Robot Polishing Force and Speed Planning Method and System Considering the Surface Shape Accuracy and Processing Efficiency of Optical Elements

Abstract

The present invention belongs to the technical field of robotic automated force-controlled polishing of optical elements, and specifically discloses a method and system for robotic polishing force and speed planning considering the surface shape accuracy and processing efficiency of optical elements. It includes: establishing a material removal model of a small grinding head polishing device based on Preston's theory; obtaining the surface shape data of the detection points of the optical element and offline planning the polishing path of the optical element; fitting discrete tool points, obtaining a parameterized position curve, evenly sampling points to obtain surface shape optimization dwell points, and establishing a unit material removal matrix in combination with the material removal model; constructing the first and second optimization models to obtain optimized contact forces and feed speeds. The present invention can realize the optimization of contact forces and feed speeds during the processing of optical elements, and obtain high-quality optical elements with high efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of robotic automated force-controlled polishing of optical elements, and particularly relates to a method and system for planning the polishing force and speed of a robot considering the surface shape accuracy and processing efficiency of optical elements. Background Art

[0002] With the development of science and technology, high-precision optical systems such as weaponry and space exploration have increasingly high requirements for the accuracy of optical elements, and the processing quantity is increasing, which poses a relatively severe challenge to the efficiency and accuracy of optical element processing. As a classic polishing method for optical elements, small grinding head polishing obtains a Gaussian-like removal function through the design of the polishing device, thus ensuring its shape correction ability and enabling controllable removal of the surface material of optical elements. Currently, small grinding head polishing of optical elements mostly adopts a constant force-variable speed polishing method, that is, the optimal surface shape accuracy of the optical element is obtained by solving the dwell time of optical element polishing. However, due to the existence of the maximum speed limit during the polishing process, it is easy to result in poor polishing effect of the optical element. The constant polishing force during polishing will affect the overall polishing efficiency, and obtaining the feed speed by obtaining the dwell time is likely to cause uneven speed and make the robot movement unstable. By optimizing the contact force and speed of grinding and polishing simultaneously and adopting a variable force-variable speed polishing method for polishing, the overall polishing efficiency can be improved, and the influence of the maximum speed limit on the polishing effect can be reduced by changing the contact force. Therefore, it is necessary to study the force-speed joint optimization method for optical element polishing to obtain better surface shape accuracy and higher polishing efficiency.

[0003] Through the above analysis, the problems and defects existing in the prior art are as follows:

[0004] (1) Traditional small grinding head polishing often obtains the feed speed of robot polishing by optimizing the dwell time, which is likely to cause uneven speed and lead to unstable robot movement.

[0005] (2) Traditional small grinding head polishing only optimizes the speed or dwell time, and the limitation of the maximum polishing speed often results in poor polishing effect of the optical element.

[0006] (3) Traditional small grinding head polishing does not consider the optimization of the contact force, and using a constant contact force for optical element polishing often leads to low polishing efficiency of the optical element.

[0007] The difficulties and defects in solving the above problems are as follows:

[0008] Traditional constant-force polishing with a small grinding head has limited ability to obtain a better surface shape, and has defects such as uneven feed speed and low polishing efficiency. When jointly optimizing the polishing contact force and polishing speed, there is a coupling effect between the contact force and polishing speed on the material removal amount of the optical element surface. Therefore, how to decouple the polishing contact force and polishing speed, obtain a smooth and feasible planned contact force and feed speed, and improve the processing efficiency while ensuring high-quality surface shape is the difficulty in solving this problem. Summary of the Invention

[0009] In view of the above defects or improvement requirements of the prior art, the present invention provides a method for planning the polishing force and speed of a robot considering the surface shape accuracy and processing efficiency of an optical element. Its purpose is to obtain a higher-quality surface shape of the optical element, and at the same time improve the polishing efficiency of the optical element on the premise of stable robot operation.

[0010] To achieve the above object, the present invention provides a method for jointly optimizing the force and speed for polishing an optical element with a small grinding head, including the following steps:

[0011] S1. Based on Preston's theory, establish a material removal model for the small grinding head polishing device.

[0012] S2. Obtain the surface shape data of the detection points of the optical element, and offline plan the polishing path of the optical element to obtain discrete tool position points.

[0013] S3. Fit the discrete tool points to obtain a parameterized position curve, uniformly take points to obtain surface shape optimization stationary points, and establish a unit material removal matrix in combination with the material removal model.

[0014] S4. Construct the first optimization model. Specifically, take the surface shape accuracy after processing the optical element as the optimization target, take the polishing contact force and the dwell time at the stationary point as the optimization variables, consider the feasibility of the contact force and the dwell time, and then solve the coupled optimal force-speed relationship through the least squares optimization algorithm.

[0015] S5. Construct the second optimization model. Take the processing efficiency of the optical element as the optimization target, take the end feed speed of the robot as the optimization variable, consider the motion limit of the robot and the feasibility of the contact force, use the interior point method as the optimization method to obtain the feed speed during the processing of the optical element, and calculate the polishing contact force of the optical element by back-calculating according to the force-speed coupling relationship.

[0016] As a further preference, in step S1, based on Preston's theory, the polishing removal amount of the optical element per unit time can be obtained as:

[0017]

[0018] Among them, h(x, y) is the magnitude of the material removal at the point (x, y) during the polishing of the grinding head. K is the Preston coefficient that can be regarded as a constant. P a (x, y, t) is the polishing pressure at this point at time t. For the planetary small grinding head device, it can be regarded as a constant. V(x, y, t) is the relative velocity between the grinding head and the workpiece at this point at time t. T is the polishing duration.

[0019] As a further preference, by analyzing and calculating the velocity distribution of the planetary small grinding head, the material removal model during the polishing of the polishing device can be obtained as:

[0020]

[0021] Among them, is the distance from the calculation point to the center of the polishing device, F is the polishing contact force, R p is the radius of the grinding head, n p is the angular velocity ratio of the revolution and rotation of the grinding head, ω1 is the angular velocity of the revolution of the planetary grinding head, and e is the eccentricity of the grinding head. α is the contact angle between the calculation point and the center of the grinding head during the movement of the grinding head. α0 is the limit of α, which is related to the position of the calculation point within the contact area of the grinding head and can be calculated by the following formula:

[0022]

[0023] As a further preference, step S3 mainly includes:

[0024] First, for the obtained discrete tool point positions P o perform spline fitting to construct a parameterized spline path.

[0025] Further, for the obtained parameterized spline path, perform uniform parameter selection to obtain the actual dwell points P r ={P r0 , P r1 ,..., P rb}.

[0026] As a further preference, construct a unit material removal matrix according to the actual dwell points, the surface shape data point positions of the optical element, and the material removal model as:

[0027]

[0028] Among them, h1(r ij ) is the removal amount per unit time for the i-th surface shape data point when the grinding head is at the j-th dwell point with a unit contact force. a is the total number of surface shape data points, and b is the total number of polishing dwell points.

[0029] As a further preference, in step S4, the first-step optimization model is constructed as follows:

[0030]

[0031] s.t.M i >F min t min

[0032] where J is the objective function, H is the vectorized surface shape data of the optical element, is the 2-norm of the vector, R0 is the unit material removal matrix, M is the vectorized representation of the product of the contact force and the dwell time, and M i represents the product of the contact force and the dwell time at the i-th dwell point. F min and t min respectively represent the minimum allowable contact force and the shortest dwell time during the polishing process.

[0033] As a further preference, in step S4, the least squares solver lsqnonlin in Matlab is used to solve the constructed optimization model, and the force-velocity relationship capable of obtaining the optimal surface shape of the optical element is obtained.

[0034] As a further preference, in step S5, the second-step optimization model is constructed as follows:

[0035]

[0036] where is the objective function, ds is the arc length interval between adjacent dwell points, s i represents the i-th dwell point. a is the acceleration of the robot's movement, and a max is the maximum allowable acceleration of the robot. F max represents the maximum contact force. v is the speed of the robot's movement, and v max is the maximum speed of the robot's movement. t i is the dwell time at the i-th dwell point.

[0037] The robot's movement speed is smoothed and fitted using a B-spline curve, which is expressed as:

[0038]

[0039] where {c i} are the control points, i = 0, 1,..., n; u is the parameter of the B-spline curve, which is related to the arc length displacement at the dwell point and reflects the position of the dwell point in the entire path, and N i,p (u) is the p-th order B-spline basis function, and its recurrence expression is:

[0040]

[0041] Among them, U = {u0, u1, …, u m} is the node vector, and m = n + p + 1.

[0042] As a further optimization, the path is segmented according to the speed control points. Only the values of some speed control points are optimized for each segment. The last p + 1 control points of each part of the speed curve are used as the starting control points of the next part of the speed curve for optimization, ensuring the smoothness of the overall speed curve.

[0043] As a further optimization, the optimization model is solved by using the interior point method through the nonlinear optimization toolbox fmincon of Matlab, and the values of the speed control points can be obtained, and then the speed spline curve can be obtained. Combining the optimal force-speed coupling relationship for optical element processing, the contact force information during the polishing process can be obtained.

[0044] Combining all the above technical solutions, the advantages and positive effects of the present invention are as follows:

[0045] First, by fully considering various factors in the material removal model of small grinding head polishing, the present application constructs a preliminary optimization model with the optimal surface shape during optical element polishing as the optimization goal and the contact force and dwell time as the optimization variables. The optimal force-speed coupling relationship is obtained, realizing the acquisition of the optimal surface shape of optical element polishing and ensuring the processing quality.

[0046] The present application constructs a speed spline curve based on the obtained optimal force-speed coupling relationship, with the goal of optimal processing time for the speed spline curve, and the feasibility of the maximum robot running speed, the maximum robot running acceleration, and the maximum contact force as the constraint conditions. By performing segmented optimization, the optimal speed and contact force are obtained, realizing the improvement of the processing efficiency of optical elements while obtaining high-quality surface shape accuracy.

[0047] The present application directly uses the feed speed of robot polishing as the optimization variable and fits the feed speed curve with B-spline. Combining the optimal force-speed coupling relationship and the feed speed curve to obtain the contact force, realizing the acquisition of smooth feed speed and contact force curves and ensuring the stable operation of the robot.

[0048] Second, in view of the problems of limited high-quality control ability of surface shape accuracy and low processing efficiency in the high-precision polishing of optical elements, the present invention proposes a method for planning the polishing force and speed of a robot based on the coupling of force and speed. In traditional polishing methods, due to the limitation of the movement speed of the robot itself and the use of a constant polishing force for polishing optical elements, it is difficult to further improve the surface shape accuracy of optical elements. By establishing an accurate material removal model and using the optimization of the force-speed coupling of the robot, the changing polishing contact force and polishing speed jointly affect the final surface shape effect, increasing the control freedom, solving the problem that it is difficult to further improve the surface shape accuracy during traditional constant-force polishing, and effectively improving the polishing accuracy.

[0049] The technological progress of the present invention is also reflected in improving the processing efficiency of optical elements. Traditional polishing methods mostly rely on manual operation or simple constant-force automation polishing, with low efficiency and difficulty in achieving the expected accuracy. The present invention has been optimized in terms of processing efficiency. By planning the polishing path and performing precise force-speed control in the force control mode of the robot, through the change of the polishing contact force, the polishing speed of the robot can be fully utilized, thus significantly improving the polishing speed and processing efficiency. This technological progress enables the present invention to be applicable to large-scale production, reducing production costs, and is especially suitable for the efficient manufacturing of large optical lenses and curved mirrors.

[0050] In addition, the present invention significantly improves the stability of processing accuracy in practical applications. The robot needs to be driven by the speed of path points. To achieve deterministic polishing, traditional optical element processing methods solve the dwell time of the robot at path points and drive the robot movement by converting the dwell time into the movement speed of the robot. However, the method of converting the dwell time into the movement speed of the robot may cause sudden changes in the speed of the robot, thus affecting the processing quality of the robot for optical elements. The present invention constructs a speed curve through a B-spline curve and directly plans the processing speed of the robot, making the obtained robot speed smooth and ensuring the stable operation of the robot during the processing of optical elements. This technological progress improves the smoothness of the robot processing movement and the stability of the optical element processing, providing stable high-quality optical elements for precision optical systems.

[0051] Finally, the present invention has made remarkable progress in terms of automation. Traditional polishing methods rely on manual experience, are difficult to replicate, and lack the ability of intelligent adjustment. The present invention introduces an adaptive optimization algorithm and combines it with the force control technology of the robot, making the polishing process more intelligent and capable of automatically adjusting polishing parameters according to the surface shape of different elements. This technological progress enables the robot to achieve high-precision automatic polishing in the manufacturing of complex optical elements, providing a reliable intelligent solution for the optical manufacturing industry, and further improving the industrial automation level and product quality stability. Description of the Drawings

[0052] Figure 1 This is the flowchart of the robot polishing force and speed planning method considering the surface shape accuracy and processing efficiency of the optical element in the embodiment of the present invention;

[0053] Figure 2 In (a) and (b), they are the schematic diagrams of the small grinding head device and its principle in the embodiment of the present invention;

[0054] Figure 3 This is the schematic diagram of the workpiece surface shape data in the embodiment of the present invention;

[0055] Figure 4 This is the schematic diagram of the surface shape data points and the dwell points in the embodiment of the present invention;

[0056] Figure 5 In (a) and (b), they are the schematic diagrams of the polished surface shape, feed speed, feed acceleration, and polishing contact force planned by using the proposed optical element processing force and speed planning method in the embodiment of the present invention;

[0057] Figure 6 This is the speed - time schematic diagram of the optical element polishing in the embodiment of the present invention under the proposed method and the case where the contact force is not considered in the planning.

[0058] In all the drawings, the same reference numerals are used to represent the same elements or structures, where: 1 - servo motor, 2 - coupling, 3 - support frame, 4 - planetary gear set, 5 - elastic coupling, 6 - flexible polishing head.

[0059] Specific implementation description

[0060] In order to make the objectives, technical solutions, and advantages of the present invention more clear and understandable, the following further details the present invention in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used 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.

[0061] The robot polishing force and speed planning system of the present invention realizes the efficient polishing treatment of the optical element surface through the precise cooperation among various components. First, the servo motor 1, as the core driving device of the system, provides power for the polishing system through precise speed and angle control. The output end of the servo motor is connected to the coupling 2 to ensure that the driving torque of the servo motor can be stably transmitted to the subsequent transmission system. The use of the coupling effectively reduces the power loss during the transmission process, enabling the feed speed to be precisely controlled. Combined with the accurate control of the contact force in robot processing, the effective control of the polishing process is thus achieved.

[0062] The support frame 3 plays a role of support and fixation in the entire device. The support frame stably installs each transmission component at a predetermined position, ensuring the stability and precision during the polishing process. A planetary gear set 4 is installed on the support frame, which is used to further adjust the rotational speed and torque. The planetary gear set can accurately control the speed of the polishing head by adjusting the transmission ratio, ensuring the accurate acquisition of the appropriate material removal model during the polishing process using the grinding head. At the same time, the transmission structure of the planetary gear set can provide flexible adjustment, enabling the system to operate smoothly under different loads.

[0063] An elastic coupling 5 is installed at the end of the servo motor and the planetary gear set. This component not only transmits power from the planetary gear set to the flexible polishing head but also has a certain buffering and vibration absorption function. The existence of the elastic coupling can absorb irregular vibrations or sudden impacts during the polishing process, thereby ensuring the smoothness of the polishing process and reducing damage to the optical element caused by unnecessary impacts. At the same time, the elastic coupling protects the mechanical device while accurately transmitting power, extending the service life of the system.

[0064] Finally, the flexible polishing head 6 directly contacts the optical element and performs the polishing task. The design of the flexible polishing head ensures uniform force application to the optical surface and can adapt to the curved surface structure to achieve fine polishing. When the polishing head contacts the workpiece surface, the servo motor, planetary gear set, and elastic coupling work together to make the movement and force application of the polishing head reach the expected value. At the same time, through the force control mode and speed planning of the robot, the polishing head can dynamically adjust the contact force and moving speed according to the surface shape of the optical element, realizing efficient and fine polishing to meet the high-precision surface requirements of the optical element.

[0065] The "Robot Polishing Force and Speed Planning Method Considering the Surface Shape Accuracy and Processing Efficiency of Optical Elements" of the present invention has broad industrial application prospects. The following lists two specific industrial application examples:

[0066] Example 1: Precision Polishing of High-Precision Optical Lenses

[0067] In the manufacturing of high-precision optical lenses, such as lenses used in lasers, astronomical telescopes, and microscopes, the optical surface shape accuracy is crucial. Traditional polishing methods cannot meet the high requirements for surface shape accuracy and are prone to generating small errors and surface shape distortions. The present invention realizes high-precision control of the polishing process through precise force-speed coupling planning, thereby meeting the strict flatness and smoothness requirements of optical elements. In specific applications, based on the surface shape detection data of the optical lens, using the first and second optimization models of the present invention, the surface of the lens is optimally polished through a small grinding head device to achieve precise material removal and obtain an optical surface shape that meets the design standards. This application significantly improves the manufacturing yield and surface shape consistency of high-precision lenses, reduces surface defects, and meets the requirements of high-precision instruments.

[0068] Embodiment 2: High-Efficiency Machining of Large Optical Mirrors

[0069] In large optical systems such as satellites and lidars, there is a great demand for high-efficiency precision machining of mirrors, and certain surface shape accuracy and consistency are required. Traditional manual polishing is difficult to meet the precision and efficiency requirements of large-area optical elements. Through the method of the present invention, the polishing path and feed speed are planned under the variable contact force control of the robot, and the large mirror is accurately and efficiently surface machined according to the material removal model, ensuring the accuracy of the optical surface, and at the same time significantly improving the machining speed and efficiency. The force-speed joint planning method of the present invention can accelerate the production process while meeting the surface shape accuracy, greatly reducing the manufacturing cost of large optical elements and making them more suitable for large-scale and high-precision optical application scenarios such as satellites and radars.

[0070] In view of the existing problems, the present invention provides a force-speed optimization method for deterministic polishing of optical elements that simultaneously ensures the optimal surface shape and the optimal efficiency. The present invention will be described in detail below with reference to the accompanying drawings.

[0071] As Figure 1 shown, the force-speed optimization method for deterministic polishing of optical elements provided by the embodiment of the present invention includes:

[0072] S1. Based on Preston's theory, establish a material removal model for the small grinding head polishing device.

[0073] S2. Obtain the surface shape data of the detection points of the optical element, and offline plan the polishing path of the optical element to obtain discrete tool position points.

[0074] S3. Fit the discrete tool points to obtain a parameterized position curve, uniformly take points to obtain surface shape optimization stationary points, and establish a unit material removal matrix in combination with the material removal model.

[0075] S4. Construct the first optimization model. Specifically, taking the surface shape accuracy of the optical element after machining as the optimization target, taking the polishing contact force and the dwell time of the stationary point as the optimization variables, considering the feasibility of the contact force and the dwell time, and then solving through the least squares optimization algorithm to obtain the coupled optimal force-speed relationship.

[0076] S5. Construct the second optimization model. Taking the machining efficiency of the optical element as the optimization target, taking the end feed speed of the robot as the optimization variable, considering the motion limit of the robot and the feasibility of the contact force, and using the interior point method as the optimization method to obtain the feed speed during the machining of the optical element, and inversely calculate the polishing contact force of the optical element according to the force-speed coupling relationship.

[0077] The present invention will be further described below with specific embodiments.

[0078] Step S1 specifically includes:

[0079] According to Figure 2 the shown small grinding head polishing device and principle, based on the Preston theory, the polishing removal amount of the optical element per unit time can be obtained as:

[0080]

[0081] where h(x, y) is the magnitude of the material removal amount at the point (x, y) during grinding head polishing. K is the Preston coefficient that can be regarded as a constant. P a (x, y, t) is the polishing pressure at this point at time t. V(x, y, t) is the relative speed between the grinding head and the workpiece at this point at time t. T is the polishing duration.

[0082] Using the planetary small grinding head polishing device, the grinding head is a surface grinding head. The pressure within the polishing area of the grinding head can be regarded as a constant and can be expressed as:

[0083]

[0084] where F is the polishing contact force, and R p is the radius of the polishing grinding head.

[0085] By analyzing the speed distribution of the planetary small grinding head and combining formulas (1) - (2), the material removal model during polishing of the polishing device can be obtained as:

[0086]

[0087] where is the distance of the calculation point from the center of the polishing device. F is the polishing contact force, and R p is the radius of the grinding head, n p is the angular velocity ratio of the revolution and rotation of the grinding head, ω1 is the angular velocity of the revolution of the planetary grinding head, and e is the eccentricity of the grinding head.

[0088] α is the contact angle between the calculation point and the center of the grinding head during the movement of the grinding head. α0 is the limit of α and is related to the position of the calculation point within the contact area of the grinding head, indicating the contact situation between each point in the polishing area and the grinding head when the grinding head makes one revolution. The α0 corresponding to each point in the contact area can be expressed as:

[0089]

[0090] Furthermore, step S2 specifically includes:

[0091] The original surface shape of the optical element is obtained by a laser interferometer. The data is discrete and is obtained by discrete sampling of the surface of the optical element. After obtaining the surface shape data of the optical element, the polishing path of the optical element is planned offline in combination with the size and surface shape data of the optical element to obtain discrete tool points. As Figure 4 shown, in this embodiment, a spiral polishing trajectory is used for planning, and discrete tool points P o .

[0092] Further, step S3 specifically includes:

[0093] According to the obtained discrete tool points, spline fitting is performed on the tool position points. In this embodiment, B-spline curve fitting is used to fit the discrete position points P o , and the obtained position curve can be expressed as:

[0094]

[0095] where d i is the position spline control point, i = 0, 1,..., n; u is the parameter on the B-spline curve. N i,p (u) is the p-th order B-spline basis function, and its recurrence expression is:

[0096]

[0097] where U = {u0, u1,..., u m} is the knot vector, m = n + p + 1, where u0 = u1 =... = u p = 0, u m-p = u m-p+1 =... = u m = 1. In this embodiment, the centripetal parameter method is used to parameterize the discrete tool points P o , and the knot vector U is obtained accordingly. Combining formula (5) and formula (6), the control points {d i} of the position curve can be obtained.

[0098] After obtaining the knot vector and the control points, a parameterized spline curve can be generated. Set the actual dwell points P r for surface shape optimization, and the number of them is a. Discrete points are obtained using a uniform parameterization interval as the actual dwell points for surface shape optimization, and the coordinates of the actual dwell points are obtained.

[0099]

[0100] After obtaining the coordinates of the actual dwell points, by calculating the distances between each actual dwell point and the surface shape detection points, and combining formula (3), set F = 1N to establish a unit material removal matrix.

[0101]

[0102] Among them, r ij represents the distance between the i-th surface shape detection point and the j-th actual residence point, and h1(r ij ) is the removal amount per unit time of polishing the i-th surface shape data point with a unit contact force when the grinding head is at the j-th residence point. a is the total number of surface shape detection points, and b is the total number of polishing residence points.

[0103] Further, step S4 specifically includes:

[0104] The material removal amount in the polishing process can be obtained from formula (9).

[0105] q = Rt (9)

[0106] Among them, q = [q1, q2,..., q a T , representing the removal amount at each surface shape number detection point. t = [t1, t2,..., t b T , representing the residence time of the polishing grinding head at each polishing residence point. R is the removal matrix, and its relationship with the unit removal matrix and the polishing contact force can be obtained through formula (3) and formula (8).

[0107]

[0108] Rearranging formula (9) and formula (10), the relationship between the material removal amount and the obtained unit material removal matrix is obtained.

[0109]

[0110] Among them, t i and F i are respectively the residence time and the polishing contact force at the i-th residence point.

[0111] Therefore, the residual surface shape of each surface shape data point after polishing can be obtained as e s .

[0112] e s = H - R0M (12)

[0113] Among them, e s is the vectorized representation of the residual surface shape data. H is the vectorized optical element surface shape data, M is the vectorized representation of the product of the contact force and the residence time, and M i represents the product of the contact force and the residence time at the i-th residence point.

[0114] Considering the root mean square value of the residual surface shape data to be optimal to ensure obtaining the optimal optical element surface shape. ​​

[0115] The objective function J of the optimization model can be established.

[0116]

[0117] To ensure that the optimized contact force and dwell time can be achieved by the robot, with the minimum dwell time and minimum contact force as the constraint conditions, combined with formula (13), the first-step optimization model can be established.

[0118]

[0119] Among them, F min , t min respectively represent the minimum contact force and the shortest dwell time allowed during the polishing process.

[0120] For the established optimization model, the least-squares solver lsqnonlin in Matlab can be used to solve it, and the force-velocity relationship for obtaining the optimal optical element surface shape can be obtained.

[0121] Furthermore, step S5 includes:

[0122] To separately obtain the optimized polishing contact force and polishing feed rate, it is necessary to decouple the optimal force-velocity relationship obtained in step S4.

[0123] To ensure the machining efficiency, the present invention takes the time-optimal as the optimization goal to optimize the polishing feed rate. Therefore, the objective function of the optimization model is

[0124]

[0125] Among them, ds is the arc length interval between adjacent dwell points, and v is the speed of the robot movement. To ensure the smoothness of the speed curve, a p-th order B-spline curve is used to fit the speed curve, expressed as:

[0126]

[0127] Among them, {c i} are the control points, i = 0, 1,..., n; u is the parameter of the B-spline curve, which is related to the arc length displacement at the dwell point and reflects the position of the dwell point in the entire path. Optimizing the solution of the feed rate is to optimize the solution of the control points of the speed curve.

[0128] To ensure the smooth movement of the robot, the movement of the robot should meet its movement limitations. Therefore, the maximum speed and maximum acceleration of the robot operation are considered as the constraint conditions for the feed rate planning.

[0129]

[0130] Among them, v max is the maximum allowable speed of the robot's movement, a is the acceleration of the robot's movement, and a max is the maximum allowable acceleration of the robot's movement. The acceleration of the robot's operation can be obtained by differentiating the velocity curve, as shown in the formula:

[0131]

[0132] While the movement limitations of the robot itself meet the requirements, the contact force during robot polishing should also meet the force control requirements. Since there is a coupling relationship M between the dwell time and the contact force, and the velocity is directly related to the dwell time, the limitation of the contact force will affect the limitation requirements of the velocity. To ensure the realizability of the planned contact force, it should be ensured that the planned contact force does not exceed the maximum contact force. Combining the coupling relationship between the contact force and the dwell time, the limitation of the maximum contact force on the feed velocity can be obtained as:

[0133]

[0134] Combining formulas (15) to (19), an optimization model can be obtained with the processing efficiency of the optical element as the optimization objective, the end feed velocity of the robot as the optimization variable, considering the movement limitations of the robot and the realizability of the contact force.

[0135]

[0136] By using the nonlinear optimization toolbox fmincon in Matlab and adopting the interior point method to solve the optimization model, the values of the velocity control points can be obtained, and then the velocity spline curve can be obtained. At the same time, to improve the solution efficiency of the velocity planning, the path is segmented according to the velocity control points, and only the values of some velocity control points are optimized for each segment. Moreover, the last p + 1 control points of each part of the velocity curve are used as the starting control points of the next part of the velocity curve for optimization to ensure the smoothness of the overall velocity curve.

[0137] Based on the obtained velocity curve and combining the coupling relationship between the dwell time and the contact force, the contact force value at the dwell point can be obtained, and the planned contact force curve can be obtained, thereby realizing the decoupling of the polishing contact force and the feed velocity.

[0138]

[0139] This embodiment uses Figure 3 the shown surface shape as the original surface shape during the polishing of the optical element, sets the maximum speed limit to 10 mm / s, and the maximum acceleration limit to 50 mm / s 2 , and the maximum contact force limit to 15 N. As Figure 6As shown, compared with the result of constant-force polishing with the average force of the planned contact force, the variable-force and variable-speed polishing performed in this embodiment can obtain higher processing efficiency while improving the surface shape accuracy compared to polishing with constant force and variable speed.

[0140] It should be noted that the embodiments of the present invention can be implemented through hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those of ordinary skill in the art can understand that the above devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code is provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits of programmable hardware devices such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable logic devices such as field programmable gate arrays, or can be implemented by software executed by various types of processors, or can be implemented by a combination of the above hardware circuits and software, such as firmware.

[0141] It is easy for those skilled in the art to 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 should be included in the protection scope of the present invention.

Claims

1. A method for planning the polishing force and speed of a robot considering the surface shape accuracy and processing efficiency of optical elements, characterized in that, It includes the following steps: S1. Based on Preston theory, establish a material removal model for the small grinding head polishing device; S2. Obtain the surface shape data of the detection points of the optical element, and offline plan the polishing path of the optical element to obtain discrete tool position points; S3. Fit the discrete tool points to obtain a parameterized position curve, evenly sample points to obtain surface shape optimization dwell points, and combine with the material removal model to establish a unit material removal matrix; S4. Construct the first optimization model; specifically, take the surface shape accuracy after processing the optical element as the optimization objective, take the polishing contact force and the dwell time of the dwell point as the optimization variables, consider the feasibility of the contact force and the dwell time, and then solve through the least squares optimization algorithm to obtain the coupled optimal force-speed relationship; S5. Construct the second optimization model; take the processing efficiency of the optical element as the optimization objective, take the end feed speed of the robot as the optimization variable, consider the motion limit of the robot and the feasibility of the contact force, use the interior point method as the optimization method to obtain the feed speed during the processing of the optical element, and calculate the polishing contact force of the optical element by back-calculating according to the force-speed coupling relationship; In the step S1, based on Preston theory, the polishing removal amount of the optical element per unit time can be obtained as: where h(x, y) is the magnitude of the material removal at the point (x, y) during the grinding head polishing; K is the Preston coefficient that can be regarded as a constant; P a (x, y, t) is the polishing pressure at this point at time t. For the planetary small grinding head device, it can be regarded as a constant; V(x, y, t) is the relative speed between the grinding head and the workpiece at this point at time t; T is the polishing duration; By analyzing and calculating the speed distribution of the planetary small grinding head, the material removal model during polishing of the polishing device can be obtained as: Among them, To calculate the distance of the point from the center of the polishing device, F is the polishing contact force, and R p is the radius of the grinding head, and n p is the angular velocity ratio of the revolution and rotation of the grinding head, ω1 is the angular velocity of the revolution of the planetary grinding head, e is the eccentricity of the grinding head; α is the contact angle between the calculation point and the center of the grinding head during the movement of the grinding head; α0 is the limit of α, which is related to the position of the calculation point within the contact area of the grinding head and can be calculated by the following formula: The step S3 mainly includes: First, for the obtained discrete tool point positions P o perform spline fitting to construct a parametric spline path; Uniform parameter selection is performed on the obtained parametric spline path to obtain the actual stationary points P for surface shape optimization r ={P r0 , P r1 ,..., P rb}; Construct a unit material removal matrix according to the actual dwell points, the position of the surface shape data points of the optical element, and the material removal model as: where h1(r ij ) is the removal amount per unit time per unit contact force at the i-th surface shape data point when the grinding head is at the j-th stationary point; a is the total number of surface shape data points, and b is the total number of polishing stationary points.

2. The robot polishing force and speed planning method considering the surface shape accuracy and processing efficiency of the optical element according to claim 1, characterized in that In the step S4, the first optimization model is constructed as: s.t.M i >F min t min where J is the objective function, H is the vectorized surface shape data of the optical element, is the 2-norm of the vector, R0 is the unit material removal matrix, M is the vectorized representation of the product of the contact force and the dwell time, and M i represents the product of the contact force and the dwell time at the i-th dwell point; F min and t min represent the minimum allowable contact force and the shortest dwell time during the polishing process, respectively.

3. The robot polishing force and speed planning method considering the surface shape accuracy and processing efficiency of the optical element according to claim 1, characterized in that, In the step S4, the constructed optimization model is solved using the least squares solver lsqnonlin in Matlab to obtain the force-speed relationship that can obtain the optimal surface shape of the optical element.

4. The robot polishing force and speed planning method considering the surface shape accuracy and processing efficiency of the optical element according to claim 1, characterized in that In the step S5, the second optimization model is constructed as: Among them, is the objective function, ds is the arc length interval between adjacent stationary points, and s i represents the i-th stationary point; a is the acceleration of the robot's movement, and a max is the maximum acceleration allowed for the robot; F max represents the maximum contact force; v is the speed of the robot's movement, and v max is the maximum speed of the robot's movement; t i is the dwell time at the i-th stationary point, and M i represents the product of the contact force and the dwell time at the i-th stationary point; The robot moving speed is smoothly fitted using a B-spline curve, expressed as: Among them, {c i} are the control points i = 0, 1,..., n; u is the parameter of the B-spline curve, which is related to the arc length displacement at the stationary points and reflects the position of the stationary points in the entire path. N i,p (u) is the p-th B-spline basis function, and its recurrence expression is: Among them, U = {u0, u1, …, u m} is the node vector, and m = n + p + 1; The path is segmented according to the speed control points. Only the values of some speed control points are optimized in each segment. The last p + 1 control points of each part of the speed curve are used as the starting control points of the next part of the speed curve for optimization to ensure the smoothness of the overall speed curve; Through the nonlinear optimization toolbox fmincon of Matlab, the interior point method is used to solve the optimization model, and the values of the speed control points can be obtained, and then the speed spline curve can be obtained; combined with the optimal force-speed relationship for optical element processing, the contact force information during the polishing process can be obtained.

5. A robot polishing force and speed planning system that takes into account the surface shape accuracy and processing efficiency of optical elements and implements the robot polishing force and speed planning method according to any one of claims 1 to 4, characterized in that, It includes the following modules: Material removal model establishment module: Based on Preston theory, establish a material removal model for the small grinding head polishing device to obtain the material removal amount of the optical element per unit time; Surface shape data acquisition and path planning module: Used to obtain the surface shape data of the detection points of the optical element, and based on these data, offline plan the polishing path to generate discrete tool position points; Dwell point fitting and material removal matrix calculation module: Used to perform spline fitting on the discrete tool position points to generate a parameterized path curve, evenly sample points to obtain the dwell point position, and combine with the material removal model to construct a unit material removal matrix; Optimization calculation module: including a first-step optimization model, aiming at the surface shape accuracy of the optical element, calculating the optimal force-speed relationship through the least squares algorithm; And a second-step optimization model, aiming at the processing efficiency, optimizing the feed speed and contact force of the robot through the interior point method.

6. The robot polishing force and speed planning system considering the surface shape accuracy and processing efficiency of the optical element according to claim 5, characterized in that, It also includes: A servo motor (1) for providing power output; A coupling (2) connected to the output end of the servo motor for transmitting power; A support frame (3) for fixing and supporting each component; A planetary gear set (4) installed on the support frame and connected to the coupling for adjusting the transmission ratio to accurately control the rotation speed of the polishing head and ensure the acquisition of a suitable material removal model; An elastic coupling (5) connected to the output end of the planetary gear set for transmitting power and absorbing vibration; A flexible polishing head (6) connected to the elastic coupling for contacting the optical element and realizing high-precision polishing with uniform force application, wherein the movement and force application of the flexible polishing head are accurately controlled by the cooperation of the servo motor, the planetary gear set and the elastic coupling.

7. The robot polishing force and speed planning system considering the surface shape accuracy and processing efficiency of optical elements according to claim 5, characterized in that The first-step optimization model in the optimization calculation module is solved through the least squares solver lsqnonlin in Matlab to obtain the optimal force-speed relationship for the surface shape accuracy of the optical element.

8. The robot polishing force and speed planning system considering the surface shape accuracy and processing efficiency of the optical element according to claim 5, characterized in that, The second-step optimization model in the optimization calculation module is solved using the interior point method. The velocity control points are optimized using the nonlinear optimization toolbox fmincon in Matlab, and the moving speed of the robot is smoothly fitted through B-spline curves, thereby obtaining the smooth speed curve of the overall path and the polishing contact force information.

Images