Robot trajectory time parameterization method for complex curved surface machining

Abstract

The application provides a robot trajectory time parameterization method for complex curved surface machining, comprising the following steps: S1. obtaining an initial path point of a mechanical arm end of a robot, and fitting the initial path point to form a trajectory curve; S2. determining a desired linear velocity of the mechanical arm end based on the trajectory curve, and determining a desired eigenvalue velocity based on the desired linear velocity; S3. determining discrete time information of the mechanical arm end based on the eigenvalue velocity, fitting the discrete time information to obtain a continuous trajectory curve, and processing the continuous trajectory curve according to a set requirement frequency to obtain a final axis angle value list.

Description

Technical Field

[0001] This invention relates to a processing method, and more particularly to a method for time parameterization of robot trajectory for machining complex curved surfaces. Background Technology

[0002] In applications involving the precision manufacturing of complex curved surfaces, the motion speed of the end effector is often related to the curvature of the current trajectory point. Therefore, to avoid quality issues caused by uneven processing layer thickness, the entire motion trajectory needs to be a variable-speed motion where the linear velocity of the robot's end effector is adjusted according to the curvature. Furthermore, during robot motion, there are limitations on the robot's joint angles, speed, acceleration, and other constraints, which may prevent the robot from following the predetermined trajectory. Consequently, ordinary trajectory generation methods produce significant trajectory and speed fluctuations, making it difficult to meet the above requirements and ultimately resulting in substandard surface quality after adding or subtracting materials from the curved surface.

[0003] Therefore, in order to solve the above-mentioned technical problems, it is urgent to propose a new technical approach. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a time parameterization method for robot trajectory in the machining of complex curved surfaces. Based on the initially set trajectory points and linear velocity of the robot's end effector, the method fits spline curves to the trajectory points and performs smoothing processing. The desired linear velocity of the robot's end effector is calculated based on the curvature of the curve. Then, through reachability analysis, the robot motion trajectory that satisfies the constraints and is optimized to meet the desired linear velocity is obtained. The trajectory is smooth and stable, thereby ensuring the quality of the parts to be machined.

[0005] This invention provides a method for time parameterization of robot trajectory in complex curved surface machining, comprising the following steps:

[0006] S1. Obtain the initial path points at the end of the robot's robotic arm and fit the initial path points to form a trajectory curve;

[0007] S2. Determine the desired linear velocity of the robotic arm's end effector based on the trajectory curve, and then determine the desired characteristic velocity from the desired linear velocity;

[0008] S3. Determine the discrete time information of the robotic arm end effector based on the characteristic value velocity, and fit the discrete time information to obtain a continuous trajectory curve. Process the continuous trajectory curve according to the set required frequency to obtain the final list of axis angle values.

[0009] Furthermore, step S1 specifically includes:

[0010] The list of coordinates p of the initial path points and the normal vector n of each point is fitted into a B-spline trajectory curve;

[0011] Interpolate the B-spline trajectory curve.

[0012] Further, when interpolating the B-spline curve, the included angle dθ between the normal vectors of adjacent points on the B-spline curve satisfies dθ < dθ0, where dθ0 is a set angle threshold.

[0013] Where: n i represents the normal vector of the i-th point of the B-spline curve.

[0014] Further, in step S2, determining the expected linear velocity of the end of the robotic arm based on the trajectory curve specifically includes:

[0015] Fit each point of the interpolated B-spline trajectory curve again to form a three-dimensional spline curve C(u);

[0016] Calculate the first derivative C'(u) and the second derivative C”(u) of the three-dimensional spline curve C(u);

[0017] Project the three-dimensional spline curve C(u) onto the machining plane, and calculate the curvature κ(u) of the projected curve after the three-dimensional spline curve C(u) is projected onto the machining plane:

[0018] Where:

[0019] C' n (u) = C'(u) - n p ·(C'(u)·n p );

[0020] C' n '(u) = C”(u) - n p ·(C”(u)·n p ); The normal vector n of the machining plane p is: n p = n × C'(u); n represents the normal vector of the current point;

[0021] Calculate the curvature radius r of each point of the projected curve:

[0022] Determine the expected linear velocity v of each path point h : v h = v c ·(r + 0.5·f pn ·d) / r;

[0023] Where: v c represents the initially set linear velocity, d is the thickness of the workpiece to be machined, f pnf is a coefficient, which is used when the projected curve is concave and the process is additive manufacturing, or when the projected curve is convex and the process is subtractive manufacturing. pn =-1; when the projected curve is concave and the machining process is subtractive, or when the projected curve is convex and the machining process is additive, f pn =1.

[0024] Furthermore, determining the desired eigenvalue velocity from the desired linear velocity specifically includes:

[0025] The path between two adjacent points on the projected curve is taken as the path segment, and the two endpoints p of the path segment are taken as the path segments. i and p i+1 The mean of the expected linear velocities is taken as the expected linear velocity of path segment i.

[0026] The desired time dt is obtained by dividing the distance between the two endpoints of path segment i by the desired linear velocity of path segment i. hi ;

[0027] Set the eigenvalue step size ds for path segment i, and calculate the eigenvalue velocity vs for path segment i. hi :

[0028] vs hi =ds / dt hi ;

[0029] Construct a feature value list S, which is an arithmetic sequence, and the number of feature values ​​in the feature value list S is the same as the number of path points and they correspond one-to-one.

[0030] Construct the pose matrix T of the robotic arm's end effector:

[0031] Where R is the rotation matrix of the pose matrix, and p is the coordinate of the path point;

[0032] The inverse of the pose matrix T yields the axis angle values ​​J of each joint of the robot's arm. i And form a list of axis angle values ​​J;

[0033] Constraints on the angles, angular velocities, and angular accelerations of each axis of the robot arm [J] lim ω lim a lim Transformed into constraints on eigenvalue velocity and eigenvalue acceleration [vs lim as lim ];

[0034] Constructing independent variables: The independent variables are constructed using the eigenvalue acceleration and the square of the eigenvalue velocity as follows:

[0035]

[0036] The reachability analysis method is adopted to calculate from the last path point of the trajectory curve at the end of the robotic arm to the first path point. During the calculation, the controllable set K of the independent variables is recursively calculated based on the eigenvalue acceleration and eigenvalue velocity constraints. The controllable set K contains the value range of the eigenvalue velocity of each path point.

[0037] A greedy algorithm is used to calculate the optimal characteristic velocity value for each path segment in the controllable set K, from the first path point to the last path of the trajectory curve at the end of the robotic arm. b The solution process is as follows:

[0038]

[0039] stx i [1] = x i-1 [1]+2*ds*x i [0]

[0040] x i [1]∈K i+1 [1]

[0041] in: vs i+1 Let x be the actual characteristic velocity of the robotic arm's end effector on the i-th path segment. i [0] = as i .

[0042] The beneficial effects of this invention are as follows: Based on the trajectory points and linear velocity of the robot's end effector initially set, the invention fits spline curves to the trajectory points and performs smoothing processing. The desired linear velocity of the robot's end effector is calculated based on the curve curvature. Then, through reachability analysis, a robot motion trajectory that satisfies the constraints and is optimized to meet the desired linear velocity is obtained. The trajectory is smooth and stable, thereby ensuring the quality of the parts to be processed. Attached Figure Description

[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0044] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0045] The present invention will be further described in detail below:

[0046] This invention provides a method for time parameterization of robot trajectory in complex curved surface machining, comprising the following steps:

[0047] S1. Obtain the initial path points at the end of the robot's robotic arm and fit the initial path points to form a trajectory curve;

[0048] S2. Determine the expected linear velocity of the end of the robotic arm based on the trajectory curve, and determine the expected eigenvalue velocity from the expected linear velocity;

[0049] S3. Determine the discrete time information of the end of the robotic arm based on the eigenvalue velocity, fit the discrete time information to obtain a continuous trajectory curve, and process the continuous trajectory curve according to the set required frequency to obtain the final list of axis angle values. Through the above method, based on the trajectory points and linear velocity of the end of the robotic arm of the initially set robot, by fitting a spline curve to the trajectory points, performing smoothing processing, calculating the expected linear velocity of the end of the robot according to the curve curvature, and then calculating through reachability analysis to obtain a robot motion trajectory that meets the constraint conditions and takes meeting the expected linear velocity as the optimization goal, and the trajectory is smooth and stable, thus ensuring the quality of the parts to be processed.

[0050] In this embodiment, step S1 specifically includes:

[0051] Fit the coordinates p of each point of the initial path points and the list of normal vectors n of each point into a B-spline trajectory curve; this fitting process is a prior art and will not be elaborated here.

[0052] Perform interpolation processing on the B-spline trajectory curve.

[0053] Among them: when performing interpolation processing on the B-spline curve, the included angle dθ of the normal vectors of adjacent points of the B-spline curve satisfies dθ < dθ0, where dθ0 is a set angle threshold;

[0054] Among them: n i represents the normal vector of the i-th point of the B-spline curve. Since the initial path points are obtained by projecting on the stl model, there are sudden changes in the normal vectors of each point. Through the above constraints, the occurrence of such sudden changes can be effectively avoided, ensuring the smoothness of the finally fitted curve.

[0055] In this embodiment, in step S2, determining the expected linear velocity of the end of the robotic arm based on the trajectory curve specifically includes:

[0056] Fit each point of the B-spline trajectory curve after interpolation processing again to form a three-dimensional spline curve C(u);

[0057] Calculate the first derivative C'(u) and the second derivative C”(u) of the three-dimensional spline curve C(u);

[0058] Project the three-dimensional spline curve C(u) onto the machining plane, and calculate the curve curvature κ(u) of the projected curve after the three-dimensional spline curve C(u) is projected onto the machining plane:

[0059] Among them:

[0060] C' n (u)=C'(u)-n p ·(C'(u)·n p );

[0061] C' n '(u)=C(u)-n p ·(C(u)·n p ); the normal vector n of the machining plane p For: n p = n × C'(u); n represents the normal vector of the current point;

[0062] Calculate the radius of curvature r at each point of the projected curve: In the above, the radius of curvature of each path point is calculated through the above process;

[0063] Determine the desired linear velocity v at each path point h :v h =v c ·(r+0.5·f pn ·d) / r;

[0064] Where: v c This represents the initial linear velocity, d is the thickness of the workpiece to be processed, and f is the linear velocity. pn f is a coefficient, which is used when the projected curve is concave and the process is additive manufacturing, or when the projected curve is convex and the process is subtractive manufacturing. pn =-1; when the projected curve is concave and the machining process is subtractive, or when the projected curve is convex and the machining process is additive, f pn =1.

[0065] In this embodiment, determining the desired characteristic value velocity from the desired linear velocity specifically includes:

[0066] The path between two adjacent points on the projected curve is taken as the path segment, and the two endpoints p of the path segment are taken as the path segments. i and p i+1 The mean of the expected linear velocities is taken as the expected linear velocity of path segment i.

[0067] The desired time dt is obtained by dividing the distance between the two endpoints of path segment i by the desired linear velocity of path segment i. hi ;

[0068] Set the eigenvalue step size ds for path segment i, and calculate the eigenvalue velocity vs for path segment i. hi :

[0069] vs hi =ds / dt hi ;

[0070] Construct a feature value list S, which is an arithmetic sequence, and the number of feature values ​​in the feature value list S is the same as the number of path points and corresponds one-to-one; that is, by querying any value in this list, we can obtain information such as the axis angle value of the corresponding path point, which is convenient for subsequent calculations and simplifies the calculation process.

[0071] Construct the pose matrix T of the robotic arm's end effector:

[0072] Where R is the rotation matrix of the pose matrix, and p is the coordinate of the path point;

[0073] The inverse of the pose matrix T yields the axis angle values ​​J of each joint of the robot's arm. i And form a list of axis angle values ​​J;

[0074] Constraints on the angles, angular velocities, and angular accelerations of each axis of the robot arm [J] lim ω lim a lim Transformed into constraints on eigenvalue velocity and eigenvalue acceleration [vs lim as lim ]; specifically:

[0075] The constraint conditions are transformed into generalized second-order constraints, and the list of axis angle values ​​J is continuously differentiated with respect to the eigenvalue s:

[0076] J' and J” are the first and second differentials of J with respect to s;

[0077] Therefore, we can conclude that:

[0078] ω lim =J'·as lim , This completes the transformation of the constraints.

[0079] Constructing independent variables: The independent variables are constructed using the eigenvalue acceleration and the square of the eigenvalue velocity as follows:

[0080]

[0081] The reachability analysis method is adopted, starting from the last path point of the trajectory curve at the end of the robotic arm and calculating towards the first path point. During the calculation process, the controllable set K of the independent variables is recursively calculated based on the eigenvalue acceleration and eigenvalue velocity constraints. The controllable set K contains the value range of the eigenvalue velocity of each path point. The reachability analysis method and the recursive calculation method are existing methods, which determine the value range of the linear velocity at each path point, and will not be elaborated here.

[0082] A greedy algorithm is used to calculate the optimal characteristic velocity value for each path segment in the controllable set K, from the first path point to the last path of the trajectory curve at the end of the robotic arm. b The solution process is as follows:

[0083]

[0084] stx i [1] = x i-1 [1]+2*ds*x i [0]

[0085] x i [1]∈K i+1 [1]

[0086] in: vs i+1 Let x be the actual characteristic velocity of the robotic arm's end effector on the i-th path segment. i [0] = as i , as i Let be the eigenvalue acceleration. The greedy algorithm is an existing algorithm and will not be elaborated here.

[0087] Based on this optimal characteristic velocity value, the discrete-time information of the robotic arm's end effector can be determined. This discrete-time information is then fitted to obtain a continuous trajectory curve. The continuous trajectory curve is processed according to a set required frequency to obtain the final list of axis angle values. In other words, after obtaining the optimal characteristic velocity for each path segment—for example, in the path from point i to point i+1—the distance between these two points divided by the optimal characteristic velocity yields the motion time t. Then, by querying the characteristic value list S for points i and i+1, the axis angle values ​​for these two points can be obtained. The change in axis angle value from point i is then... Let t be the event of the axis angle value at point i+1. By solving the above process for each point, we obtain several correspondences between t and axis angle values. Then, by fitting existing fitting methods, such as the least squares method, we obtain a continuous curve of axis angle values ​​with respect to time. On this curve, for example, if the processing requirement is an interval time of 0.1s, we extract an axis angle value every 0.1 seconds. These extracted axis angle values ​​form a list, which is the final optimal axis angle value list. The robot's robotic arm can work according to this axis angle value list, thus completing the robot trajectory time parameterization process.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for time parameterization of robot trajectory in complex curved surface machining, characterized in that: Includes the following steps: S1. Obtain the initial path points at the end of the robot's robotic arm and fit the initial path points to form a trajectory curve; S2. Determine the desired linear velocity of the robotic arm's end effector based on the trajectory curve, and then determine the desired characteristic velocity from the desired linear velocity; S3. Determine the discrete time information of the robotic arm end effector based on the characteristic value velocity, and fit the discrete time information to obtain a continuous trajectory curve. Process the continuous trajectory curve according to the set required frequency to obtain the final list of axis angle values. Step S1 specifically includes: The coordinates of each point on the initial path point and the normal vectors of each point The list is fitted to a B-spline trajectory curve; Interpolation processing is performed on the B-spline trajectory curve; In step S2, determining the desired linear velocity of the robotic arm's end effector based on the trajectory curve specifically includes: The points of the interpolated B-spline trajectory curve are fitted again to form a three-dimensional spline curve. ; Calculate 3D spline curves first derivative and second derivative ; 3D spline curve Project onto the machining plane and calculate the 3D spline curve. The curvature of the projected curve after being projected onto the machining plane : ;in: ； ; Normal vector of the machining plane for: ; This represents the normal vector of the current point; Calculate the radius of curvature at each point of the projected curve. : ; Determine the desired linear velocity at each path point : ; in: This represents the initially set linear velocity. The thickness of the workpiece to be processed. The coefficient is used when the projected curve is concave and the process is additive manufacturing, or when the projected curve is convex and the process is subtractive manufacturing. When the projected curve is concave and the machining process is subtractive, or when the projected curve is convex and the machining process is additive, ; The determination of the desired eigenvalue velocity from the desired linear velocity specifically includes: The path between two adjacent points on the projected curve is taken as the path segment, and the two endpoints of the path segment are used as the path segments. and The mean of the expected linear velocities is taken as the expected linear velocity of path segment i. The desired time is obtained by dividing the distance between the two endpoints of path segment i by the desired linear velocity of path segment i. ; Set the step size of the feature values ​​for path segment i Calculate the eigenvalue velocity of path segment i. : ； Construct a feature value list S, which is an arithmetic sequence, and the number of feature values ​​in the feature value list S is the same as the number of path points and they correspond one-to-one. Construct the pose matrix T of the robotic arm's end effector: ;in, The rotation matrix of the pose matrix, The coordinates of the path points; The inverse of the pose matrix T yields the axis angle values ​​of each joint of the robot's arm. And form a list of axis angle values. .

2. The method for time parameterization of robot trajectory for machining complex curved surfaces according to claim 1, characterized in that: When interpolating a B-spline curve, the angle between the normal vectors of adjacent points of the B-spline curve is... satisfy ,in, The set angle threshold; in: , Let represent the normal vector of the i-th point of the B-spline curve.

3. The method for time parameterization of robot trajectory for machining complex curved surfaces according to claim 1, characterized in that: Determining the desired eigenvalue velocity from the desired linear velocity also includes: Constraints on the angles, angular velocities, and angular accelerations of each axis of the robot arm. This is transformed into constraints on eigenvalue velocity and eigenvalue acceleration. ; Constructing independent variables: The independent variables are constructed using the eigenvalue acceleration and the square of the eigenvalue velocity as follows: ； The reachability analysis method is adopted to calculate from the last path point of the trajectory curve at the end of the robotic arm to the first path point. During the calculation, the controllable set K of the independent variables is recursively calculated based on the eigenvalue acceleration and eigenvalue velocity constraints. The controllable set K contains the value range of the eigenvalue velocity of each path point. A greedy algorithm is used to calculate the optimal characteristic velocity value for each path segment in the controllable set K, from the first path point to the last path of the trajectory curve at the end of the robotic arm. The solution process is as follows: in: , Let be the actual characteristic velocity of the robotic arm's end effector on the i-th path segment. .

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