Wafer conveying corner point interpolation and speed optimization method, system, device and storage medium

Abstract

The application relates to the technical field of wafer conveying, and discloses a wafer conveying corner point interpolation and speed optimization method, system, device and medium. The method determines control points of a corner point connection curve based on the position of a corner point in an original multi-section trajectory, characteristic parameters of trajectories before and after the corner point and spatial geometric constraints, and constructs a second-order continuous corner point connection curve connected with the two trajectories before and after the corner point based on the control points; the maximum resultant acceleration in the corner point passing process is determined according to the maximum static friction force between the wafer and a mechanical finger, centripetal acceleration constraints, tangential acceleration constraints and speed constraints are established based on the curvature of the corner point connection curve and the maximum resultant acceleration; the corner point connection curve is optimized in the shortest time under the above constraints to obtain the optimal speed profile of the wafer passing through the corner point connection curve. The application can make the trajectory transition and speed change of the corner point area meet the static friction condition, reduce the risk of wafer sliding, wafer falling and wafer collision and rubbing, and improve the wafer corner point passing efficiency.

Description

Technical Field

[0001] This application relates to the field of semiconductor wafer transfer technology, and in particular to a method, system, device and storage medium for wafer transfer corner interpolation and speed optimization. Background Technology

[0002] Wafer transfer robots are crucial actuators used for wafer handling and transfer in semiconductor manufacturing. Due to the limitations of process cavity layout, wafer transfer paths typically consist of multiple trajectory segments, with corner points formed at the junctions of adjacent segments. To ensure rapid, accurate, and smooth wafer transfer within a limited space, the trajectory transition methods and throughput speeds in corner areas need to be rationally planned.

[0003] In applications such as vacuum environments, wafers and robotic fingers often cannot be fixed together by air pressure adsorption; they are typically kept relatively stationary by static friction. When the robotic arm accelerates excessively in corner areas, the wafer is prone to relative slippage, leading to problems such as wafer slippage, wafer drop, decreased pick-and-place accuracy, cavity collisions, and even material damage. Therefore, trajectory planning in corner areas not only needs to consider trajectory continuity and smoothness but also needs to simultaneously satisfy the static friction constraints between the wafer and the robotic fingers.

[0004] like Figure 2 As shown, wafer transfer trajectories typically need to switch between multiple workstations. For example, when transferring from workstation 0 to workstation 3, the trajectory may need to pass through corner point 1 and corner point 2 sequentially. Without corner point interpolation, the wafer usually needs to slow down to zero or near zero speed when passing through the corner to avoid a sudden change in velocity direction at the corner causing acceleration to exceed the static friction constraint. While this method reduces the risk of slippage, it significantly increases the single transfer time and reduces the transfer cycle time. If the existing arc connection method is used to handle the corner, the turning radius of the arc connection trajectory is limited by the working cavity space and wafer size when the angle between the trajectory before and after the corner is small, making it difficult to increase. This results in the wafer still needing to slow down significantly when passing through the arc connection section. Furthermore, in actual operation, if the speed of the connection trajectory cannot be dynamically adjusted according to curvature changes and static friction constraints, it will further limit the wafer transfer efficiency. Without interpolation, the wafer can only reduce its speed to 0 when passing through corner 1 and corner 2 to meet the static friction constraint. However, the existing circular arc connection method has a small turning radius and low passing speed when the corner angle is small, making it difficult to balance wafer transfer cycle time and stability.

[0005] Therefore, existing technologies still suffer from problems such as low throughput in corner areas, easy slippage or chip loss, and limited overall transport efficiency. These problems are particularly prominent in applications such as vacuum wafer transport, where the working cavity space is small and the wafer is held on the mechanical finger by static friction. Summary of the Invention

[0006] This application provides a method, system, device, and storage medium for wafer transfer corner interpolation and speed optimization to solve the problems in the prior art where corner areas are constrained by workspace and static friction, resulting in low throughput, easy slippage or chip drop, and limited transfer cycle time.

[0007] This application provides a method for wafer transport corner interpolation and speed optimization in a first aspect, comprising: determining control points of a corner connection curve based on the corner positions in the original multi-segment trajectory of wafer transport, characteristic parameters of the two trajectories before and after the corner, and spatial geometric constraints; constructing a second-order continuous corner connection curve at the connection point of the two trajectories before and after the corner based on the control points; determining the maximum resultant acceleration during the corner passage process based on the maximum static friction between the wafer and the robotic finger; establishing centripetal acceleration constraints, tangential acceleration constraints, and velocity constraints based on the curvature or radius of curvature of the corner connection curve and the maximum resultant acceleration; and optimizing the corner connection curve in the shortest time under the centripetal acceleration constraints, the tangential acceleration constraints, and the velocity constraints to obtain the optimal velocity profile of the wafer passing through the corner connection curve.

[0008] Furthermore, the characteristic parameters of the two segments of the trajectory before and after the corner point include the interpolation distance of the first segment, the interpolation distance of the second segment, the tangential angle, and the angular deviation; the spatial geometric constraint characterizes the spatial constraint relationship formed by the boundary of the working cavity and the wafer diameter.

[0009] Furthermore, the control points include a first control point, a last control point, an intermediate control point, and other control points. The first control point and the last control point are determined based on the first interpolation distance and the last interpolation distance, respectively. The intermediate control point is determined based on the angular deviation. The other control points are symmetrically distributed relative to the intermediate control point and their positions are adjusted according to the tangential angle according to a preset rule, so that when the tangential angle increases, the other control points shift towards the intermediate control point, and when the tangential angle decreases, the other control points shift towards the first control point and the last control point.

[0010] Furthermore, the maximum combined acceleration is determined based on the ratio of the maximum static friction force to the mass of the wafer, and the sum of the square of the tangential acceleration and the square of the centripetal acceleration is not greater than the square of the maximum combined acceleration.

[0011] Furthermore, the tangential acceleration constraint includes setting the tangential acceleration to zero at the intermediate control point with the smallest radius of curvature among the control points, while retaining only the centripetal acceleration constraint.

[0012] Furthermore, at the remaining control points, tangential acceleration limits are determined based on the centripetal acceleration corresponding to each point and the maximum resultant acceleration, and velocity limits are determined based on the radius of curvature corresponding to each point and the maximum resultant acceleration.

[0013] Furthermore, when establishing the velocity constraints, a velocity constraint is applied to the corner connection curve, wherein the linear velocity modulus does not exceed the preset maximum linear velocity, and an acceleration constraint is applied to the curve, wherein the total acceleration modulus does not exceed the preset maximum acceleration, and the smaller value between the preset maximum acceleration and the maximum combined acceleration is used as the upper limit of the effective acceleration.

[0014] Furthermore, when optimizing the corner connection curve in the shortest time, velocity constraints and acceleration constraints are set for the start and end points of the corner connection curve.

[0015] Furthermore, the shortest time optimization takes the shortest total transit time of the wafer along the corner connection curve as the objective function.

[0016] Furthermore, the shortest time optimization is solved using the velocity profile method or numerical optimal control method.

[0017] Furthermore, when using the velocity profile method, the optimal velocity profile is generated by forward scanning and backward scanning, wherein the forward scanning accelerates at the maximum tangential acceleration, the backward scanning decelerates at the maximum deceleration, and the lower bound of the forward scanning result and the backward scanning result is taken as the optimal velocity profile.

[0018] This application provides a wafer transport corner interpolation and speed optimization system in a second aspect, comprising: a control point determination unit, used to determine control points of a corner connection curve based on the corner position in the original multi-segment trajectory of wafer transport, characteristic parameters of the two trajectories before and after the corner, and spatial geometric constraints; a connection curve construction unit, used to construct a second-order continuous corner connection curve at the connection point of the two trajectories before and after the corner based on the control points; a constraint establishment unit, used to determine the maximum resultant acceleration during the corner passage process based on the maximum static friction between the wafer and the robotic finger, and establish centripetal acceleration constraints, tangential acceleration constraints, and speed constraints based on the curvature or radius of curvature of the corner connection curve and the maximum resultant acceleration; and a speed optimization unit, used to optimize the corner connection curve in the shortest time under the centripetal acceleration constraints, the tangential acceleration constraints, and the speed constraints to obtain the optimal speed profile of the wafer passing through the corner connection curve.

[0019] This application provides a computer device in a third aspect, including a memory and a processor, characterized in that the memory stores computer-readable instructions, which, when executed by the processor, cause the processor to perform the wafer transfer corner interpolation and speed optimization method as described in any of the above technical solutions.

[0020] In a fourth aspect, this application also provides a storage medium storing computer-readable instructions, characterized in that, when the computer-readable instructions are executed by one or more processors, the one or more processors cause the one or more processors to perform the wafer transfer corner interpolation and speed optimization method as described in any of the above technical solutions.

[0021] Compared with existing technologies, the above technical solution has at least the following beneficial effects: by constructing a second-order continuous connection trajectory in the corner region, and by coordinating the centripetal acceleration, tangential acceleration, and running speed during the corner passage process based on the static friction constraint between the wafer and the mechanical finger, and then optimizing the corner passage process for the shortest time, a smooth transition and rapid passage in the corner region can be achieved under the premise of meeting the wafer stability maintenance conditions. This reduces the risk of wafer slippage, chipping, and rubbing at the corner, and improves the operational stability and overall transfer efficiency of the wafer transfer process.

[0022] The above technical solution also has the following advantages: by combining the interpolation distance, tangential angle, angular deviation and spatial geometric constraints of the trajectory before and after the corner point to adjust the distribution of control points, and by setting differentiated acceleration and speed limits for the intermediate control points and other control points respectively, and by forming the optimal speed profile through the speed profile solution method, the corner point connection trajectory can better adapt to different corner point shapes and spatially constrained working conditions, further improving the rationality of speed planning, working condition adaptability and engineering feasibility of the corner point area, thereby improving the film transfer cycle time and operational robustness under different transfer tasks. Attached Figure Description

[0023] Figure 1 A flowchart illustrating the wafer transfer corner interpolation and speed optimization method provided in this application; Figure 2 This is a schematic diagram of the wafer transfer trajectory in existing technology; Figure 3 A schematic diagram illustrating the relationship between corner point and control point parameters provided in this application; Figure 4 A schematic diagram of the corner connection curve provided for this application; Figure 5 The comparison diagram of the corner point interpolation trajectory before and after optimization is provided for this application; Figure 6 The comparison diagram of trajectory velocity curves before and after optimization is provided for this application; Figure 7 A schematic diagram of the wafer transfer corner interpolation and speed optimization system provided in this application; Figure 8 A basic structural block diagram of the computer device provided in this application. Detailed Implementation

[0024] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only a part of the embodiments of the present application, and not all of them. Other implementation methods obtained by those skilled in the art based on the embodiments of the present application without creative effort are all within the protection scope of the present application.

[0025] In this application, the connection point between two adjacent segments of the original multi-segment trajectory in wafer transport can be referred to as a corner point. The two segments of the trajectory before and after the corner point can be any of the following: a straight line, an arc, or a curve. In some scenarios, although the position can remain continuous at the corner point, there may still be discontinuities in speed or the speed may drop to zero. In vacuum wafer transport scenarios, the wafer and the robotic fingers are usually kept relatively stationary by static friction. Therefore, when designing the trajectory transition in the corner point area, it is necessary to consider not only the smoothness of the trajectory but also the speed and acceleration limitations caused by static friction conditions to reduce the risk of wafer slippage, chipping, and collision during the corner point passage process.

[0026] In this application, the corner transition curve refers to the transition curve used to connect two segments of the trajectory before and after a corner point in the corner region. This transition curve is determined by a set of control points, which include at least a first control point, a last control point, an intermediate control point, and other control points located on either side of the intermediate control point. By rationally setting the positions of the control points, a transition curve that meets the requirements of a smooth transition can be formed in the corner region, providing a geometric basis for subsequent velocity optimization based on static friction constraints.

[0027] Figure 1 This is a flowchart illustrating the wafer transfer corner interpolation and speed optimization method provided in this application. Figure 1As shown, the method of this application may include the following steps: Step S100, determining the control points of the corner connection curve based on the corner positions in the original multi-segment trajectory of wafer transfer, the characteristic parameters of the two trajectories before and after the corner, and spatial geometric constraints; Step S200, constructing a second-order continuous corner connection curve at the connection point of the two trajectories before and after the corner based on the control points; Step S300, establishing centripetal acceleration constraints, tangential acceleration constraints, and velocity constraints during the corner passage process based on the radius of curvature of the corner connection curve and the maximum static friction force between the wafer and the robotic finger; Step S400, optimizing the corner connection curve in the shortest time under the centripetal acceleration constraints, tangential acceleration constraints, and velocity constraints to obtain the optimal velocity profile of the wafer passing through the corner connection curve. Through the above steps, a smooth and efficient transition of the wafer in the corner region can be achieved while satisfying the static friction constraints.

[0028] Step S100 will be explained below. Step S100 is used to determine the control points of the corner connection curve based on the corner position, the characteristic parameters of the two trajectories before and after the corner, and the spatial geometric constraints. The purpose of step S100 is to construct a set of control points for the corner region that can reflect the corner geometry and spatial constraints, given that the original multi-segment trajectories are already given, so that a corner connection curve that meets the requirements of smooth transition can be formed based on this set of control points.

[0029] In this embodiment, step S100 may include steps S101 and S102. In step S101, a series of control points are set. The number of control points is not fixed and can be set according to the transition requirements of the corner area; in one example, five control points can be set. At the same time, it is also necessary to obtain the feature parameters of the two segments of the trajectory before and after the corner. These feature parameters may include the interpolation distance of the first segment (corner_distance_pre), the interpolation distance of the second segment (corner_distance_next), the tangential angle between the two segments of the trajectory (angle), and the angular deviation (corner_deviation), etc. In addition, it is also necessary to limit the range of selectable positions of the control points by combining the spatial geometric constraints formed by the boundary of the working cavity and the wafer diameter. In this embodiment, the spatial geometric constraints are used to limit the passable range of the corner connection curve and the outer edge of the wafer in the working cavity. The boundary of the working cavity is used to restrict the corner connection curve from exceeding the movable area of ​​the robotic arm, and the wafer diameter is used to determine the safe clearance of the outer edge of the wafer relative to the boundary of the working cavity during the corner passage. The values ​​of the front interpolation distance, the back interpolation distance, and the angular deviation must simultaneously satisfy the avoidance relationship between the mechanical fingers, the outer edge of the wafer, and the boundary of the working cavity. While satisfying the above spatial geometric constraints, the front interpolation distance, the back interpolation distance, or the angular deviation can be appropriately increased to increase the local radius of curvature of the corner connection curve, reduce the peak centripetal acceleration during the corner passage process, and make the subsequently constructed corner connection curve smoother.

[0030] In this embodiment, the initial interpolation distance represents the setback distance of the first control point relative to the corner point in the direction of the initial trajectory, the subsequent interpolation distance represents the setback distance of the last control point relative to the corner point in the direction of the subsequent trajectory, the angular deviation represents the degree of deviation of the intermediate control point relative to the corner point, and the tangential angle between the two trajectories is used to characterize the degree of inflection between the two trajectories before and after the corner point. By combining the above parameters, the local trajectory morphology of the corner point region and the space constraints in the process cavity can be reflected simultaneously, so that the determined control point not only meets the requirements for smooth trajectory transition, but also meets the requirements for safe passage of the wafer in a limited space.

[0031] In step S102, the positional relationship of each control point is determined based on the corner point position and the aforementioned characteristic parameters.

[0032] Figure 3 This diagram illustrates the relationship between corner points and control point parameters. In one example, let the corner point position be... The interpolation distance in the first segment is The interpolation distance of the latter part is Angular deviation is Let the unit vector pointing from the corner point to the direction of retreat of the preceding trajectory be... The unit vector pointing from the corner point to the retreat direction of the subsequent trajectory is The unit vector pointing from the corner point to the middle control point is Then the first control point, the last control point, and the intermediate control points can be represented as follows:

[0033]

[0034]

[0035] in, Indicates the first control point. Indicates the last control point. This indicates an intermediate control point. In some embodiments, It can be obtained by synthesizing the tangential directions of the two segments of the trajectory before and after the corner point, or it can be determined along the bisector of the angle between the corner points. In this way, the first control point, the last control point, and the intermediate control point can reflect the geometric relationship of the trajectory before the corner point, the trajectory after the corner point, and the offset direction of the corner point, respectively.

[0036] In this embodiment, the remaining control points can be determined based on the positional relationship between the first control point, intermediate control point, and last control point. Specifically, the remaining control points are located on both sides of the intermediate control point and are symmetrically distributed relative to the intermediate control point. The larger the tangential angle, the greater the degree of inflection between the two trajectory segments before and after the corner point. In this case, the remaining control points can be moved closer to the intermediate control point to enhance the curve convergence ability in the corner point region. Conversely, the smaller the tangential angle, the smaller the degree of inflection between the two trajectory segments before and after the corner point. In this case, the remaining control points can be moved closer to the first and last control points to extend the smooth transition range. Thus, the shape of the corner point connection curve can be adaptively adjusted according to different corner point shapes.

[0037] In a specific example, the first and last control points can be determined along the trajectory directions before and after the corner point, respectively. The intermediate control points can be determined along the bisector of the angle between the corner points or by the intermediate direction jointly determined by the trajectories before and after the corner point. This is because the first and last control points correspond to the transition start and end points of the trajectories before and after the corner point, respectively, while the intermediate control points are primarily used to adjust the overall curvature and transition shape of the corner area. The symmetrical distribution of the remaining control points on both sides of the intermediate control points allows the connecting curve to form a smoother geometric change trend in the corner area.

[0038] After determining the control points in step S100, a set of control points is obtained that simultaneously considers the characteristic parameters of the two trajectory segments before and after the corner point, as well as the spatial geometric constraints of the working cavity. This set of control points provides the foundation for the subsequent construction of the corner connection curve. Furthermore, since the positions of each control point can reflect the connection relationship, degree of inflection, and spatial constraints of the trajectory before and after the corner point, the corner connection curve constructed based on this set of control points can better balance trajectory smoothness and subsequent speed optimization requirements. Next, step S200 of constructing the corner connection curve based on the control points will be explained.

[0039] Next, step S200 will be explained. Step S200 is used to construct a second-order continuous connection curve model of the corner region based on the control points obtained in step S100. Through this step, a continuous trajectory that meets the requirements of smooth transition can be formed between the two trajectories before and after the corner, providing a geometric basis for subsequently establishing velocity and acceleration constraints based on static friction constraints. In this embodiment, second-order continuity can be understood as the corner connection curve and the two trajectories before and after the corner satisfying at least positional continuity, tangential direction continuity, and curvature change continuity or acceleration change continuity at the connection point. By making the corner connection curve satisfy second-order continuity, the abrupt changes in velocity direction and acceleration in the corner region can be reduced, the impact of the robot's movement can be reduced, and the risk of wafer slippage relative to the robot finger can be reduced.

[0040] In this embodiment, step S200 may include steps S201 to S205. In step S201, according to the control point... Establish a second-order continuous transition curve model.

[0041] In some embodiments, the corner connection curve can be represented as a parametric curve determined by both control points and basis functions: ,in: The corresponding parameter on the curve point, It is the first One control point, This represents the basis functions corresponding to the curve type. Basis functions can be polynomial functions, rational functions, piecewise functions, or other functions whose smooth curve shape can be determined by control points. Using the parametric curve model described above, corner connection curves that satisfy the second-order continuity requirement can be constructed based on control points without limiting the specific curve type. It should be understood that the connection curve model can be any of the following forms: Bezier curve, spline curve, B-spline curve, polynomial curve, etc., as long as it satisfies the second-order continuity requirement at the connection between the two segments of the trajectory before and after the corner point.

[0042] In a specific example, the Bezier curve is used as the corner connection curve for illustration.

[0043] Figure 4 A schematic diagram of the corner connection curve provided in this application. For example... Figure 4 As shown, in step S202, when 5 control points are set in step S101, a 4th-order Bezier curve model can be established. In a specific example, the 5 control points used for the corner connection curve are as follows: , , , , ,in, This is the starting point of the curve connecting the corner points. The endpoint of the curve is where the corner points connect. , , Used to adjust the shape of the curve connecting corner points. Dashed line connection. , , , , A control polygon is formed, with the thick solid line representing the actual corner connection curve determined by the control points. The actual corner connection curve is not required to pass through all intermediate control points; rather, it is determined by the control points and their corresponding basis functions. The actual corner connection curve can be represented as:

[0044] in, These are the parameters for the corner connection curve. For the first One control point, , , This is used to influence the curvature of the curve and its connection trend with the preceding and following trajectories. Thus, using the Bezier curve model described above, the local shape of the corner connection curve can be changed by adjusting the position of the control points, so as to meet the smooth transition requirements at the connection between the two segments of the trajectory before and after the corner point. That is, the abrupt connection at the original corner point is transformed into a continuous curve connection.

[0045] exist Figure 4 middle, This indicates that the corner connection curve starts at the origin. Tangential direction at the point, This indicates that the corner connection curve ends at the endpoint. The tangential direction at the starting point. By making the tangential direction at the starting point... The tangential direction of the trajectory should be consistent with that of the preceding segment, and the tangential direction at the endpoint should also be consistent with that of the preceding segment. By aligning the tangential direction with the subsequent trajectory segment, the corner connection curve can maintain tangential continuity with the preceding and following trajectory segments at the connection point. Furthermore, by constraining the continuity of the curve's second derivative through control points and basis functions, the corner connection curve can satisfy the second-order continuity requirement at the connection point, thereby reducing abrupt changes in velocity direction and acceleration at the corner.

[0046] In step S203, the first derivative of the Bezier curve model is taken to obtain the velocity vector of the curve trajectory, i.e.:

[0047] The velocity vector is used to characterize the corner connection curve in terms of parameters. The tangential change trend at the point. Since the corner connection curve needs to be used for both velocity planning and acceleration constraints, obtaining the velocity vector through first-order differentiation is beneficial for subsequently describing the motion state of the wafer along the curve trajectory.

[0048] In step S204, the second derivative of the Bezier curve model is taken to obtain the acceleration vector of the curve trajectory, i.e.:

[0049] Acceleration vectors are used to characterize the corner connection curves in terms of parameters. The curvature changes at each location. By combining the velocity vector and acceleration vector, the curvature and radius of curvature of the curve at each location can be further calculated, thus providing a basis for establishing centripetal acceleration constraints.

[0050] In step S205, the arc length of the corner connection curve is parameterized, and a mapping relationship between the arc length of the curve and the position on the curve is established.

[0051] In one example, when the corner connection curve uses a Bezier curve, the Bezier curve can be discretely sampled based on the DeCasteljau algorithm to obtain multiple control parameters. Corresponding curve points By accumulating the distances between adjacent curve points, the corresponding arc length sample value can be obtained. Therefore, control parameters are established. With curve arc length The mapping relationship between them can be used to correlate the velocity values ​​in the subsequent velocity profile with the actual positions on the corner connection curve, thus facilitating velocity optimization based on the radius of curvature and acceleration constraints at different positions.

[0052] like Figure 4 As shown, let The position of the arc length on the curve connecting the corner points The corresponding curve points, This refers to the normal direction or centripetal direction at that point. Let be the radius of curvature at that point. Used to characterize the corner connection curve at position. The degree of local curvature at a point indicates the degree of curvature. A smaller radius of curvature indicates a sharper curve at that location; a larger radius of curvature indicates a gentler curve. When a wafer moves along the corner junction curve, in... The centripetal acceleration generated at the point along Direction, therefore, can be based on Establish subsequent centripetal acceleration and velocity constraints.

[0053] In this embodiment, based on the arc length on the corner connection curve The radius of curvature at a point can be determined by analyzing its velocity and acceleration vectors. ,Right now:

[0054] curvature With radius of curvature satisfy:

[0055] Centripetal acceleration can be expressed as:

[0056] This shows that when the radius of curvature When the radius of curvature is small, the curvature of the corner connection curve is greater at that location, resulting in a larger centripetal acceleration at the same speed; when the radius of curvature is small... When the radius of curvature is large, the curvature of the corner connection curve at that location is smaller, and the corresponding centripetal acceleration at the same speed is smaller. Therefore, the radius of curvature can serve as an important basis for establishing the corner passage speed constraint.

[0057] Next, step S300 will be explained. Step S300 is used to establish velocity and acceleration constraints at the control point and along the entire corner connection curve based on the wafer static friction constraint and the corner connection curve. Through this step, the geometric characteristics of the corner connection curve can be correlated with the actual stress conditions of the wafer in a vacuum environment.

[0058] In this embodiment, step S300 may include steps S301 to S303. In step S301, the maximum static friction constraint between the wafer and the robotic finger is denoted as... Wafer quality is denoted as Then, the maximum allowable combined acceleration of the wafer under the condition of no relative slippage is:

[0059] And satisfy:

[0060] in, Indicates tangential acceleration. This represents centripetal acceleration. Using the above relationship, the static friction constraint between the wafer and the robotic finger can be directly converted into a dynamic upper bound constraint in corner region velocity optimization.

[0061] In step S302, under the premise of satisfying the maximum static friction constraint, the velocity and acceleration of each control point are limited respectively. In this embodiment, since the curvature and centripetal acceleration are greatest at the middle control point, the tangential acceleration at the middle control point is set to 0, and only the centripetal acceleration constraint is retained. In this way, the centripetal acceleration budget required for turning can be satisfied first at the most dangerous position, thereby reducing the risk of wafer slippage at that position. For the other control points besides the middle control point, the tangential acceleration limit can be determined according to the centripetal acceleration and the maximum resultant acceleration corresponding to each point, that is:

[0062] The velocity limit is determined based on the radius of curvature and the maximum resultant acceleration at each point, i.e.:

[0063] in, Indicates the first radius of curvature at each control point This represents the upper limit of effective acceleration. Therefore, the upper limits of local velocity and local tangential acceleration at different control points can be obtained.

[0064] In step S303, global velocity and acceleration constraints are further applied to the entire corner connection curve. In one example, the linear velocity magnitude can be set to not exceed a preset maximum linear velocity. The velocity constraint, and the total acceleration modulus not exceeding the preset maximum acceleration. Acceleration constraints. Thus, based on the constraints determined by static friction in the local curve area, the running speed of the corner connection curve can be further limited by combining the allowable motion performance boundaries of the equipment itself. In actual solution, the preset maximum acceleration can be used... With the maximum resultant acceleration determined by static friction constraints The smaller value among the two is taken as the effective acceleration upper limit, thus simultaneously satisfying the requirements of wafer stability and device operational capability. It should be noted that the maximum combined acceleration determined by the maximum static friction force and wafer mass, and the preset maximum acceleration, can represent different types of constraints. The maximum combined acceleration determined by the maximum static friction force and wafer mass characterizes the upper limit of physical safety that the wafer can withstand without relative slippage; the preset maximum acceleration characterizes the upper limit of device movement allowed by the robot drive mechanism or control system. When both exist simultaneously, the effective acceleration upper limit is taken as the smaller of the two to simultaneously satisfy the limitations on wafer stability and device movement capability.

[0065] Step S300 obtains a set of velocity and acceleration constraints for the corner connection curve at each control point and along the entire curve. Since these constraints simultaneously consider curvature radius variation, wafer static friction limits, and device motion capabilities, they provide a feasible solution space for subsequent shortest-time optimization. In some embodiments, the corner connection curve can be discretized, and the upper velocity limit for each discrete point can be determined based on its curvature radius and allowable centripetal acceleration. The upper velocity limits of each discrete point form a velocity upper limit profile distributed along the corner connection curve. This velocity upper limit profile is used to transform the geometric characteristics, static friction constraints, and device motion constraints of the corner connection curve into path-related constraints in the velocity planning process, enabling subsequent shortest-time optimization to employ different allowable velocities at different curvature radii.

[0066] Next, step S400 will be explained. Step S400 is used to optimize the shortest time for the process of the wafer passing through the corner connection curve under the above geometric constraints, velocity constraints and acceleration constraints, so as to obtain the optimal velocity profile that satisfies all constraints.

[0067] In this embodiment, step S400 may include steps S401 to S403. In step S401, velocity and acceleration constraints are set for the starting and ending points of the corner connection trajectory, and an objective function that minimizes the total travel time is established. In one example, the objective function can be expressed as: ,in, This represents the total transit time along the corner junction curve of the wafer. This represents the total arc length of the curve connecting the corner points. Indicates the position of the wafer at the arc length. The speed at the corner point. By setting the above objective function, the corner point problem can be transformed into a time-optimal problem under various constraints.

[0068] In step S402, the optimal running speed of the trajectory is solved based on velocity constraints, acceleration constraints, start-end boundary conditions, and displacement constraints. In one embodiment, the shortest time optimization can also employ a 7-segment S-shaped velocity planning framework. This framework can establish a total trajectory time function based on the start-end velocity, end-end velocity, maximum tangential acceleration, jerk, acceleration segment displacement, deceleration segment displacement, and constant velocity segment velocity, and limit the constant velocity segment velocity based on a velocity upper limit profile. The velocity upper limit profile can be determined by the radius of curvature and allowable centripetal acceleration at each discrete point of the corner connection curve, for example:

[0069] in, Representing discrete points The speed limit at that point, Indicates the preset maximum linear velocity. This indicates the maximum permissible centripetal acceleration. Representing discrete points The radius of curvature at that point. Subsequently, the velocity of the uniform segment can be iteratively solved within a preset velocity range, and the process ends based on whether the difference in the trajectory running time obtained from two adjacent iterations is less than the convergence threshold.

[0070] in Indicates the first The trajectory running time obtained in the next iteration This represents the convergence threshold. Using the above method, velocity planning results that meet time optimization requirements can be obtained while satisfying the upper velocity profile and acceleration constraints.

[0071] In step S403, when using the velocity profile method, an optimal velocity profile is generated through forward and backward scans. The forward scan accelerates at the maximum tangential acceleration to obtain a forward velocity result that satisfies the acceleration constraint; the backward scan decelerates at the maximum deceleration to obtain a backward velocity result that satisfies the deceleration constraint and the endpoint boundary condition. Taking the lower bounds of the forward and backward scan results at each position yields the time-optimal velocity profile that satisfies all constraints. This method allows the wafer to maintain high throughput in corner regions while avoiding the disruption of static friction holding conditions due to excessively high local velocities.

[0072] Figure 5 A comparison diagram of the corner point interpolation trajectory before and after optimization provided in this application. (See attached image.) Figure 5As shown, the trajectories corresponding to the original method and the optimized method (i.e., the method in this application) are both used to connect the two segments of the trajectory before and after the corner point, and their overall trajectory directions are basically consistent. Compared with the original method, the optimized method constructs a second-order continuous corner connection curve through control points in the corner transition region, so that the trajectory gradually transitions from a nearly horizontal trajectory in the first segment to a steep trajectory in the second segment, avoiding obvious abrupt changes or sudden turns at the corner point. Thus, the optimized method can improve the local transition morphology of the corner region while basically maintaining the original spatial position of the transmission path, making the corner connection trajectory smoother, and providing a continuous trajectory basis for subsequent speed optimization based on radius of curvature and static friction constraints.

[0073] Figure 6 A comparison chart of trajectory velocity curves before and after optimization is provided for this application. Figure 6 As shown, the speed curves of both the original method and the optimized method (i.e., the method of this application) include a process of accelerating from the starting position to a preset speed, maintaining a higher speed in a portion of the trajectory range, decelerating at corners or in high-curvature regions, accelerating again after leaving the high-curvature region, and decelerating to zero before the endpoint. Compared to the original method, the optimized method limits the speed near corners and within the speed switching range based on the radius of curvature of the corner connection curve and static friction constraints, reducing the speed curve to a safe speed range in high-curvature regions and restoring a higher operating speed while satisfying centripetal acceleration constraints, tangential acceleration constraints, and equipment speed constraints. Therefore, the optimized method can avoid wafer slippage at corners due to excessive speed or sudden acceleration changes, while reducing unnecessary stops or excessive deceleration, thus balancing wafer transport safety and transport cycle time. This embodiment also provides a wafer transport corner interpolation and speed optimization system.

[0074] Figure 7 This is a schematic diagram of the wafer transfer corner interpolation and speed optimization system provided in this application. Figure 7 As shown, the system 10 may include a control point determination unit 11, a connection curve construction unit 12, a constraint establishment unit 13, and a speed optimization unit 14. Specifically, the control point determination unit 11 determines the control points of the corner connection curve based on the corner positions in the original multi-segment trajectory of wafer transport, the characteristic parameters of the two trajectories before and after the corner, and spatial geometric constraints. The connection curve construction unit 12 constructs a second-order continuous corner connection curve at the connection point between the control points and the two trajectories before and after the corner. The constraint establishment unit 13 determines the maximum resultant acceleration during the corner passage process based on the maximum static friction between the wafer and the robotic finger, and establishes centripetal acceleration constraints, tangential acceleration constraints, and speed constraints based on the curvature or radius of curvature of the corner connection curve and the maximum resultant acceleration. The speed optimization unit 14 optimizes the corner connection curve in the shortest time under the above constraints to obtain the optimal speed profile of the wafer passing through the corner connection curve.

[0075] In one example, the control point determination unit 11 can be further used to determine the positions of the first control point, the last control point, the intermediate control point, and the remaining control points based on the front interpolation distance, the rear interpolation distance, the tangential angle, the angular deviation, and the spatial geometric constraints formed by the working cavity boundary and the wafer diameter. The constraint establishment unit can be further used to determine the maximum combined acceleration based on the maximum static friction force and the wafer mass, and establish centripetal acceleration constraints, tangential acceleration constraints, and velocity constraints at each control point based on the maximum combined acceleration. Through the synergistic effect of each unit, the same technical effect as the aforementioned method embodiment can be achieved at the system level.

[0076] This embodiment also provides a computer device. Figure 8 A basic structural block diagram of the computer device provided in this application. (For example...) Figure 8 As shown, the computer device may include a processor, memory, non-volatile storage medium, and network interface connected via a system bus. The memory and non-volatile storage medium may store computer-readable instructions, which, when executed by the processor, cause the processor to perform the steps of the aforementioned wafer transfer corner interpolation and speed optimization method. The processor provides computing and control capabilities to support the operation of the entire device; the network interface is used for data interaction with external terminals, controllers, or servers.

[0077] This embodiment also provides a storage medium storing computer-readable instructions. When executed by one or more processors, the computer-readable instructions cause the one or more processors to perform the steps of the wafer transfer corner interpolation and speed optimization method described above. The storage medium can be a disk, optical disk, read-only memory, random access memory, or other medium capable of storing program instructions.

[0078] It should be noted that the number of control points, curve forms, and velocity profile solution methods shown in the above embodiments are merely illustrative examples and are not intended to limit the scope of protection of this application. Without departing from the technical concept of this application, those skilled in the art can make substitutions or adjustments to the number of control points, the form of the connecting curves, the constraint establishment method, or the shortest time optimization solution method, and such substitutions or adjustments should all fall within the scope of protection of this application.

Claims

1. A method for wafer transfer corner interpolation and speed optimization, characterized in that, include: Based on the corner positions in the original multi-segment trajectories of wafer transport, the characteristic parameters of the two trajectories before and after the corner, and spatial geometric constraints, the control points of the corner connection curve are determined. Based on the control points, construct a second-order continuous corner connection curve at the connection point between the two segments of the trajectory before and after the corner point; The maximum resultant acceleration during the corner crossing process is determined based on the maximum static friction between the wafer and the mechanical finger. Centripetal acceleration constraints, tangential acceleration constraints, and velocity constraints are established based on the curvature or radius of curvature of the corner connection curve and the maximum resultant acceleration. Under the centripetal acceleration constraint, the tangential acceleration constraint, and the velocity constraint, the corner connection curve is optimized for the shortest time to obtain the optimal velocity profile of the wafer passing through the corner connection curve.

2. The wafer transfer corner interpolation and speed optimization method according to claim 1, characterized in that, The characteristic parameters of the two segments of the trajectory before and after the corner point include the interpolation distance of the first segment, the interpolation distance of the second segment, the tangential angle, and the angular deviation. The spatial geometric constraints characterize the spatial constraint relationship formed by the boundary of the working cavity and the wafer diameter.

3. The wafer transfer corner interpolation and speed optimization method according to claim 2, characterized in that, The control points include the first control point, the last control point, the intermediate control points, and the remaining control points; The first control point and the last control point are determined based on the first interpolation distance and the last interpolation distance, respectively. The intermediate control point is determined based on the angular deviation. The remaining control points are symmetrically distributed relative to the intermediate control point and their positions are adjusted according to the tangential angle according to a preset rule, so that when the tangential angle increases, the remaining control points shift towards the intermediate control point, and when the tangential angle decreases, the remaining control points shift towards the first control point and the last control point.

4. The wafer transfer corner interpolation and speed optimization method according to claim 1, characterized in that, The maximum combined acceleration is determined based on the ratio of the maximum static friction force to the mass of the wafer, and the sum of the square of the tangential acceleration and the square of the centripetal acceleration is not greater than the square of the maximum combined acceleration.

5. The wafer transfer corner interpolation and speed optimization method according to claim 3, characterized in that, The tangential acceleration constraint includes: Among the control points, the tangential acceleration is set to zero at the intermediate control point with the smallest radius of curvature, while only the centripetal acceleration constraint is retained.

6. The wafer transfer corner interpolation and speed optimization method according to claim 3, characterized in that, At the remaining control points, tangential acceleration limits are determined based on the centripetal acceleration corresponding to each point and the maximum resultant acceleration, and velocity limits are determined based on the radius of curvature corresponding to each point and the maximum resultant acceleration.

7. The wafer transfer corner interpolation and speed optimization method according to claim 1, characterized in that, When establishing the velocity constraints, a velocity constraint that the linear velocity modulus does not exceed the preset maximum linear velocity and an acceleration constraint that the total acceleration modulus does not exceed the preset maximum acceleration are applied to the corner connection curve. The smaller value between the preset maximum acceleration and the maximum combined acceleration is used as the upper limit of the effective acceleration.

8. The wafer transfer corner interpolation and speed optimization method according to claim 1, characterized in that, When optimizing the corner connection curve for the shortest time, velocity constraints and acceleration constraints are set for the start and end points of the corner connection curve.

9. The wafer transfer corner interpolation and speed optimization method according to claim 1, characterized in that, The shortest time optimization uses the shortest total transit time of the wafer along the corner connection curve as the objective function.

10. The wafer transfer corner interpolation and speed optimization method according to claim 1 or 9, characterized in that, The shortest time optimization is solved using the velocity profile method or numerical optimal control method.

11. The wafer transfer corner interpolation and speed optimization method according to claim 10, characterized in that, When using the velocity profile method, the optimal velocity profile is generated by forward scanning and backward scanning. The forward scanning accelerates the target velocity at the maximum tangential acceleration, and the backward scanning decelerates the target velocity at the maximum deceleration. The lower bound of the forward scanning result and the backward scanning result is taken as the optimal velocity profile.

12. A wafer transfer corner interpolation and speed optimization system, characterized in that, include: The control point determination unit is used to determine the control points of the corner connection curve based on the corner position in the original multi-segment trajectory of wafer transfer, the characteristic parameters of the two trajectories before and after the corner, and the spatial geometric constraints. The connecting curve construction unit is used to construct a second-order continuous corner connecting curve based on the control point and the connection between the two segments of the trajectory before and after the corner point; The constraint establishment unit is used to determine the maximum resultant acceleration during the corner passing process based on the maximum static friction between the wafer and the mechanical finger, and to establish centripetal acceleration constraints, tangential acceleration constraints and velocity constraints based on the curvature or radius of curvature of the corner connection curve and the maximum resultant acceleration. The velocity optimization unit is used to optimize the corner connection curve in the shortest time under the centripetal acceleration constraint, the tangential acceleration constraint and the velocity constraint, so as to obtain the optimal velocity profile of the wafer passing through the corner connection curve.

13. A computer device, comprising a memory and a processor, characterized in that, The memory stores computer-readable instructions, which, when executed by the processor, cause the processor to perform the wafer transfer corner interpolation and speed optimization method as described in any one of claims 1 to 11.

14. A storage medium storing computer-readable instructions, characterized in that, When the computer-readable instructions are executed by one or more processors, the one or more processors perform the wafer transfer corner interpolation and speed optimization method as described in any one of claims 1 to 11.

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