Curved surface mapping track optimization and multi-modal force control method for complex wall surface polishing

Abstract

The invention discloses a curved surface mapping track optimization and multi-modal force control method for complex wall surface polishing. The method can efficiently meet the polishing requirement of a complex curved surface. A polishing track is determined by introducing a projection technology, a path optimization model is constructed, and multi-node force fusion attitude control is combined, so that interpolation point calculation and attitude change and position planning matching are realized, and a robot polishing path including a polishing position, an attitude and adjustment parameters is effectively generated. According to the multi-mode force control method, a force control mode is dynamically adjusted by combining radial height state switching of state classification of convex and concave path sections; multi-node fusion attitude control is further introduced, the surface contact force of a sand disc is accurately tracked, the tail end attitude of the robot is dynamically adjusted to follow the curved surface characteristics, the problems of irregular curved surfaces, unstable force control and the like in the traditional grinding technology are solved, and the method can be widely applied to automatic efficient grinding operation in the fields of buildings, ships and the like; and efficient and high-precision grinding of the complex curved surface is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial robot automation, and specifically relates to a method for optimizing the curved surface mapping trajectory and multi-modal force control for complex wall surface grinding, which is particularly suitable for high-efficiency and high-precision grinding operations on large-curvature complex curved surfaces such as building walls and ship hulls. Background Art

[0002] In a complex wall surface environment, traditional manual grinding methods are limited by the personal skills and physical strength of operators, and have the disadvantages of high labor intensity, low efficiency, and poor work consistency, which easily lead to unqualified surface flatness and smoothness. In recent years, with the rapid development of industrial intelligence, automated robots have gradually been applied to grinding tasks. However, existing grinding robots still have the following defects in terms of structural design and function implementation:

[0003] (1) In terms of grinding path planning, for complex curved surface operations, existing robots mostly design grinding paths based on fixed trajectories or approximate interpolation schemes. For convex and concave regions with complex curvature changes, there are often problems such as insufficient trajectory accuracy and low efficiency caused by frequent path adjustments.

[0004] (2) In terms of end-effector attitude adjustment, existing robots often cannot dynamically adapt to the drastic changes in wall surface curvature and cannot make efficient attitude adjustments for complex curved surfaces, which easily leads to over-cutting and under-cutting in local areas, thus affecting the grinding effect.

[0005] (3) The force control strategy lacks flexibility, and traditional force control methods are difficult to adjust the grinding force in real time to adapt to the curvature complexity and surface material of different regions, resulting in difficulty in ensuring the machining quality and stability of the wall surface.

[0006] Therefore, in order to solve the problems of low grinding path accuracy, poor force control effect, and insufficient dynamic performance in a complex curved surface environment, there is an urgent need for a wall surface grinding control method based on curved surface mapping trajectory optimization and multi-modal force control. The present invention proposes an efficient grinding solution for a complex wall surface environment in response to the above problems. Summary of the Invention

[0007] To solve the above technical problems, the present invention proposes a method for optimizing the curved surface mapping trajectory and multi-modal force control for complex wall surface grinding. The system combines trajectory optimization modeling, dynamic adjustment of the attitude of the end effector of the robotic arm, and a hybrid force control strategy, and can efficiently adapt to the grinding requirements of complex curved surfaces. By constructing a path optimization model and introducing multi-node force fusion attitude control, the grinding efficiency and accuracy of the robotic system are further improved.

[0008] To achieve the above object, the technical solution adopted by the present invention is:

[0009] A method for optimizing the curved surface mapping trajectory and multi-modal force control for complex wall surface grinding, comprising the following steps:

[0010] (1) Utilize the relative position relationship between the target curved surface S(x, y, z) and the reference plane P(x, y, z), simplify the curved surface area to the two-dimensional plane S(x, z) through projection technology, discretize the curve to generate grid points, and identify the set of feature points {Δ, □, ○, ◇};

[0011] (2) Define the path segment types for the combination of feature points, and classify the path segments into convex segments and concave segments; use the simulated annealing algorithm to optimize the interpolation points s * for the convex path segments, and use the linear interpolation method to add interpolation points s # for the concave path segments, and generate the globally optimal grinding trajectory Q(x, z) containing the information of interpolation points and path turning points;

[0012] (3) According to the trajectory optimization result in step (2), design a continuous adjustment model for the attitude of the end effector of the robotic arm based on cell division and splicing, and ensure the effective contact between the end effector of the robotic arm and the curved surface through topological configuration planning;

[0013] (4) Based on the height state State B of the path segments in steps (2) and (3), adopt the multi-modal force control method, enable the adaptive impedance control when State B = 0, enable the constant force control mode when State B = 1, and coordinate the movement speed of the end effector of the robotic arm and the rotation speed of the grinding motor to achieve wall surface grinding under different force control modes;

[0014] (5) On the basis of step (4), introduce a multi-node fusion attitude control method with a force feedback mechanism, construct the fusion attitude control through three equally spaced multi-node sensing systems, and further optimize the contact force distribution on the working plane of the end effector of the robotic arm.

[0015] As a further improvement of the present invention, in step (1), when the curve is discretized to generate grid points, it is equally spaced along the curve S(x, z) into N + 1 grid points, in the form of: S(x, z) = {s0, s1,..., s N};

[0016] Extract the feature points {Δ, □, ○, ◇} from the grid points and classify them. Among them: Δ represents the upper tangent point of the curved surface and the reference plane; □ represents the lower tangent point of the curved surface and the reference plane; ○ and ◇ respectively represent the upward intersection point and the downward intersection point.

[0017] As a further improvement of the present invention, the raised path segments in path classification include Δ-◇, Δ-Δ, ○-◇, ○-Δ, and the sunken path segments include ◇-□, ◇-○, □-○, □-□;

[0018] Judge the status flag State according to the radial height difference Δz of the path segment B : When State B =0, the radial height difference is greater than 1.5mm; when State B =1, the radial height difference is less than or equal to 1.5mm.

[0019] As a further improvement of the present invention, in the step (2), during the interpolation point optimization process, a secondary interpolation plan is introduced for the raised path segment, and the interpolation point optimization objective is to minimize the grinding path removal area. The optimization objective function is:

[0020]

[0021] where Q(x,z) represents the path function generated by interpolation, s* represents the interpolation point, and the simulated annealing algorithm is used to solve the optimal interpolation point s*.

[0022] As a further improvement of the present invention, in the step (3), the attitude adjustment of the end effector of the robotic arm is planned based on the topological configuration divided by cells, including the following steps:

[0023] Decompose the target surface into several cells c i , plan the attitude transition between cells through the attitude configuration set ζ; according to the continuity judgment between cells, if the cells belong to the continuous configuration *,*,*,…∈ζ, then keep the current attitude; if the cells are discontinuous *,*,*,…∈ζ, then calculate the attitude rotation matrix R(α,β,γ) for dynamic adjustment.

[0024] As a further improvement of the present invention, in the step (4), the hybrid force control strategy includes the following steps:

[0025] When State B =0: Adopt the adaptive impedance control strategy and establish an impedance model:

[0026]

[0027] where: A(q) is the robot Jacobian matrix, C is the Coriolis / centrifugal torque vector, x∈R 3 is the Cartesian position vector of the end effector of the robotic arm, Λ=(AM -1 A T ) -1 is a (3*3) inertial transformation matrix of the end effector of the robotic arm, F g= A |T τ g , F f = A ||T τ f , F a = A ||T τ a is the force mapping matrix at the end, A || is the dynamically consistent generalized inverse matrix of matrix A;

[0028] When State B = 1: Enable force-position hybrid control, and the control model is as follows:

[0029]

[0030] where: q ∈ R n , n = 7 is the vector of joint variables, M(q) is the inertia matrix, is the vector of Coriolis / centrifugal torques, g(q) is the vector of gravitational torques, and τ is the control torque.

[0031] As a further improvement of the present invention, in the step (5), the multi-node sensing system includes three equally spaced force sensors arranged to record the contact force Each sensor node adopts an impedance control model:

[0032]

[0033] where: is the contact force at node i, e i = x i - x i 0 represents the generalized position of node i, and are the velocity and acceleration of node i respectively, and are the inertia, damping and stiffness parameters of node i respectively.

[0034] As a further improvement of the present invention, the multi-node sensing system introduces a virtual node c, and establishes a force coupling relationship through the following generalized variables:

[0035]

[0036] where: is a generalized non-linear monotonically decreasing function, w1 and w2 are weight coefficients. Due to the node position relationship, nodes 1 and 2 can share the attitude offset α, and node 3 and the virtual node share the offset β.

[0037] Adopting the technical solution of the present invention has the following beneficial effects:

[0038] (1) By discretizing the wall surface curve and the reference plane and extracting feature points, the inventor of the present invention realizes the secondary optimization of path interpolation, obtains the optimal grinding trajectory, significantly reduces path redundancy and improves grinding efficiency;

[0039] (2) The present invention uses the cell topology model to finely and continuously adjust the attitude of the end effector of the robotic arm, effectively avoiding over-cutting or under-cutting phenomena caused by attitude mismatch during the grinding process;

[0040] (3) The hybrid force control mode based on dynamic switching of force control states of the present invention can select an appropriate control mode according to the real-time height difference, and at the same time coordinate the motor speed and the movement speed, maintaining the consistency of the grinding surface while ensuring rapid material removal;

[0041] (4) The present invention establishes multi-node fusion attitude control, which can perform real-time attitude adjustment and force feedback control of the end effector of the robotic arm in a complex curved surface environment, reducing over-cutting and under-cutting that may be caused by position control grinding. Brief Description of the Drawings

[0042] Figure 1 is a schematic diagram of path planning and mesh parameterization of the present invention;

[0043] Figure 2 is a schematic diagram of the positional relationship of cells between the curved surface and the reference plane of the present invention;

[0044] Figure 3 is a schematic diagram of the cell splicing state of the attitude of the end effector of the robotic arm of the present invention;

[0045] Figure 4 is a schematic diagram of the sensor layout of the multi-node perception system of the present invention;

[0046] Figure 5 is a flowchart of the algorithm implementation of an example of the present invention;

[0047] Figure 6 is a schematic diagram of the positional relationship of three force sensors of the end effector of the robotic arm of the present invention. Detailed Embodiment

[0048] The following further describes the present invention in detail in conjunction with the drawings and specific embodiments:

[0049] The present invention provides a wall grinding method based on curved surface mapping trajectory optimization and multi-modal force control, including the following steps:

[0050] Step 1, determining the grinding trajectory through projection technology, realizing the calculation of interpolation points, the control of attitude change and its matching with position planning, and effectively generating a robot grinding path including grinding position, attitude, and force control strategy adjustment;

[0051] Step 2: A multi-modal fusion response hybrid force control algorithm based on radial height state switching introduces multi-node fusion attitude control to accurately track the contact force on the surface of the sanding disc and dynamically adjust the attitude of the robot end effector.

[0052] The robot grinding path planning in Step 1 includes the following steps:

[0053] Step 1-1: Perform secondary optimal path planning based on the curved surface modeling trajectory, search for the positions of trajectory interpolation points, determine the concave and convex positions on the wall surface, and obtain the optimal grinding trajectory.

[0054] Step 1-2: According to Step 1-1, further model the attitude of the robot end effector, optimize the contact problem between the end effector plane of the robotic arm and the curved surface, and dynamically adjust the attitude of the robot end effector.

[0055] Step 1-1 includes:

[0056] (1): Simplify the target curved surface: Decompose the curved surface to be ground into several cells, and project the curved surface S(x, y, z) to be ground and the reference plane P(x, y, z) onto the two-dimensional plane of the O-XY plane to obtain the two-dimensional curves S(x, z) and P(x, z).

[0057] (2): As shown in the attachment, discretize the path along the curve S(x, z) into N + 1 grid points as follows: Figure 1 0 =: s0, s1, s2... s

[0058] , s N-1 , s N : = s end

[0059] (3): Search for the path turning points of the protrusions and depressions on the wall surface according to the grid. The path points need to satisfy the following constraints:

[0060] Subject to:

[0061]

[0062] Where: e si The normal of curve S, Δ represents the upper tangent point of the curved surface and the plane, □ is the lower tangent point, ◇ is the downward intersection point, and ○ is the upward intersection point.

[0063] (4): Define the path segment types according to the combination of feature points: The protrusion segments are Δ-◇, Δ-Δ, ○-◇, ○-Δ, and the depression segments are ◇-□, ◇-○, □-○, □-□.

[0064] (5): Further, grid search feature points {□○Δ◇} are adopted for path planning. By analyzing the position information between path points, the raised and sunken areas on the workpiece surface are distinguished, and the height difference of the raised path segment in the z direction is analyzed. According to the change of the height difference, the states of grid points are further classified as follows:

[0065]

[0066] Among them: State B = 0, the radial distance between the surface to be polished and the reference plane is greater than 1.5 mm. When State B = 1, the radial distance is less than 1.5 mm. Different force control modes are adopted in different states to provide polishing signals for subsequent force control. B

[0067] (6): It is necessary to perform quadratic programming on the original modeling mapping trajectory S(x,z) to reduce the number of path segments and improve the efficiency of the polishing operation. Between the turning path point sets {□○Δ◇}, interpolation points s*a (s*a∈s a , a∈i) are constructed to divide the existing path segments. A continuously differentiable function Q(x,z) i is established between the interpolation points s*a, s j . a .

[0068] (7): In the domain of the function Q(x,z) a in step (6), m finite intervals are divided, and piecewise functions are constructed by different linear expressions in each interval. This function is topologized to the entire polishing path to obtain the generalized function Q(x,z).

[0069] (8): On the basis of step (7), the problem of optimizing the selection of interpolation points is transformed into the problem of minimizing the polishing removal area. The optimization model is as follows:

[0070]

[0071] (9) The simulated annealing algorithm is used to solve the optimal interpolation points s * between each raised path segment. For the sunken path segment, interpolation points s # are added in combination with the traditional linear interpolation method to ensure the smoothness of the end of the robotic arm during the contact with the surface to be polished. Further, the interpolation points s * , s # in the raised and sunken path segments and the path turning point s i information are fused to solve the optimal trajectory planning.

[0072] Step 1-2: Based on the optimal grinding trajectory in Step 1-1, optimize the posture of the end effector of the robotic arm. The specific steps are as follows:

[0073] (1): According to the analysis at the microscopic level of contact, the positional relationship between the curved surface and the reference plane can be divided into eight categories. As shown in the appendix, according to the grid division idea in Step 1-1, the curved surface is divided into several cells c Figure 2 and spliced to meet the grinding requirements, ensuring that the plane of the end effector of the robotic arm is in full contact with the curved surface to be ground or removing materials; i

[0074] (2): Define ζ as the set of all valid configurations, and M as the set of all reachable cells c i on the curved surface. The end posture is also represented by M because there is a one-to-one correspondence between it and the curved surface cells. The configuration D ∈ ζ can continuously execute tasks without changing the end posture, and there are countless non-overlapping configurations D in the set ζ.

[0075] (3): Further define {*,*,*,…} as the n-cell fusion cell. If it means the cells are discontinuous; conversely, if {,*,*,*,…} ∈ D, it means the cells are in a continuous state.

[0076] (4) According to Step (3), taking the example of covering a rectangular curved surface, as shown in the appendix Figure 3 only consider the splicing situation between two points m1, m2 ∈ M. For example, taking the initial cell c1, there are 4 cases where the cells are continuous and another 4 cases where the cells are continuous. The situations are as follows:

[0077]

[0078] (5) Further construct the topological configuration, whose elements are cells and the configuration is D. Each cell is assigned an index to record the possible configuration combinations. Since the number of cell types is limited, the configuration set {*,*,*,…} should also be limited. Therefore, there are only two possibilities for a curved surface at the generalized level: First, continuously execute tasks without changing the end posture; Second, continuously adjust the end posture according to the state of the configuration D during the execution of tasks to adapt to the changes of the curved surface, that is the set of, and the sorting of the set is as follows:

[0079]

[0080] (6) After establishing the topological configuration, according to the sorting of the set, search for the node cell c between and {*,*,*,…} ∈ D i ​Index for corresponding posture planning. Further, match the posture index with the position index, and map the end position and posture to the manipulator joint space to solve the trajectory planning.

[0081] Step 2 A multi-modal force control method based on radial height state switching includes the following steps:

[0082] Step 2-1: According to the radial height State of Step 1-1 B With different states, adjust the corresponding force control strategy, fuse the grinding motor speed, and quickly remove the surface material;

[0083] Since the adjustment of the end effector posture of the manipulator in Step 1-2 is only based on position control and lacks flexibility, and due to the complexity of the wall surface, the local plane B fitted by the end effector of the manipulator may intersect with the reference plane A in space. When in the grinding state State B = 1, if the working plane of the end effector of the manipulator remains parallel to the reference plane, problems such as jitter and undercut may occur;

[0084] Step 2-2: On the basis of the posture control of the end effector of the manipulator in Step 1-2, introduce a force feedback mechanism, construct a multi-node perception system with three equal intervals, and perform multi-node force fusion posture control;

[0085] The specific steps of Step 2-1 are as follows:

[0086] (1): Force control strategy deployment mechanism:

[0087] According to the state flag State of Step 1-1 B Switch the control strategy. When z > 1.5 mm, that is, State B = 0. The system switches to adaptive impedance control to optimize grinding by adjusting the contact impedance. At the same time, establish a coupling model between the motor speed and the radial height difference to achieve rapid removal of the surface material. When z < 1.5 mm, that is, State B = 0. The system switches to adaptive constant force control to keep the force applied to the wall within the desired range and ensure stable and efficient grinding effect;

[0088] (2): When State B = 0, perform adaptive impedance control. Consider the translational motion model of the robot's radial grinding as follows:

[0089]

[0090] Where: A(q) is the robot Jacobian matrix, C is the Coriolis / centrifugal torque vector, x ∈ R 3 is the Cartesian position vector of the end effector of the manipulator, Λ = (AM-1 A T ) -1 is a (3*3) inertial conversion matrix of the end effector of the robotic arm, F g = A |T τ g , F f = A ||T τ f , F a = A ||T τ a is the force mapping matrix at the end, and A || is the dynamically consistent generalized inverse matrix of matrix A;

[0091] (3): According to the dynamic response between the force on the end effector of the robotic arm and the position of the robotic arm, the robotic arm is compliant to grind to the desired position. The real-time displacement of the end effector of the robotic arm is as follows:

[0092]

[0093] where: K d and B d are appropriate inertial and damping matrices, which are positive definite and are usually set as constant diagonal matrices, x d , x e represent the desired position and the current position respectively, are the desired speed and the current speed.

[0094] (4): When State B = 1, during the contact process between the end effector of the robotic arm and the wall, position control in the horizontal direction needs to be implemented and force control considering its radial translation needs to be considered. The force-position hybrid control model is established as follows

[0095]

[0096] where: q ∈ R n , n = 7 is the vector of joint variables, M(q) is the inertial matrix, is the vector of Coriolis / centrifugal torques, g(q) is the vector of gravitational torques, and τ is the control torque.

[0097] (5) According to the radial height state switching of the trajectory planning in step 1-1, the force control strategy is switched in real time, and the grinding motor speed is fused to quickly remove the surface material to meet the requirements of the wall flatness.

[0098] According to step 2-1, the radial grinding force of the end effector of the robotic arm can be kept stable. However, due to the large working surface of the end effector of the robotic arm, only considering the regulation of the radial force cannot meet the grinding quality. Therefore, on the basis of step 2-1, the multi-node force fusion attitude control of step 2-2 is carried out to optimize the contact force on the working plane of the end effector of the robotic arm.

[0099] The specific steps of step 2-1 are as follows:

[0100] (1): As shown in the appendix Figure 4 , a multi-node sensing system is constructed by three equally spaced force sensors. Each sensor node adopts an impedance control model, which is described as a second-order linear system. The force-position relationship of node i can be expressed as

[0101]

[0102] Where: is the contact force at node i, e i =x i -x i 0 represents the generalized position of node i, and are the velocity and acceleration of node i respectively, and are the inertia, damping and stiffness parameters of node i respectively;

[0103] (2) Regard the end effector of the robotic arm as a single-degree-of-freedom system of the interaction between the object and the environment, and establish the mass motion equation:

[0104] (3) As shown in the appendix Figure 4 , introduce a virtual node c on the x-axis. In order to realize the fusion control of multiple nodes, establish the force coupling relationship between each node:

[0105]

[0106] Where: is a generalized non-linear monotonically decreasing function, w1 and w2 are weight coefficients. Due to the node position relationship, nodes 1 and 2 can share the attitude offset α, and node 3 and the virtual node share the offset β.

[0107] (4) Replace the generalized variable x with the attitude offsets α and β, and combine the impedance models of each node to obtain the entire surface contact dynamics system:

[0108]

[0109] Where: represent the required inertia, damping and stiffness matrices of each node respectively, The internal matrix relationship with Similarly, and There is a certain coupling relationship. The initial expected rotation angle deviations e α , e β , which is expressed as e α = α d - α0, e β = β d - β0.

[0110] The control strategy in Step 2-2 can achieve multi-node force fusion control of the end effector of the robotic arm, ensuring precise attitude adjustment and force feedback control in a complex environment. When the external force F ext is equal for each node in the dynamic system, the attitude adjustment process of the end effector of the robotic arm ends.

[0111] Next, in combination with the attached Figure 5 and specific implementation manners, the present invention will be further described in detail:

[0112] This example provides a wall grinding method based on curved surface mapping trajectory optimization and multi-modal force control. First, a smooth and efficient trajectory is obtained through interpolation point optimization, and then the end attitude is dynamically adjusted based on this trajectory, and the force control mode is dynamically switched. The specific implementation steps are as follows:

[0113] The first stage: constructing the optimal grinding path, including searching for interpolation points of the trajectory and marking concave and convex features, etc.

[0114] Step 1: Curved surface data acquisition and preprocessing

[0115] (1): Using a three-dimensional laser scanner with the model number LMS-Z420i to scan the wall surface at a spatial resolution of 1 mm to obtain a point cloud data set P = {p1(x1, y1, z1), p2(x2, y2, z2),..., p n (x n , y n , z n )};

[0116] (2): Using the ORPEF algorithm to perform plane search on the point cloud data to identify the reference plane P(x, y, z), and the fitting accuracy is better than 0.1 mm;

[0117] (3): Projecting the three-dimensional point cloud data onto the O-XZ plane to generate a two-dimensional curve S(x, z) and a reference curve P(x, z);

[0118] Step 2: Marking and classifying curve feature points

[0119] (1): Discretize the curve S(x, z) at equal intervals into 100 segments, forming 101 sampling points {s0, s1,..., s 100};

[0120] (2): Calculate the tangent vector V si and the normal vector e si , and mark four types of feature points: upper tangent point (Δ), lower tangent point (□), upward intersection point (○), downward intersection point (◇);

[0121] (3): Based on the combination of feature points, divide the convex segments (Δ-◇, Δ-Δ, ○-◇, ○-Δ) and concave segments (◇-□, ◇-○, □-○, □-□);

[0122] (4): Calculate the maximum radial height difference Δz_max of each path segment, and set the status flag:

[0123] State B = 1 when Δz_max ≤ 1.5 mm;

[0124] State B = 0 when Δz_max > 1.5 mm;

[0125] Step 3: Optimization of trajectory interpolation points

[0126] (1) Optimization of convex segments (State B = 0): Use the simulated annealing algorithm (initial temperature 1000, cooling coefficient 0.95) to search for the optimal interpolation point s*;

[0127] (2) The optimization objective is to minimize the function f(s*) = ∫|Q(x, z; s*) - P(x, z)| 2 dx;

[0128] (3) Record the optimal interpolation point s*_opt and generate a cubic spline interpolation curve;

[0129] (4): Optimization of concave segments - Set 3 equally spaced interpolation points s # _j = s_p + j·(s_q - s_p) / 4, j = 1, 2, 3, and use Catmull-Rom spline interpolation to construct a smooth path;

[0130] Step 4: Trajectory integrity - Verify and perform curvature continuity analysis to ensure that the curvature change rate at the feature points < 0.02 m -1 ·s -1 ;

[0131] Second stage: End pose adjustment based on the optimal grinding trajectory

[0132] Step 5: Divide the surface area passed by the optimal polishing trajectory into 10×10 regular grid cells, and calculate the normal vector \(n_{ij}\) at the center point of each cell \(c_{ij}\); assign a unique index \(D_{ij}=10\cdot(i - 1)+j\) to each cell for subsequent pose matching.

[0133] Step 6: Define the set of pose configurations \(\zeta=\{D1,D2,\cdots,D_m\}\), where each configuration represents a set of allowed poses, and calculate the included angle \(\theta_{ij}=\arccos(n_i\cdot n_j)\) between the normal vectors of adjacent cells.

[0134] Step 7: According to Steps 1 - 2, establish a continuity judgment criterion, and further construct the topological relation matrix \(T\) and the set of continuous regions \(\{C1,C2,\cdots,C_p\}\).

[0135] Step 8: Trajectory - pose mapping and switching point determination. Map the optimized trajectory \(Q(x,z)\) onto the surface cells to obtain a cell sequence \(\{c_1,c_2,\cdots,c_k\}\), and analyze the sequence of continuous regions \(S = [C_{s1},C_{s2},\cdots,C_{sq}]\) passed by the trajectory.

[0136] Step 9: For each pair of adjacent regions \((C_{sj},C_{s_{j + 1}})\), determine the optimal pose conversion point, and further use the spherical linear interpolation (SLERP) algorithm to perform continuous pose adjustment.

[0137] The third stage: Multi - modal force control with mixed modes and pose adjustment with multi - node fusion

[0138] Step 10: Based on the first and second stages, design the force control mode of the end - effector of the robotic arm according to the State B flag obtained in the trajectory planning: When State B changes from 0 to 1: impedance control → force - position hybrid control, when State B changes from 1 to 0: force - position hybrid control → impedance control;

[0139] Step 11: According to the State B state switching, adjust the radial force control of the end - effector of the robotic arm in real - time. At the same time, construct a multi - node force sensing system for the end - effector of the robotic arm:

[0140] (1): Uniformly set three force sensors (node 1 - b, node 2 - r, node 3 - l respectively) at the bottom of the end - effector of the robotic arm as shown in the appendix Figure 6 , and the three nodes form an equilateral triangle. Each sensor node is responsible for collecting the contact force signal at that point

[0141] (2): Establish a control strategy based on multi-node force fusion. Introduce a virtual node c on the x-axis in the grinding direction to coordinate the force coupling control of the three actual sensor nodes. The force coupling relationship between each node is modeled as follows:

[0142]

[0143] (3): During the control process, replace the generalized variable x with the attitude angle offsets α and β. Combine the impedance models of each sensor node to establish an overall surface contact dynamics model:

[0144]

[0145] The present invention proposes a multi-sensor fusion hybrid force control algorithm that optimizes the grinding trajectory through surface modeling and geometric mapping, combined with radial height state switching. On the one hand, it realizes the calculation of interpolation points, the control of attitude changes, and their matching with position planning, effectively generating a robot grinding path that includes grinding position, attitude, and force control strategy adjustment. On the other hand, it accurately tracks the surface contact force of the grinding disc, dynamically adjusts the attitude of the robot end, and real-time adjusts the grinding force to ensure a uniform effect, thus significantly improving the grinding efficiency and quality.

[0146] The above is only a preferred embodiment of the present invention, and it is not a limitation of the present invention in any other form. Any modification or equivalent change made according to the technical essence of the present invention still belongs to the scope protected by the present invention.

Claims

1. A method for optimizing curved surface mapping trajectory and multi-modal force control for complex wall surface grinding, characterized in that, Including the following steps: (1) Utilize the relative position relationship between the target surface S(x, y, z) and the reference plane P(x, y, z), simplify the surface area to the two-dimensional plane S(x, z) through projection technology, discretize the curve to generate grid points, and identify the set of feature points {Δ, □, ○, ◇}; (2) Define the path segment type according to the feature point combination, and classify the path segments into convex segments and concave segments; use the simulated annealing algorithm to optimize the interpolation point s for the convex path segment. * , add interpolation points s by linear interpolation method for the concave path segment # , generate the global optimal grinding trajectory Q(x,z) including the interpolation point and path turning point information; (3) According to the trajectory optimization result of step (2), based on cell division and splicing, design a continuous attitude adjustment model for the end effector of the robotic arm, and ensure effective contact between the end effector of the robotic arm and the surface through topological configuration planning; (4)Based on the path segment height state State in steps (2) and (3) B , the multi-modal force control method is adopted. When State B = 0, the adaptive impedance control is enabled. When State B = 1, the constant force control mode is enabled, and the movement speed of the end effector of the robotic arm and the rotation speed of the grinding motor are coordinated to achieve wall grinding under different force control modes; (5) On the basis of step (4), introduce a multi-node fusion attitude control method with a force feedback mechanism, construct a fusion attitude control through three equally spaced multi-node sensing systems, and further optimize the contact force distribution on the working plane of the end effector of the robotic arm.

2. A method for optimizing curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 1, characterized in that, In the step (1), the curve is discretized to generate grid points, and the curve S(x, z) is equally spaced into N + 1 grid points, in the form of: S(x, z) = {s0, s1,..., s N}; Extract the feature points {Δ, □, ○, ◇} from the grid points and classify them. Among them: Δ represents the upper tangent point of the surface and the reference plane; □ represents the lower tangent point of the surface and the reference plane; ○ and ◇ represent the upward intersection point and the downward intersection point respectively.

3. A method for optimizing curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 2, characterized in that, In path classification, the convex path segments include Δ-◇, Δ-Δ, ○-◇, ○-Δ, and the concave path segments include ◇-□, ◇-○, □-○, □-□; Judge the status flag State according to the radial height difference Δz of the path segment B : When State B = 0, the radial height difference is greater than 1.5 mm; when State B = 1, the radial height difference is less than or equal to 1.5 mm.

4. A method for optimizing the curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 1, characterized in that, In step (2), during the interpolation point optimization process, a quadratic interpolation plan is introduced for the convex path segment. The interpolation point optimization objective is to minimize the removal area of the grinding path, and the optimization objective function is: where Q(x, z) represents the path function generated by interpolation, s* represents the interpolation point, and the simulated annealing algorithm is used to solve the optimal interpolation point s*.

5. A method for optimizing the curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 1, characterized in that, In step (3), the attitude adjustment of the end effector of the robotic arm is planned based on the topological configuration of cell division, including the following steps: Decompose the target surface into a number of cells c i , and plan the attitude transitions between cells through the attitude configuration set ζ; according to the continuity judgment between cells, if the cells belong to continuous configurations *, *, / , … ∈ ζ, then maintain the current attitude; if the cells are discontinuous *, *, *, … ∈ ζ, then calculate the attitude rotation matrix R(α, β, γ) for dynamic adjustment.

6. A method for optimizing curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 1, characterized in that, In step (4), the hybrid force control strategy includes the following steps: When State B = 0: An adaptive impedance control strategy is adopted to establish an impedance model: where: A(q) is the robot Jacobian matrix, C is the Coriolis / centrifugal torque vector, x ∈ R 3 is the Cartesian position vector of the end-effector of the robotic arm, Λ = (AM -1 A T ) -1 is a (3*3) inertia transformation matrix of the end-effector of the robotic arm, F g = A |T τ g , F f = A ||T τ f , F a = A ||T τ a is the force mapping matrix at the end, A || is the dynamically consistent generalized inverse matrix of matrix A; When State B = 1: Enable the force-position hybrid control, and the control model is as follows: where: q ∈ R n , n = 7 is the vector of joint variables, M(q) is the inertia matrix, is the vector of Coriolis / centrifugal torques, g(q) is the vector of gravitational torques, and τ is the control torque.

7. A method for optimizing the curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 1, characterized in that, In the step (5), the multi-node sensing system includes three equally spaced force sensor arrangements that respectively record the contact forces. Each sensor node adopts an impedance control model: Wherein: is the contact force at node i, represents the generalized position of node i, and are the velocity and acceleration of node i respectively, and are the inertia, damping and stiffness parameters of node i respectively.

8. A method for optimizing curved surface mapping trajectory and multi-modal force control for complex wall surface grinding according to claim 7, characterized in that, The multi-node sensing system introduces a virtual node c and establishes a force coupling relationship through the following generalized variables: Wherein: is a generalized non-linear monotonically decreasing function, w1 and w2 are weight coefficients. Due to the node position relationship, nodes 1 and 2 can share the attitude offset α, and node 3 and the virtual node share the offset β.

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