A ball head adaptive positioning method based on impedance parameter optimization

Abstract

The application discloses a kind of ball head adaptive seat-in method based on impedance parameter optimization, comprising the following steps: S1: adaptive generation ball head seat-in process reference seat-in trajectory, and by actual contact force and reference trajectory deviation construct ball head seat-in impedance control model;S2: based on artificial fish school algorithm adjustment impedance parameter, adaptive setting and optimization impedance parameter;S3: based on model reference design adaptive impedance controller, the impedance parameter of decision calculation is adaptively corrected to automatically correct control action.The application has the advantages that: 1) adaptive seat-in can realize the active alignment of the positioner end to ball head position, reduce the stress condition in seat-in process;2) specific impedance controller is constructed to improve the robustness of ball head to unknown environment in seat-in process, ensure component pose accuracy and compliance.

Description

Technical Field

[0001] This invention relates to a ball head positioning technology, and more particularly to a ball head adaptive positioning method based on impedance parameter optimization, which is mainly used for ball head positioning of attitude adjustment positioners in automated aircraft assembly. Background Technology

[0002] Attitude adjustment mechanisms consisting of multiple CNC positioners and their end-cell ball joints are widely used in the digital assembly of aircraft components. The process of driving the positioners to accurately place the process ball joint, which is fixed to the aircraft component, into the end-cell ball joint is called ball joint positioning. To ensure the attitude adjustment accuracy of the component and to prevent changes in the relative positions of the ball joint and the end-cell ball joint after positioning, the fit clearance between the process ball joint and the end-cell ball joint is designed to be extremely small. In addition, excessive contact stress during positioning may damage the aircraft structure. The entire process should be carried out under low-stress conditions. Therefore, achieving accurate and smooth positioning of aircraft components is very difficult.

[0003] Currently, common ball joint positioning methods can be broadly categorized into passive positioning and active positioning. Based on the different methods of ball joint alignment, active positioning can be further divided into measurement-based positioning and adaptive positioning. Passive positioning uses a special mechanical structure to adjust the relative position of the ball joint and socket to release the forced contact stress caused by positional deviations. However, it suffers from poor self-stability, making it difficult to guarantee the stable support of the component by the adjustment mechanism during the posture adjustment process. Measurement-based positioning focuses on obtaining the accurate relative positional relationship between the ball joint and socket. However, it only considers the positional accuracy of the ball joint and socket fit, neglecting the compliance of the positioning process, making it difficult to guarantee the low contact stress requirement between the ball joint and socket. Unlike measurement-based positioning, which directly compensates for the relative positional deviation of the ball joint and socket, adaptive positioning achieves active alignment of the ball joint position at the end of the positioner by establishing a force-position coupling relationship between the drive system and the positioning system. Impedance control, by constructing a specific controller system with suitable impedance characteristics, achieves indirect dynamic control of the actuator's position and force.

[0004] To address the challenge of accurately and smoothly positioning the ball joints of large aircraft components, this invention proposes an adaptive ball joint positioning method based on impedance parameter optimization. An impedance control model for ball joint positioning is constructed using actual contact force and reference trajectory deviation, and the impedance parameters are optimized using an artificial fish swarm algorithm. To improve the robustness of the impedance controller in unknown environments, an adaptive impedance control method for ball joint positioning is further designed based on the model reference. Summary of the Invention

[0005] The purpose of this invention is to provide a ball head adaptive positioning technology based on sliding mode control to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution, comprising the following steps:

[0007] An adaptive ball-head positioning method based on impedance parameter optimization includes the following steps:

[0008] S1: Adaptively generate a reference positioning trajectory for the ball head positioning process, and construct an impedance control model for ball head positioning based on the actual contact force and the deviation of the reference trajectory;

[0009] S2: Adjusting impedance parameters based on artificial fish swarm algorithm, adaptively tuning and optimizing impedance parameters;

[0010] S3: Model reference design-based adaptive impedance controller, which adaptively corrects the impedance parameters calculated by the decision to automatically correct the control action.

[0011] Preferably, the reference positioning trajectory in step S1 is represented as follows:

[0012]

[0013] In the formula F X F Y F W These are the component forces in each direction of the ball head and ball socket contact, which can be acquired by a three-dimensional force sensor; v0 is the initial lifting velocity of the positioner; and t is time.

[0014] Preferably, the impedance control model in step S1 can be expressed as:

[0015] M d (X″-X″ d )+B d (X′-X′ d )+K d (XX d ) = F e -F d

[0016] F e =B e (X′-X′ e )+K e (XX e )

[0017] Where M d B d and M d These represent the inertia matrix, damping matrix, and stiffness matrix of the target impedance model, respectively, and X represents the actual trajectory of the positioner's end effector. d For the reference motion trajectory of the positioner end, F e F is the actual contact force between the ball socket and the ball head at the end of the locator. d X represents the desired force between the ball joint and the ball head at the end of the locator; eFor environmental location, B e For environmental equivalent damping, K e This refers to the environmental equivalent stiffness.

[0018] The expression for the target impedance model along any coordinate axis in the Cartesian coordinate system is:

[0019] m d (x″-x″ d )+b d (x′-x′ d )+k d (xx d )=f e -f d

[0020] f e =b e (x′-X′ e )+k e (xx e )

[0021] Let ΔX = XX d , representing the position change at the actuator end, which is also the correction amount of the actuator output trajectory after applying the ideal impedance model. Furthermore, performing a Laplace transform on the impedance control model yields its expression in the frequency domain:

[0022]

[0023] Preferably, the process of optimizing impedance control parameters using the artificial fish swarm algorithm in step S2 is as follows:

[0024] 4.1 Parameter initialization, m d b d and k d Let N be the inertia matrix, damping matrix, and stiffness matrix of the target impedance model, respectively. Let the size of the artificial fish swarm be N, with a range of [m...]. d1 m d2 ]、[b d1 b d2 ] and [k d1 k d2 This generates a 3x3 array of initial parameters, where each column represents three parameters to be optimized for an artificial fish.

[0025] 4.2 Foraging behavior, i.e., the parameter fine-tuning stage, setting the current state of the artificial fish to X. i =[m di b di k di ], m di b di k di They are respectively brick, bd and k d Given the parameters of the current state, let the artificial fish's activity radius be R and its activity step size be d. Within this range, randomly select a state X. i And calculate the corresponding food concentration Y. i Determine whether the moving condition is met. After trying no more than M times, if the moving condition is still not met, move one step randomly according to the activity step size d.

[0026] 4.3 includes two parameter comparison stages:

[0027] 4.3.1 Clustering behavior, setting the current state of the artificial fish to X i Explore the number of partners n in the current field f and center position X c =[m dc b dc k dc If Y c / n f >δY i If the artificial fish companion center has sufficient food and is not too crowded, then move one step towards the companion center; otherwise, perform the foraging behavior in section 4.2, where δ is the crowding factor, set to P.

[0028] 4.3.2 Tail-end collision behavior: Set the current state of the artificial fish to X. i Explore the number of partners n in the current field f And among the partners, the largest partner X j If Y j / n f >δY i This indicates that partner X j If the state has a high food concentration and is not too crowded around it, then it will move towards its partner X. j If the direction is not specified, move forward one step; otherwise, execute 4.2 foraging behavior, where δ is the crowding factor, set to Q.

[0029] 4.4 Determine the next adjustment direction for the parameters. Compare the results of 4.3.1 and 4.3.2, output the parameter with the higher food concentration, and repeat steps 4.2 and 4.3, with the number of iterations not exceeding L.

[0030] Preferably, the adaptive impedance controller in step S3 is expressed as follows:

[0031]

[0032] In the formula, e(t) is the force error in a certain degree of freedom direction, p(t) is the time-varying adaptive proportional force feedback coefficient, d(t) is the time-varying adaptive differential force feedback coefficient, g(t) is the auxiliary function term related to e(t) and e(t)′; σ0, σ1, σ2, and σ' are correction factors and are all small positive numbers. Attached Figure Description

[0033] Figure 1 Composition of the ball head positioning system;

[0034] Figure 2 Ball head insertion impedance control model;

[0035] Figure 3 The model reference adaptive impedance control system consists of [the following components]. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] An adaptive ball-head positioning method based on impedance parameter optimization includes the following steps:

[0038] S1: Adaptively generate a reference positioning trajectory for the ball head positioning process, and construct an impedance control model for ball head positioning based on the actual contact force and the deviation of the reference trajectory;

[0039] S2: Adjusting impedance parameters based on artificial fish swarm algorithm, adaptively tuning and optimizing impedance parameters;

[0040] S3: Model reference design-based adaptive impedance controller, which adaptively corrects the impedance parameters calculated by the decision to automatically correct the control action.

[0041] The reference positioning trajectory in step S1 is represented as follows:

[0042]

[0043] In the formula F X F Y F W These are the component forces in each direction of the ball head and ball socket contact, which can be acquired by a three-dimensional force sensor; v0 is the initial lifting velocity of the positioner; and t is time.

[0044] The impedance control model in step S1 is as follows: Figure 2 As shown, it can be represented as:

[0045] M d (X″-X″ d )+B d (X′-X′ d )+K d (XX d ) = F e -F d

[0046] F e =B e (X′-X′ e )+K e (XX e )

[0047] Where M d B d and M d These represent the inertia matrix, damping matrix, and stiffness matrix of the target impedance model, respectively, and X represents the actual trajectory of the positioner's end effector. d For the reference motion trajectory of the positioner end, F e F is the actual contact force between the ball socket and the ball head at the end of the locator. d X represents the desired force between the ball joint and the ball head at the end of the locator; e For environmental location, B e For environmental equivalent damping, K e This refers to the environmental equivalent stiffness.

[0048] The expression for the target impedance model along any coordinate axis in the Cartesian coordinate system is:

[0049] m d (x″-x″ d )+b d (x′-x′ d )+k d (xx d )=f e -f d

[0050] f e =b e (x′-x′ e )+k e (xx e )

[0051] Let ΔX = XX d , representing the position change at the actuator end, which is also the correction amount of the actuator output trajectory after applying the ideal impedance model. Furthermore, performing a Laplace transform on the impedance control model yields its expression in the frequency domain:

[0052]

[0053] The impedance control described above can better adapt the actuator end effector to the current contact environment by adjusting the target impedance parameters. A better combination of parameters often leads to better impedance control. However, in practical applications, the optimization of impedance parameters is a complex multi-objective coupled problem, and the global optimal solution for multiple parameters cannot be obtained by relying on experience or simple experimental predictions.

[0054] The artificial fish swarm algorithm is a swarm intelligence algorithm based on natural phenomena, used to solve for global optima. Its core principle is global optimization of the swarm. This invention combines the model of simulating fish swarm search with traditional optimization techniques, and has the advantages of adaptive, unsupervised search and fast convergence. It can be used for parameter tuning and optimization of impedance control.

[0055] The process of optimizing impedance control parameters using the artificial fish swarm algorithm in step S2 is as follows:

[0056] 4.1 Parameter initialization, m d b d and k d Let be the inertia matrix, damping matrix, and stiffness matrix of the target impedance model, respectively. Let the size of the artificial fish swarm be N, where N is set to 100, and the range be [m]. d1 m d2 ]、[b d1 b d2 ] and [k d1 k d2 This generates a 3x3 array of initial parameters, where each column represents three parameters to be optimized for an artificial fish.

[0057] 4.2 Foraging behavior, i.e., the parameter fine-tuning stage, setting the current state of the artificial fish to X. i =[m di b di k di ], m di b di k di They are m d b d and k d Given the parameters of the current state, let the artificial fish's activity radius be R and its activity step size be d. Within this range, randomly select a state X. i And calculate the corresponding food concentration Y. i Determine whether the moving condition is met. After trying no more than 50 times, if the moving condition is still not met, move one step randomly according to the activity step size d.

[0058] 4.3 includes two parameter comparison stages:

[0059] 4.3.1 Clustering behavior, setting the current state of the artificial fish to Xi Explore the number of partners n in the current field f and center position X c =[m dc b dc k dc If Y c / n f >δY i If the artificial fish companion center has sufficient food and is not too crowded, then move one step towards the companion center; otherwise, perform the foraging behavior in section 4.2, where δ is the crowding factor, set to 90.

[0060] 4.3.2 Tail-end collision behavior: Set the current state of the artificial fish to X. i Explore the number of partners n in the current field f And Y among the partners j Biggest Partner X j If Y j / n f >δY i This indicates that partner X j If the state has a high food concentration and is not too crowded around it, then it will move towards its partner X. j If the direction is not specified, move forward one step; otherwise, execute 4.2 foraging behavior, where δ is the crowding factor, set to 50.

[0061] 4.4 Determine the direction of parameter adjustment for the next step. Compare the results of 4.3.1 and 4.3.2, output the parameter with the higher food concentration, and repeat steps 4.2 and 4.3, with the number of iterations not exceeding 500.

[0062] Using the artificial fish swarm algorithm for offline tuning of impedance control parameters can achieve good impedance control results. However, conventional impedance control does not consider the impact of changes in environmental parameters on the stability and response characteristics of the impedance system. Therefore, further steady-state error and dynamic performance analysis of the designed target impedance model is required.

[0063] Considering a target impedance control model in a single direction in Cartesian coordinates, when the actuator end contacts the environment, the environmental dynamics equation f e =b e (x′-x′ e )+k e (xx e ) get: k e x+b e x′=f e +k e x e +b e x′ e Furthermore, the expression for the actual trajectory of the actuator end effector can be obtained as follows:

[0064]

[0065] The reference trajectory x is typically planned. d It is a constant, i.e., x d =x d Since ′=0, substituting the above equation into the target impedance control model M d (X″-X″ d )+B d (X′-X′ d )+K d (XX d ) = F e -F d We can obtain:

[0066]

[0067] Expected contact force f d It is a constant value, i.e., f d "=f d When the actuator end is in contact with the environment and in a stable state, the difference e between the expected contact force and the actual contact force is a constant, i.e., e″ = e′ = 0. Therefore, from the above formula, the steady-state error of the contact force of the target impedance model is:

[0068]

[0069] It can be seen that the steady-state error of the contact force in the target impedance model is affected by the environmental parameter k. e and environmental location x e The effect is that if the stiffness or position of the environment changes during the interaction between the actuator end and the environment, the steady-state characteristics of the target impedance system will also be disrupted.

[0070] In actual placement, it is difficult to accurately estimate environmental parameters and location. When the drive positioner contacts the process ball joint at its end, the position of the hoisted component is difficult to maintain. This means that environmental parameters may change during ball joint placement, thereby compromising the stability and response characteristics of the designed target impedance system. To address this issue, this invention proposes a model reference design-based adaptive impedance controller. This controller identifies changes in contact environmental conditions online, makes decisions based on the identified impedance system state and pre-defined reference model criteria, and adaptively corrects the impedance parameters calculated from the decisions to automatically adjust the control action. The composition of the model reference adaptive impedance control system is as follows: Figure 3 As shown.

[0071] The basic principle of model reference adaptive control is: based on the structure of the controlled object and the specific control performance requirements, a reference model is designed to make its output y... mExpress the desired response of the adjustable system to the desired input r; then, in each control cycle, express the reference model output y. m Subtracting the output y of the controlled object directly yields the generalized error signal e = y. m -y, the adaptive mechanism modifies the adjustable impedance controller parameters using the generalized error signal and the target impedance output u according to certain criteria, that is, it generates an adaptive control law that makes e tend to 0, that is, it makes the actual output of the object approach the output of the reference model, and finally achieves consistency.

[0072] During the contact process between the ball head and the ball socket, the spatial position of the end of the positioner is the main reference input of the positioning control system. This invention considers the adaptive controller as adding a spatial position correction Δx′ to the original correction of the standard impedance controller. Therefore, the position input of the motion control system can be expressed as: x r =x d +Δx+Δx′, where x r This refers to the position input of the motion control system. The position correction Δx′ provided by the adaptive controller can be obtained by referring to the position-based adaptive impedance control method, and its expression is: Δx′=p(t)e(t)+d(t)e(t)′+g(t), where e(t) is the force error in a certain degree of freedom direction, p(t) is the time-varying adaptive proportional force feedback coefficient, d(t) is the time-varying adaptive differential force feedback coefficient, and g(t) is an auxiliary function term related to e(t) and e(t)′.

[0073] In the specific implementation of the adaptive algorithm, the system input of the ideal reference model can be set to 0, and the system state variable e can also be set to 0. Considering the continuity of the system output, the adjustment rules of the coefficients p(t), d(t), and g(t) can be obtained:

[0074]

[0075] During the component insertion process, the desired contact force between the ball head and the socket should be as small as possible, so the desired contact force f is... d Taking zero, and simultaneously using the σ-correction method to compensate for the influence of the lack of a dynamic model, the new control law is:

[0076]

[0077] Where σ0, σ1, σ2, and complement are correction factors and are all small positive numbers. Substituting the above equation into the control quantity of Δx′=p(t)e(t)+d(t)e(t)′+g(t) yields the final adaptive impedance control term.

[0078] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A ball head adaptive docking method based on impedance parameter optimization, characterized in that, The method comprises the following steps: S1: adaptively generating a reference entry trajectory for a ball head entry process, and constructing an impedance control model for the ball head entry based on actual contact force and deviation of the reference trajectory; S2: adjusting impedance parameters based on an artificial fish swarm algorithm, and adaptively setting and optimizing the impedance parameters; S3: automatically correcting control actions by adaptively correcting the impedance parameters calculated by decision-making based on a model reference adaptive impedance controller; The reference entry trajectory in the step S1 is expressed as: In the formula F X F Y F W These are the component forces in each direction of the ball head and ball socket contact, which can be acquired by a three-dimensional force sensor; v0 is the initial lifting velocity of the positioner; t is time. The impedance control model in the step S1 can be expressed as: M d (X"-X d ") + B d (X'-X d ') + K d (X-X d ) = F e -F d F e = B e (X' - X e ') + K e (X - X e ) where M d , B d and K d are the inertia, damping and stiffness matrices of the target impedance model, X is the actual motion trajectory of the manipulator end-effector, X d is the reference motion trajectory of the manipulator end-effector, F e is the actual contact force between the ball and the socket of the manipulator end-effector, F d is the desired contact force between the ball and the socket of the manipulator end-effector; X e is the environment position, B e is the environment equivalent damping, and K e is the environment equivalent stiffness. The expression of the target impedance model in any coordinate axis direction of the Cartesian coordinate system is: m d (x″-x′ d ′)+b d (x′-x′ d )+k d (x-x d )=f e -f d f e = b e (x' - x e ') + k e (x - x e ) Let ΔX = X - X d , which represents the position change of the actuator end, i.e. the trajectory correction amount of the actuator output after the impedance model is managed, and the impedance control model is subjected to Laplace transformation to obtain an expression in the frequency domain range as follows: The process of the artificial fish swarm algorithm for optimizing the impedance control parameters in the step S2 is as follows: 4.1 Parameter initialization, m d , b d and k d are the inertia matrix, damping matrix and stiffness matrix of the target impedance model, respectively, the artificial fish swarm size is set to N, and the ranges are [m d1 , m d2 ], [b d1 , b d2 ] and [k d1 , k d2 ], respectively, to generate an initial parameter array of 3 rows and 3 columns, each row representing three parameters of an artificial fish to be optimized; 4.2 Foraging behavior, i.e., the parameter fine-tuning stage, setting the current state of the artificial fish to X. i =[m di ,b di ,k di ], m di ,b di ,k di They are m d b d and k d Given the parameters of the current state, let the artificial fish's activity radius be R and its activity step size be d. Within this range, randomly select a state X. i And calculate the corresponding food concentration Y. i Determine whether the moving condition is met. After trying no more than M times, if the moving condition is still not met, move one step randomly according to the activity step size d. 4.3 comprising two parameter comparison stages: 4.3.1 Schooling behavior, set the current state of artificial fish as X i , explore the number of partners n in the current field f and the center position X c = [m dc , b dc , k dc ], if Y c / n f > δY i , it means that there are more food and less crowded in the center of the artificial fish partners, then move forward to the center position of the partners, otherwise execute 4.2 foraging behavior, where δ is the crowding factor, set to P; 4.3.2 Following behavior, set the current state of artificial fish as X i , explore the number of partners n in the current field f and the largest partner X among Y j partners j , if Y j / n f > δY i , it indicates that the state of partner X j has a higher food concentration and its surroundings is less crowded, then move one step forward in the direction of partner X j , otherwise execute 4.2 foraging behavior, where δ is the crowding factor, set as Q; 4.4 determining the next adjustment direction of the parameters, comparing the results of 4.3.1 and 4.3.2, outputting the parameter corresponding to the larger food concentration, and repeating steps 4.2 and 4.3, Wherein the iteration number is not more than L times.

2. The impedance parameter optimization based ball seating adaptive method of claim 1, wherein, The expression form of the adaptive impedance controller in the step S3 is: In the formula, e(t) is the force error in a certain degree of freedom direction, p(t) is a time-varying adaptive proportional force feedback coefficient, d(t) is a time-varying adaptive differential force feedback coefficient, g(t) is an auxiliary function item related to e(t) and e(t)', and σ0, σ1 and σ2 are correction factors and are all small positive numbers.

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