end effector in the BCS coordinate system,

is the rotational acceleration of the TCS corresponding to the robot end effector in the BCS coordinate system.

Beneficial effects: the present invention converts the constraints in the robot milling process into potential field functions, and realizes that the repulsion corresponding to different constraints is calculated by the potential field function after the posture of the robot end effector on the first tool position is given. torque, and solve the virtual dynamic equation, so as to realize the planning of the robot end effector attitude trajectory on the entire tool path.

Preferably, the calculation formula of the tool roll angle t is as follows:

The calculation formula of the tool rake angle l is as follows:

是TCS到ECS的旋转矩阵，

是中间矩阵，下标代表矩阵对应的行数和列数。in,

is the rotation matrix from TCS to ECS,

is the intermediate matrix, and the subscripts represent the number of rows and columns corresponding to the matrix.

Beneficial effects: The present invention expands the redundant angle planning in the existing robot processing to the joint planning of the front inclination angle, the roll angle and the redundant angle by defining the front inclination angle and the roll angle in the robot milling process. Thus, the milling capability of the robot is further improved.

Preferably, the machining error index is defined as the component of the deformation in the normal vector direction of the workpiece surface when the average milling force acts on the tool of the robot end effector, and the calculation process is as follows:

将铣削力转化至BCS下^BCSF；(1) Rotation matrix through TCS to BCS

Convert the milling force to ^{BCS F under BCS} ;

Among them, f _force (l, t) is the calculation function of the average milling force under TCS when the tool rake angle l and roll angle t are;

(2) Calculate the stiffness matrix K of the robot end based on the robot joint angle θ;

K=f _stiffness (θ)

Among them, f _stiffness (θ) is the calculation function of the stiffness matrix K of the robot end;

(3) Calculate the machining error index δ

δ=| ^BCS Z _ECS (CL _i )K ^{-1 BCS} F|

Among them, CL _i is the position coordinate of the ith tool location point in the BCS coordinate system, and ^BCS Z _ECS (CL _i ) is the vector coordinate of the Z axis of the ECS at the ith tool location point under BCS.

Beneficial effects: The present invention considers the influence of different robot postures on the stiffness of the robot end and the milling force by defining the robot machining error index δ. By constraining the machining error index, combined with the proposed potential field algorithm, the high-precision robot milling attitude trajectory planning is realized.

Preferably, the potential field function with r as the constraint condition is as follows:

Among them, η is an adjustment parameter, r=θ' or l' or t' or δ'.

Beneficial effects: The present invention proposes a potential field function model for robot end effector attitude trajectory planning considering multiple constraints. Since the potential field function tends to be infinite when θ′, l′, t′, and δ′ tend to 0, it is ensured that the generated trajectory satisfies the constraints. Since the potential energy of the potential field function is always equal to 0 when any of θ', l', t', and δ' is greater than the threshold r ₀ , it avoids the influence of the repulsive moment on the attitude of the robot end when it is far away from the constraint boundary. , to ensure the stability of the robot end effector movement. Since the potential field function at least guarantees the continuity of the second-order partial derivatives, the C3 continuity ^of the robot end effector operation is guaranteed.

Preferably, step (5) adopts Runge-Kutta solution to obtain

in,

是前一刀位点出对应的机器人末端执行器姿态欧拉角与角速度，α₁,α₂,α₃是中间变量，t_gap是相邻刀位点之间的时间间隔，

是总排斥力矩，t_pre是前一刀位点对应的时刻，CL(t)是t时刻的刀位点。Among them, α _pre ,

is the Euler angle and angular velocity of the robot end effector corresponding to the previous tool position, α ₁ , α ₂ , α ₃ are intermediate variables, t _gap is the time interval between adjacent tool positions,

is the total repulsive moment, t _pre is the time corresponding to the previous tool position, and CL(t) is the tool position at time t.

Beneficial effects: The present invention transforms the robot attitude trajectory planning problem into the solution of the virtual dynamic equation, and at the given initial tool position point, the robot end effector attitude is realized by the Runge-Kutta numerical integration method on the subsequent tool position point. Planning of robot end effector pose.

Preferably, the constraint value in step S3 also includes at least one of the robot attitude singularity condition number, singularity point, vibration, and energy.

Beneficial effects: the present invention converts constraints into potential energy through a potential field function to generate a repulsive moment, so as to plan the attitude trajectory of the robot end effector. Due to the generality of the potential field function, it can also be applied to the constraints of the singularity condition number, singularity, vibration, and energy of the robot posture, so as to realize the posture trajectory planning of the robot end effector under different constraints under different working conditions.

In order to achieve the above object, according to the second aspect of the present invention, a multi-constraint robot milling attitude planning system based on the potential field method is provided, including: a computer-readable storage medium and a processor;

the computer-readable storage medium for storing executable instructions;

The processor is configured to read the executable instructions stored in the computer-readable storage medium, and execute the multi-constraint robot milling attitude planning method based on the potential field method described in the first aspect.

In general, through the above technical solutions conceived by the present invention, the following beneficial effects can be achieved:

(1) The present invention transforms the geometric and physical constraints into a virtual potential field, and the corresponding potential energy at the limit value of the constraint is infinite, so that the constrained quantity is far away from the boundary under the action of the repulsive force generated by the virtual potential field, so that the generated attitude The trajectory satisfies the geometry-physics constraints.

(2) The forward tilt angle of the end effector will also affect the mechanical properties of the robot, thereby affecting the machining accuracy. The present invention comprehensively considers the redundant angle of the robot and the forward inclination angle of the end effector, and further improves the processing quality. After taking this factor into consideration, the generated trajectory is used for milling, and the corresponding machining accuracy is significantly improved.

(3) The present invention proposes a new potential field function, which calculates the virtual dynamic equation through numerical integration to solve the attitude trajectory, and the obtained solution is a numerical value in the continuous domain, so that the robot trajectory can always ensure that C3 is continuous during the movement process, Thus, the smoothness of the generated attitude trajectory is guaranteed.

Description of drawings

Fig. 1 is the overall flow chart of a kind of multi-constraint robot milling processing attitude planning method based on potential field method provided by the present invention;

2 is a schematic diagram of a robot six-axis milling process and BCS, TCS and ECS provided by the present invention;

Fig. 3 is the rotation transformation relation between robot base coordinate system BCS and tool coordinate system TCS provided by the present invention;

FIG. 4 is a rotation transformation relationship diagram of the robot coordinate system provided by the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

As shown in FIG. 1 , the present invention provides a multi-constraint robot milling attitude trajectory planning method based on the potential field method. Based on the kinematics and mechanical model of the robot, the corresponding constraints are given, and the robot attitude trajectory planning model under the given tool path is established; then, in order to ensure that the generated attitude trajectory satisfies the geometric and physical constraints and has C3 smoothness, A potential field model is proposed, and the algorithm of the virtual repulsive moment generated by the potential field is given. Combined with the repulsive moment and the virtual modal parameters given to the robot end effector, the dynamic equation of the robot end effector attitude is constructed. , through the numerical integration algorithm, the robot attitude trajectory planning is realized.

1. Robot attitude trajectory planning model

In order to facilitate the description of the robot milling process, as shown in Figure 2, the relevant coordinate systems in the robot milling process are established, including the robot base coordinate system (BCS), the machining coordinate system (ECS) and the robot end effector coordinate system (TCS) ). Among them, BCS is the coordinate system fixed to the robot; TCS takes the tool center on the robot end effector as the origin, the tool axis direction is the Z _TCS axis, the Y _TCS axis is perpendicular to the tool axis direction and the feed direction, and X is established by the right-hand rule. _TCS axis. ECS is defined according to the tool path. The tool position in processing is used as the coordinate origin, the normal vector of the workpiece design surface is the Z _ECS axis, the tangent vector direction of the tool path is the X _ECS axis, and the Y _ECS axis is established by the right-hand rule.

Robotic multi-axis milling is shown in Figure 2. It can be seen that the tool nose point moves in translation along a given tool path, while the robot end effector rotates around the tool nose point. The toolpath consists of a series of tool positions CL, which can be generated by CAM software. The tool attitude, that is, the attitude of the robot end effector, is the planning object, and the mathematical relationship of the robot end effector attitude in the base coordinate system BCS is described by the Euler angle α. The relationship between BCS and TCS is shown in Figure 3. The pose of TCS under BCS is described by the homogeneous transformation matrix of Euler angle α as:

α _x , α _y and α _z are the Euler angles rotated around the X, Y and Z axes of the BCS, and CL _x , CL _y and CL _z are the positions of the tool position relative to the base frame.

In order to generate the machining attitude trajectory of the robot multi-axis milling, it is necessary to comprehensively satisfy the constraints of the joint angle range, the tool attitude angle and the machining error index. On the other hand, the smoothness needs to be guaranteed to ensure the dynamic characteristics of the robot and the kinematic performance ^of the tool during operation, so the trajectory needs to ensure that C3 is continuous. Therefore, the planning model of the trajectory is:

In the formula, i refers to the serial number of the tool position point on the tool path trajectory; θ, l, t, δ are the robot joint angle, the tool attitude forward inclination angle, the roll angle and the machining error index, respectively.

2 Robot end effector pose constraints

2.1 Joint angle constraints

Since the motion range of each joint angle θ of the robot is certain, in order to avoid the unreachable robot posture, the reachable space of the robot end effector posture is constrained.

通过机器人逆运动学计算函数f_ikin，可求得机器人各关节角θ，即：For the robot end-effector pose with given Euler angles α _x , α _y , α _z , the robot's end-effector pose matrix can be obtained

Through the robot inverse kinematics calculation function f _ikin , the joint angles θ of the robot can be obtained, namely:

Combined with the joint angle θ range of the robot (θ _min , θ _max ), the constraints on the posture of the robot end effector are obtained, namely:

θ=f ₁ (α _x ,α _y ,α _z )∈(θ _min ,θ _max ) (4)

2.2 Tool attitude angle constraints

In the field of five-axis milling, in order to describe the tool attitude, the concepts of rake angle and roll angle are used. In order to avoid interference collisions, it is necessary to limit the forward and roll angles within a certain range. At the same time, during the milling process of tools such as ball-end cutters, the linear velocity of the tool nose point is zero, which is not conducive to cutting. Therefore, it is necessary to ensure that the rake angle of the tool is greater than zero to prevent the tool nose point from participating in cutting.

表达式为：Unlike conventional machine tool milling, industrial robots have redundant degrees of freedom. In order to characterize this attitude characteristic of the robot, the forward tilt angle and the redundant angle of the multi-axis milling of the industrial robot are specified. As shown in Fig. 4, initially the TCS coincides with the ECS, the TCS rotates around the Z axis of the ECS by a redundant angle s, then the TCS rotates around the Y axis of the ECS by a forward tilt angle l, and finally the TCS rotates around the X axis of the ECS by a roll angle t. Homogeneous Transformation Matrix

The expression is:

根据几何关系，对上式进行逆运算：After the posture Euler angle of the robot end effector and the coordinates of the tool position point are given, the formula (1) can be used to obtain

According to the geometric relationship, inverse the above formula:

The formula for calculating the tool roll angle t is as follows:

The calculation formula of the tool rake angle l is as follows:

是TCS到ECS的旋转矩阵，

是中间矩阵，下标代表矩阵对应的行数和列数。由机器人末端执行器姿态欧拉角向前倾侧倾冗余角的映射函数f₂为：in,

is the rotation matrix from TCS to ECS,

is the intermediate matrix, and the subscripts represent the number of rows and columns corresponding to the matrix. The mapping function f ₂ of the redundant angle of forward lean and roll by the Euler angle of the robot end effector attitude is:

As a result, the constraints of the tool attitude angle and the redundant angle are transformed into implicit constraints on the Euler angles, namely:

[t,l,s]=f ₂ (α _x ,α _y ,α _z )∈([t _min ,t _max ],[l _min ,l _max ]) (10)

2.3 Processing Error Constraints

In order to characterize the machining accuracy, the component of the deformation in the normal vector direction of the workpiece surface when the average cutting force acts on the end tool of the robot is defined as the machining error index.

将铣削力转化至BCS下^BCSF；(1) Rotation matrix through TCS to BCS

Convert the milling force to ^{BCS F under BCS} ;

Among them, f _force (l, t) is the calculation function of the average milling force under TCS when the tool rake angle l and roll angle t are;

(2) Calculate the stiffness matrix K of the robot end based on the robot joint angle θ;

K=f _stiffness (θ) (12)

Among them, f _stiffness (θ) is the calculation function of the stiffness matrix K of the robot end;

(3) Calculate the machining error index δ

δ=| ^BCS Z _ECS (CL _i )K ^{-1 BCS} F| (13)

Among them, CL _i is the position coordinate of the ith tool position point under the BCS coordinate system, and BCSZ _ECS (CL _i ) is the vector coordinate of the Z axis of the ECS at the ith tool position point under BCS.

Combined with equations (3)(9)(11)(12)(13), the above equation is transformed into the function f ₃ of the Euler angle of the robot end-effector attitude:

δ=|Z _ECS (CL)K ^-1 (f ₁ (α _x ,α _y ,α _z )) ^BCS F(f ₃ (α _x ,α _y ,α _z ))|=f ₃ (α _x ,α _y ,α _z )

In order to ensure the machining accuracy, the error index is limited:

δ=f ₃ (α _x ,α _y ,α _z )∈[0,δ _max )

3. Potential Field Algorithm

The potential field algorithm constructs a potential field by converting the absolute values of the differences θ', l', t', δ' between the indicators θ, l, t, δ and the constraint limit values under different attitudes into virtual potential energy. The repulsive moment generated by the potential field acts on the robot end effector posture, so that the robot end tool tip automatically moves away from the constraint limit value during the movement along the tool path, and generates a robot end effector posture trajectory that satisfies the constraints.

In order to realize this method, on the one hand, the potential field function and repulsive moment function suitable for the multi-axis milling of the robot are proposed;

3.1 Construction of Potential Field Function and Repulsive Moment Function

The generated attitude trajectory should ensure: (1) Ensure that the robot end-effector attitude at any tool position satisfies the constraints; (2) The motion trajectory of the robot joint angle is smooth.

In order to ensure condition (1), the virtual potential energy tends to infinity when the potential energy function is required to be at the limit position of the robot attitude region.

In order to ensure condition (2), in order to avoid the generated robot trajectory from oscillation, it is required that ① the potential energy of the robot is zero when the distance is greater than the threshold r ₀ ; ② the generated trajectory is required to have the continuity of C ³ , that is, the joint angles at all positions are equal to each other. Jerk θ ⁽³⁾ should be guaranteed to be continuous.

Therefore, the potential field function must simultaneously satisfy the following constraints:

1) When any of θ′, l′, t′, and δ′ tends to 0, the potential field tends to infinity;

2) When any of θ′, l′, t′, δ′ is greater than the threshold r ₀ , the potential field is always equal to 0;

3) At least the second-order partial derivatives are guaranteed to be continuous;

which is:

Wherein, r=θ' or l' or t' or δ'. This leads to the potential field function:

The repulsive moment of the potential field is the derivative of the virtual potential energy with respect to the Euler angle of the robot end effector attitude. For robotic multi-axis milling, since Euler angles have three dimensions, the repulsive moment is:

Through the above calculation, it is realized that the joint angle, attitude angle and error index are converted into repulsive moment to act on the robot end effector, which affects the Euler angle corresponding to the end effector attitude.

3.2 Modeling and solving of virtual dynamic equations

According to the previous description of the potential field method, by assigning virtual modal parameters to the robot end effector, under the action of the virtual repulsive moment generated by the constraint, the corresponding virtual dynamic equation can be established, namely:

是总排斥力矩，ω(t)是机器人末端执行器对应的TCS在BCS坐标系下的旋转速度，

是机器人末端执行器对应的TCS在BCS坐标系下的旋转加速度。Among them, M is the virtual moment of inertia of the robot end effector, C is the virtual rotational damping, P(t) is the total potential field function, α _i is the euclidean of the TCS coordinate system rotating around the X-axis, Y-axis or Z-axis of the BCS in turn pull angle,

is the total repulsive moment, ω(t) is the rotation speed of the TCS corresponding to the robot end effector in the BCS coordinate system,

is the rotational acceleration of the TCS corresponding to the robot end effector in the BCS coordinate system.

The three directions are solved by the Runge-Kutta method, so as to realize the planning of the trajectory.

Obtained by Runge-Kutta method

in,

是前一刀位点出对应的机器人末端执行器姿态欧拉角与角速度，α₁,α₂,α₃是中间变量，t_gap是相邻刀位点之间的时间间隔，

是总排斥力矩，t_pre是前一刀位点对应的时刻，CL(t)是t时刻的刀位点。Among them, α _pre ,

is the Euler angle and angular velocity of the robot end effector corresponding to the previous tool position, α ₁ , α ₂ , α ₃ are intermediate variables, t _gap is the time interval between adjacent tool positions,

is the total repulsive moment, t _pre is the time corresponding to the previous tool position, and CL(t) is the tool position at time t.

This realizes the automatic planning of the robot end effector's attitude trajectory during the movement of the initial tool position point along the given tool path to the end of the path during multi-axis milling of the robot.

Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (7)

1. A multi-constraint robot milling attitude planning method based on a potential field method is characterized by comprising the following steps:

s1, acquiring a cutter path;

s2, initializing a virtual rotational inertia M of the robot end effector and a virtual rotational damping C of the robot end effector, initializing the posture of the robot end effector at a first knife position, and initializing constraint values theta of each joint angle of the robot_limAnd a threshold value theta₀The constraint value of the rake angle of the tool_limAnd a threshold value l₀The roll angle constraint value t_limAnd a threshold value t₀And an error index constraint value delta_limSum threshold δ₀；

S3, for each tool location point in the tool path, performing the following processing until the gesture planning of the robot end effector on the tool location point on the whole tool path is completed:

(1) taking the tool position point in the tool path as the origin of coordinates and the normal vector direction of the workpiece design surface as Z_ECSAxis in the tangential direction of the tool pathIs X_ECSAxis, establishing Y by right hand rule_ECSAxes, thereby establishing an ECS coordinate system;

(2) calculating the joint angle theta of the robot based on the relation between the TCS coordinate system and the BCS coordinate system and the kinematics of the robot; calculating a tool forward inclination angle l and a side inclination angle t based on the relation between the TCS coordinate system and the ECS coordinate system; calculating a machining error index delta based on the relation between a TCS coordinate system, a BCS coordinate system and an ECS coordinate system and the rigidity and the milling mechanics of the robot;

(3) respectively calculating absolute values of difference values of the actual value and the constraint value to obtain theta ', l', t ', delta';

(4) respectively substituting the calculated theta ', l', t ', delta' into a repulsion torque function, summing the calculated repulsion torques, and calculating to obtain the total repulsion torque applied to the end effector at the knife position, wherein the repulsion torque function is obtained by performing partial derivation on a potential field function, and the potential field function must simultaneously meet the following limitations:

1) when any of θ ', l', t ', δ' tends to 0, the potential field tends to infinity;

2) when any of θ ', l', t ', δ' is greater than the corresponding threshold, the potential field is constantly equal to 0;

3) at least ensuring the second order partial derivative to be continuous;

(5) substituting the obtained total repulsive torque into a virtual dynamic equation, and solving to obtain the robot end effector posture at the next knife position, wherein the virtual dynamic equation is as follows:

wherein M is the virtual moment of inertia of the robot end effector, C is the virtual rotational damping, P (t) is the total potential field function, alpha_iIs the Euler angle of the TCS coordinate system rotating around the X axis, the Y axis or the Z axis of the BCS coordinate system in turn,

is the total repulsive torque, ω (t) is the robot end effectorThe corresponding TCS coordinate system is the rotation speed in the BCS coordinate system,

the rotation acceleration is the rotation acceleration of a TCS coordinate system corresponding to the robot end effector under a BCS coordinate system, the BCS coordinate system is a robot base coordinate system, the ECS coordinate system is a robot processing coordinate system, and the TCS coordinate system is a robot end effector coordinate system.

2. The method of claim 1, wherein the tool roll angle t is calculated as follows:

the calculation formula of the cutter rake angle l is as follows:

wherein,

is a rotation matrix of the TCS coordinate system to the ECS coordinate system,

is an intermediate matrix and the subscripts represent the number of rows and columns corresponding to the matrix.

3. The method of claim 1, wherein the machining error indicator δ is defined as: when the average milling force acts on a cutter of the robot end effector, the component of the generated deformation in the normal vector direction of the surface of the workpiece is calculated as follows:

(1) rotation matrix from TCS coordinate system to BCS coordinate system

Converting milling force into BCS coordinate system^BCSF；

Wherein f is_force(l, t) is a calculation function of the average milling force under a TCS coordinate system when the cutter is at a forward inclination angle l and a side inclination angle t;

(2) calculating a robot tail end rigidity matrix K based on the robot joint angle theta;

K＝f_stiffness(θ)

wherein f is_stiffness(theta) is a calculation function of a robot terminal stiffness matrix K;

(3) calculating the machining error index delta

δ＝|^BCSZ_ECS(CL_i)K^-1BCSF|

Wherein, CL_iIs the position coordinate of the ith knife location point in the BCS coordinate system,^BCSZ_ECS(CL_i) Is the vector coordinate of the Z-axis of the ECS coordinate system at the ith tool location in the BCS coordinate system.

4. A method according to any one of claims 1 to 3, wherein the potential field function with r as a constraint is as follows:

where η is a control parameter, and r ═ θ 'or l' or t 'or δ'.

5. The method of claim 4, wherein step (5) is solved using a Runge Kutta to obtain

Wherein,

wherein alpha is_pre，

Is the Euler angle and angular velocity, alpha, of the robot end effector corresponding to the previous knife position₁，α₂，α₃Is an intermediate variable, t_gapIs the time interval between adjacent tool positions,

is the total repulsive torque, t_preIs the time corresponding to the previous knife location point, and CL (t) is the knife location point at time t.

6. The method of claim 1, wherein the constraint values of step S3 further include at least one of robot pose singularity condition number, singular points, vibration, energy.

7. A multi-constraint robot milling attitude planning system based on a potential field method is characterized by comprising the following steps: a computer-readable storage medium and a processor;

the computer-readable storage medium is used for storing executable instructions;

the processor is used for reading executable instructions stored in the computer-readable storage medium and executing the potential field method-based multi-constraint robot milling machining attitude planning method according to any one of claims 1 to 6.

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