Robot polishing force speed planning method and system considering surface shape precision and machining efficiency of optical element

Abstract

The invention belongs to the technical field of robot automatic force control polishing of optical elements, and particularly discloses a robot polishing force speed planning method and system considering the surface shape precision and the machining efficiency of the optical elements. The method comprises the steps that based on the Preston theory, a material removal model of the small grinding head polishing device is established; acquiring surface shape data of a detection point of the optical element, and planning a polishing path of the optical element in an off-line manner; discrete cutter points are fitted, a parameterized position curve is obtained, points are taken uniformly to obtain surface shape optimization resident points, and a unit material removal matrix is established in combination with a material removal model; and constructing a first-step optimization model and a second-step optimization model, and obtaining the optimized contact force and feed speed. According to the invention, optimization of contact force and feeding speed during optical element processing can be realized, and high-quality optical elements can be obtained with high efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot automated force-controlled polishing of optical elements, and in particular relates to a robot polishing force-speed planning method and system that considers the surface accuracy and processing efficiency of optical elements. Background Art

[0002] With the development of science and technology, high-demand optical systems such as weapons and space exploration have higher and higher requirements on the precision of optical components, and the number of processing is increasing, which poses a more severe challenge to the efficiency and precision of optical component processing. Small grinding head polishing is a classic polishing method for optical components. It obtains a Gaussian-like removal function through the design of the polishing device, thereby ensuring its shaping ability and realizing the controllable removal of the surface material of the optical component. At present, the small grinding head polishing of optical components mostly adopts a constant force-variable speed polishing method, that is, the optimal optical component surface accuracy is obtained by solving the dwell time of the optical component polishing. However, due to the existence of the maximum speed limit of the polishing process, it is easy to make the polishing effect of the optical component poor. 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 the speed to be uneven, making the robot motion unstable. By optimizing the contact force and speed of grinding and polishing at the same time and adopting a variable force-variable speed polishing method, 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 polishing optical elements to obtain better surface accuracy and higher polishing efficiency.

[0003] Through the above analysis, the problems and defects of 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 easily causes the obtained speed to be uneven, resulting in unstable robot movement.

[0005] (2) Traditional small-head polishing only optimizes the speed or dwell time. The limitation of the maximum polishing speed often leads to poor polishing effect of optical components.

[0006] (3) Traditional small-grinding head polishing does not consider the optimization of contact force. The use of constant contact force to polish optical components often leads to low polishing efficiency of optical components.

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

[0008] The ability of traditional small-grinding head constant-force polishing to obtain a better surface shape is limited, and there are defects such as uneven feed speed and low polishing efficiency. When the polishing contact force and polishing speed are jointly optimized, the effects of the contact force and polishing speed on the amount of material removed from the optical element surface are coupled. Therefore, how to decouple the polishing contact force and polishing speed, obtain smooth and feasible planned contact force and feed speed, and improve 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 needs of the prior art, the present invention provides a robot polishing force and speed planning method that takes into account the surface accuracy and processing efficiency of optical components. Its purpose is to obtain a higher quality surface shape of optical components and improve the polishing efficiency of optical components while maintaining stable robot operation.

[0010] To achieve the above object, the present invention provides a force-speed joint optimization method for polishing optical elements with a small grinding head, comprising the following steps:

[0011] S1. Based on Preston theory, a material removal model of the small grinding head polishing device is established.

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

[0013] S3, fitting discrete tool points, obtaining parameterized position curves, evenly selecting points to obtain surface shape optimization dwelling points, and establishing a unit material removal matrix in combination with the material removal model.

[0014] S4. Construct the first step optimization model. Specifically, the shape accuracy of the optical element after processing is taken as the optimization target, the polishing contact force and the dwell time of the dwell point are taken as the optimization variables, the feasibility of the contact force and the dwell time is considered, and then the optimal force-speed relationship of the coupling is obtained by solving the least squares optimization algorithm.

[0015] S5. Construct the second step optimization model. Take the processing efficiency of the optical element as the optimization target, the end feed speed of the robot as the optimization variable, consider the robot's motion limitation and the feasibility of the contact force, use the interior point method as the optimization method, obtain the feed speed during the processing of the optical element, and inversely calculate the polishing contact force of the optical element based on the force-speed coupling relationship.

[0016] As a further preferred embodiment, 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] Where h(x,y) is the amount of material removed at point (x,y) during polishing. K is the Preston coefficient which can be regarded as a constant. a (x, y, t) is the polishing pressure at the point at time t, which can be regarded as a constant for the planetary small grinding head device. V(x, y, t) is the relative speed between the grinding head and the workpiece at the point at time t. T is the polishing time.

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

[0020]

[0021] in, is the distance between the calculation point and 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 ratio of the angular velocity 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 when the grinding head moves. α0 is the limit of α, which is related to the position of the calculation point in the contact area of ​​the grinding head and can be calculated by the following formula:

[0022]

[0023] Further preferably, step S3 mainly includes:

[0024] First, for the discrete tool point position P o Perform spline fitting and construct a parameterized spline path.

[0025] Furthermore, the homogenization parameters are selected for the obtained parameterized spline path to obtain the actual residence point P for surface shape optimization. r = {P r0 ,P r1 ,...,P rb}.

[0026] Further preferably, the unit material removal matrix is ​​constructed according to the actual dwell point, the position of the surface data point of the optical element and the material removal model as follows:

[0027]

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

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

[0030]

[0031] sM i >F min t min

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

[0033] As a further preferred embodiment, in step S4, the constructed optimization model is solved by using the least square solver lsqnonlin in Matlab to obtain a force-speed relationship capable of obtaining the optimal optical element surface shape.

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

[0035]

[0036] in, is the objective function, ds is the arc length interval between adjacent dwell points, s i represents the i-th station point. a is the acceleration of the robot's movement, a max F is the maximum acceleration allowed for the robot. max represents the maximum contact force. v is the speed at which the robot moves, v max is the maximum speed of the robot. i is the residence time of the i-th residence point.

[0037] The robot moving speed is smoothly fitted using the B-spline curve, which is expressed as:

[0038]

[0039] Among them, {c i} is the control point 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, N i,p (u) is the p-order B-spline basis function, and its recursive expression is:

[0040]

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

[0042] As a further preference, the path is segmented according to the speed control points, and only the values ​​of some speed control points are optimized in each segment. The last p+1 control points of each speed curve are optimized as the starting control points of the next speed curve to ensure the smoothness of the overall speed curve.

[0043] As a further preferred method, the optimization model is solved by using the interior point method through the nonlinear optimization toolbox fmincon of Matlab to obtain the value of the speed control point and then obtain the speed spline curve. Combined with the optimal optical element processing force-speed relationship, 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, this application fully considers various factors in the material removal model of small grinding head polishing, and constructs a preliminary optimization model with the optimal surface shape when polishing optical elements as the optimization target and contact force and dwell time as optimization variables. The optimal force-speed coupling relationship is obtained, and the optimal surface shape of optical element polishing is obtained, ensuring the processing quality.

[0046] This application constructs a velocity spline curve by obtaining the optimal force-speed coupling relationship, takes the optimal processing time as the goal of the velocity spline curve, and takes the maximum speed of the robot, the maximum acceleration of the robot, and the feasibility of the maximum contact force as constraints. The optimal speed and contact force are obtained by segmented optimization, achieving the improvement of the processing efficiency of optical components while obtaining high-quality surface accuracy.

[0047] This application directly uses the feed speed of robot polishing as an optimization variable and fits the feed speed curve with B-spline. The contact force is obtained by combining the optimal force-speed coupling relationship with the feed speed curve, and a smooth feed speed and contact force curve is obtained, ensuring the smooth operation of the robot.

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

[0049] The technical progress of the present invention is also reflected in improving the processing efficiency of optical components. Traditional polishing methods mostly rely on manual operation or simple constant force automated polishing, which is inefficient and difficult to achieve the expected accuracy. The present invention optimizes the processing efficiency by planning the polishing path and performing precise force and 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, thereby significantly improving the polishing speed and processing efficiency. This technological progress enables the present invention to be suitable for large-scale production, reduce production costs, and is particularly suitable for the efficient manufacture of large optical lenses and curved reflectors.

[0050] In addition, the present invention significantly improves the stability of processing accuracy in practical applications. The robot needs the speed of the path point to be driven. In order to achieve deterministic polishing, the traditional optical element processing method solves the residence time of the robot at the path point, and drives the robot movement by converting the residence time into the robot movement speed. However, the method of converting the residence time into the robot's movement speed may cause a sudden change in the robot's speed, thereby affecting the robot's optical element processing quality. The present invention constructs a speed curve through a B-spline curve, directly plans the robot's processing speed, so that the obtained robot speed is smooth, ensuring the stable operation of the robot during the optical element processing process. This technological advancement improves the smoothness of the robot's processing movement, improves the stability of optical element processing, and provides stable high-quality optical elements for precision optical systems.

[0051] Finally, the present invention has made significant progress in automation. Traditional polishing methods rely on manual experience, are difficult to replicate, and lack intelligent adjustment capabilities. The present invention introduces an adaptive optimization algorithm and combines it with robot force control technology to make the polishing process more intelligent, and can automatically adjust polishing parameters according to the surface shape of different components. This technological advancement enables robots to achieve high-precision automatic polishing in the manufacture of complex optical components, providing a reliable intelligent solution for the optical manufacturing industry, and further improving the level of industrial automation and product quality stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A flow chart of a robot polishing force and speed planning method considering the surface accuracy and processing efficiency of an optical element according to an embodiment of the present invention;

[0053] Figure 2 (a) and (b) are schematic diagrams of the small grinding head device and its principle according to an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of workpiece surface data according to an embodiment of the present invention;

[0055] Figure 4 A schematic diagram of surface data points and resident points according to an embodiment of the present invention;

[0056] Figure 5 (a) and (b) are schematic diagrams of the post-polishing shape, feed speed, feed acceleration, and polishing contact force obtained by using the proposed optical element processing force speed planning method according to an embodiment of the present invention;

[0057] Figure 6 Schematic diagram of speed-time for polishing an optical element in an embodiment of the present invention with the proposed method and without considering contact force planning.

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

[0059] Specific implementation instructions

[0060] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended 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 efficient polishing of the surface of optical elements through precise coordination between multiple 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, so that the feed speed can be accurately controlled, combined with the accurate control of the contact force of the robot processing, thereby realizing effective control of the polishing process.

[0062] The support frame 3 plays a supporting and fixing role in the entire device. The support frame firmly installs each transmission component in a predetermined position to ensure stability and accuracy during the polishing process. A planetary gear set 4 is installed on the support frame to further adjust the speed and torque. The planetary gear set can accurately control the speed of the polishing head by adjusting the transmission ratio to ensure 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, so that the system can maintain stable operation 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 vibration or sudden impact during the polishing process, thereby ensuring the smoothness of the polishing process and reducing unnecessary impact damage to optical components. 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 on 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 of the polishing head reach the expected level. At the same time, through the robot's force control mode and speed planning, the polishing head can dynamically adjust the contact force and movement speed according to the surface shape of the optical element, achieve efficient and fine polishing, and meet the high-precision surface requirements of the optical element.

[0065] The "robot polishing force and speed planning method considering the surface accuracy and processing efficiency of optical components" of the present invention has broad industrial application prospects. Two specific industrial application examples are listed below:

[0066] Example 1: Precision polishing of high-precision optical lenses

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

[0068] Example 2: Efficient processing of large optical mirrors

[0069] In large optical systems such as satellites and lidars, there is a great demand for efficient finishing of reflectors, and certain surface accuracy and consistency are required. Traditional manual polishing is difficult to meet the precision and efficiency requirements of large-area optical components. 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 reflector is accurately and efficiently surface processed according to the material removal model, which ensures the accuracy of the optical surface and significantly improves the processing speed and efficiency. The force-speed joint planning method of the present invention can accelerate the production process while meeting the surface accuracy, greatly reducing the manufacturing cost of large optical components, making it more suitable for large-scale, 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 ensures both optimal surface shape and optimal efficiency. The present invention is described in detail below in conjunction with the accompanying drawings.

[0071] like Figure 1 As 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 theory, a material removal model of the small grinding head polishing device is established.

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

[0074] S3, fitting discrete tool points, obtaining parameterized position curves, evenly selecting points to obtain surface shape optimization dwelling points, and establishing a unit material removal matrix in combination with the material removal model.

[0075] S4. Construct the first step optimization model. Specifically, the shape accuracy of the optical element after processing is taken as the optimization target, the polishing contact force and the dwell time of the dwell point are taken as the optimization variables, the feasibility of the contact force and the dwell time is considered, and then the optimal force-speed relationship of the coupling is obtained by solving the least squares optimization algorithm.

[0076] S5. Construct the second step optimization model. Take the processing efficiency of the optical element as the optimization target, the end feed speed of the robot as the optimization variable, consider the robot's motion limitation and the feasibility of the contact force, use the interior point method as the optimization method, obtain the feed speed during the processing of the optical element, and inversely calculate the polishing contact force of the optical element based on the force-speed coupling relationship.

[0077] The present invention is further described below in conjunction with specific embodiments.

[0078] Step S1 specifically includes:

[0079] according to Figure 2 The small grinding head polishing device and principle shown in the figure, based on Preston theory, can obtain the polishing removal amount of optical components per unit time as follows:

[0080]

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

[0082] A planetary small grinding head polishing device is used, and the grinding head is a flat grinding head. The pressure in 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, R p is the radius of the polishing head.

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

[0086]

[0087] in, is the distance between the calculation point and 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 ratio of the angular velocity 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 when the grinding head moves. α0 is the limit of α, which is related to the position of the calculation point in the contact area of ​​the grinding head, indicating the contact between each point in the polishing area and the grinding head when the grinding head revolves one circle. 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 laser interferometer. The data is a discrete value 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. Figure 4 As shown, this embodiment uses a spiral polishing trajectory for planning and obtains discrete tool points P o .

[0092] Furthermore, step S3 specifically includes:

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

[0094]

[0095] Among them, 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-order B-spline basis function, and its recursive expression is:

[0096]

[0097] Among them, U={u0,u1,…,u m} is the node 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 discrete tool point P is calculated by the centripetal parameter method. o Parameterization is performed to obtain the node vector U. Combining formula (5) and formula (6), the control point {d i}.

[0098] After obtaining the node vector and control point, a parametric spline curve can be generated. Set the actual residence point P for surface shape optimization r , whose number is a. Use uniform parameterized intervals to obtain discrete points as actual resident points for surface shape optimization, and obtain the coordinates of the actual resident points.

[0099]

[0100] After obtaining the coordinates of the actual residence points, the distance between each actual residence point and the surface detection point is calculated, and combined with formula (3), F=1N is set to establish a unit material removal matrix.

[0101]

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

[0103] Furthermore, step S4 specifically includes:

[0104] The material removal amount during the polishing process can be calculated using formula (9).

[0105] q=Rt (9)

[0106] Where q=[q1,q2,…,q a ] T , represents the amount of removal at each face detection point. t=[t1,t2,…,t b ] T , represents the residence time of the polishing head at each polishing dwell 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] By reorganizing formula (9) and formula (10), we can get the relationship between the material removal amount and the obtained unit material removal matrix.

[0109]

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

[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 data. H is the vectorized optical element surface data, M is the vectorized representation of the product of contact force and dwell time, M i It represents the product of the contact force and the dwell time at the ith dwell point.

[0114] The root mean square value of the residual surface data is considered to be optimal to ensure that the optimal optical element surface shape is obtained.

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

[0116]

[0117] In order to ensure that the optimized contact force and dwell time can be achieved by the robot, the minimum dwell time and minimum contact force are used as constraints, and combined with formula (13), the first step optimization model can be established.

[0118]

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

[0120] For the constructed optimization model, the least squares solver lsqnonlin of Matlab can be used to solve it and obtain the force-speed relationship that can obtain the optimal optical element surface shape.

[0121] Further, step S5 includes:

[0122] In order to obtain the optimized polishing contact force and polishing feed speed respectively, it is necessary to decouple the optimal force-speed relationship obtained in step S4.

[0123] In order to ensure the processing efficiency, the present invention optimizes the polishing feed speed with the optimal time as the optimization target. 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. In order to ensure the smoothness of the velocity curve, a p-order B-spline curve is used to fit the velocity curve, which is expressed as:

[0126]

[0127] Among them, {c i} is the control point 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. The feed speed is optimized and solved, that is, the speed curve control point is optimized and solved.

[0128] In order to ensure the smooth movement of the robot, the robot's movement should meet its motion constraints. Therefore, the maximum speed and maximum acceleration of the robot are considered as constraints for feed speed planning.

[0129]

[0130] Among them, v max is the maximum speed allowed for the robot to move, a is the acceleration of the robot, and a max is the maximum acceleration allowed for the robot to move. The acceleration of the robot can be obtained by taking the derivative of the velocity curve, as shown in the formula:

[0131]

[0132] While the robot's own motion restrictions meet the requirements, the robot's polishing contact force should also meet the force control requirements. Since there is a coupling relationship M between the dwell time and the contact force, and the speed is directly related to the dwell time, the contact force restriction will affect the speed restriction requirements. In order to ensure the feasibility 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 maximum contact force restriction on the feed speed can be obtained as:

[0133]

[0134] Combining,Formulas (15) to (19), we can obtain an optimization model that takes the processing efficiency of the optical element as the optimization target, the end feed speed of the robot as the optimization variable, and considers the feasibility of the robot's motion constraints and contact force.

[0135]

[0136] By using Matlab's nonlinear optimization toolbox fmincon, the optimization model is solved using the interior point method to obtain the value of the speed control point, and then the speed spline curve is obtained. At the same time, in order to speed up the speed planning solution efficiency, the path is segmented according to the speed control point, and only the value of some speed control points is optimized in each segment. In addition, the last p+1 control points of each speed curve are optimized as the starting control points of the next speed curve to ensure the smoothness of the overall speed curve.

[0137] By obtaining the speed curve and combining it with 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 speed.

[0138]

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

[0140] It should be noted that the embodiments of the present invention can be implemented by 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. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as 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. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0141] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions 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 robot polishing force and speed planning method considering the surface accuracy and processing efficiency of optical components, characterized in that: The following steps are involved: S1. Based on Preston theory, a material removal model of a small grinding head polishing device is established; S2, obtaining the surface data of the optical element detection point, and offline planning the polishing path of the optical element to obtain the discrete tool position point; S3, fitting discrete tool points, obtaining parameterized position curves, evenly selecting points to obtain surface shape optimization dwelling points, and establishing a unit material removal matrix in combination with the material removal model; S4, construct the first step optimization model; specifically, take the shape accuracy of the optical element after processing as the optimization target, 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 the optimal force-speed relationship of the coupling through the least squares optimization algorithm; S5. Construct the second-step optimization model; take the processing efficiency of the optical element as the optimization target, the end feed speed of the robot as the optimization variable, consider the robot's motion limitation and the feasibility of the contact force, use the interior point method as the optimization method, obtain the feed speed during optical element processing, and inversely calculate the polishing contact force of the optical element based on the force-speed coupling relationship.

2. The robot polishing force speed planning method considering the surface accuracy and processing efficiency of optical components as claimed in claim 1, characterized in that: In step S1, based on Preston's theory, the polishing removal amount of the optical element per unit time can be obtained as: Where h(x,y) is the amount of material removed at point (x,y) during polishing; K is the Preston coefficient which can be regarded as a constant; P a (x, y, t) is the polishing pressure at the point at time t, which can be regarded as a constant for the planetary small grinding head device; V(x, y, t) is the relative speed between the grinding head and the workpiece at the point at time t; T is the polishing time; By analyzing and calculating the velocity distribution of the planetary small grinding head, the material removal model of the polishing device during polishing can be obtained as follows: in, is the distance between the calculation point and 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 ratio of the angular velocity 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 when the grinding head moves. α0 is the limit of α, which is related to the position of the calculation point in the contact area of ​​the grinding head and can be calculated by the following formula:

3. The robot polishing force speed planning method considering the surface accuracy and processing efficiency of optical components as claimed in claim 1, characterized in that: The step S3 mainly includes: First, for the discrete tool point position P o Perform spline fitting and construct parameterized spline path; The homogenization parameters are selected for the obtained parameterized spline path to obtain the actual residence point P for surface shape optimization. r = {P r0 ,P r1 ,…,P rb }; The unit material removal matrix is ​​constructed based on the actual dwell point, the position of the surface data point of the optical element and the material removal model: Among them, h1(r ij ) is the removal amount at the i-th surface data point per unit time with unit contact force when the grinding head is located at the j-th dwelling point; a is the total number of surface data points, and b is the total number of polishing dwelling points.

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

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

6. The robot polishing force speed planning method considering the surface accuracy and processing efficiency of optical components as claimed in claim 1, characterized in that: In step S5, the second step optimization model is constructed as follows: in, is the objective function, ds is the arc length interval between adjacent dwell points, s i represents the i-th station point; a is the acceleration of the robot's movement, a max F is the maximum acceleration allowed for the robot; max represents the maximum contact force; v is the speed at which the robot moves, v max is the maximum speed of the robot; t i is the residence time of the i-th residence point; The robot moving speed is smoothly fitted using the B-spline curve, which is expressed as: Among them, {c i } is the control point 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, N i,p (u) is the p-order B-spline basis function, and its recursive expression is: Among them, U={u0,u1,…,u m } is the node vector, 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 speed curve are used as the starting control points of the next speed curve for optimization to ensure the smoothness of the overall speed curve. Through Matlab's nonlinear optimization toolbox fmincon, the optimization model is solved using the interior point method to obtain the value of the velocity control point, and then the velocity spline curve; combined with the optimal optical element processing force-speed relationship, the contact force information during the polishing process can be obtained.

7. A robot polishing force and speed planning system considering the surface accuracy and processing efficiency of optical components, characterized in that: Includes the following modules: Material removal model building module: Based on Preston theory, a material removal model of a small grinding head polishing device is established to obtain the material removal amount of the optical element per unit time; Surface data acquisition and path planning module: used to acquire the surface data of the optical component detection points, and plan the polishing path offline based on these data to generate discrete tool position points; Dwell point fitting and material removal matrix calculation module: used to perform spline fitting on discrete tool position points, generate parameterized path curves, and evenly select points to obtain the dwell point positions, and build a unit material removal matrix in combination with the material removal model; Optimization calculation module: including the first step of optimizing the model, taking the surface accuracy of the optical element as the goal, and calculating the optimal force-speed relationship through the least squares algorithm; And the second step optimization model, taking machining efficiency as the goal, optimizes the robot's feed speed and contact force through the interior point method.

8. The robot polishing force and speed planning system considering the surface accuracy and processing efficiency of optical components according to claim 7, characterized in that: 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), used for fixing and supporting each component; A planetary gear set (4), mounted 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 that a suitable material removal model is obtained; 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) is connected to the elastic coupling and is used for contacting the optical element and achieving high-precision polishing with uniform force, wherein the movement and force of the flexible polishing head are precisely controlled by the cooperation of the servo motor, the planetary gear set and the elastic coupling.

9. The robot polishing force and speed planning system considering the surface accuracy and processing efficiency of optical components according to claim 7, characterized in that: The first step optimization model in the optimization calculation module is solved by the least squares solver lsqnonlin of Matlab to obtain the force-speed relationship with the best surface accuracy of the optical element.

10. The robot polishing force and speed planning system considering the surface accuracy and processing efficiency of optical components according to claim 7, characterized in that: The second step optimization model in the optimization calculation module is solved by the interior point method, and the speed control point is optimized using the nonlinear optimization toolbox fmincon of Matlab. The robot movement speed is smoothly fitted by the B-spline curve to obtain the smooth speed curve of the overall path and the polishing contact force information.

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