Adaptive admittance control method combined with iterative learning control

Abstract

The invention provides a self-adaptive admittance control method combined with iterative learning control. The mechanical arm control system is divided into inner and outer rings; an outer ring adopts a self-adaptive admittance control strategy, parameters of an admittance controller are dynamically adjusted, the uncertainty and dynamic change of the environment are compensated, and force tracking is achieved; iterative learning control is adopted in an inner ring, the problems of random non-repetitive interference in the interaction process of the mechanical arm and the environment and uncertainty of a dynamical model are solved, and position tracking is achieved. Meanwhile, an improved whale predation algorithm is adopted, iterative learning parameters are optimized, the convergence speed and tracking precision of the algorithm are improved, and the system achieves a good position tracking effect. Finally, the flexibility of the mechanical arm is guaranteed, and meanwhile control over the mechanical arm is achieved safely and efficiently.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm control and relates to an adaptive admittance control method that combines iterative learning control. Background Technology

[0002] With the rapid development of industrial automation and robotics, the demand for robotic arms in precision assembly, flexible manufacturing, and human-robot collaboration is increasing. However, when robotic arms interact with dynamic, unstructured environments, they often face problems such as random, non-repetitive disturbances, uncertainties in dynamic models, and abrupt changes in contact forces, leading to instability in the robotic arm system and making it difficult to complete high-precision trajectory tasks.

[0003] Currently, the main control methods for robotic arms include PID control, admittance control, sliding mode control, and adaptive control. While these methods can solve some problems to a certain extent, they still have many shortcomings. PID control is simple in structure and easy to implement, but its fixed gain parameters are difficult to adapt to dynamic changes in complex interactive tasks, especially when there are sudden changes in contact force or uncertain environmental stiffness, which can easily lead to overshoot or oscillation. Admittance control achieves compliant interaction by adjusting the impedance characteristics of the robotic arm, but its performance is highly dependent on parameter selection. Traditional admittance controllers use fixed parameters and cannot adapt to dynamic environmental changes, resulting in increased force tracking errors or lag in the robotic arm's response. In general, traditional control methods have significant shortcomings in terms of trajectory tracking accuracy, compliance, and anti-interference capabilities.

[0004] To address the aforementioned problems, this invention proposes a composite strategy integrating adaptive admittance control and iterative learning control. This strategy combines intelligent optimization algorithms to achieve efficient parameter optimization, thereby enabling high-precision trajectory tracking and compliant interaction in dynamic environments. This invention optimizes ILC parameters through intelligent algorithms and designs a dynamic admittance compensation mechanism, aiming to overcome the performance bottlenecks of traditional methods and provide a more efficient and robust control solution for robotic arms. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive admittance control method that combines iterative learning control to solve problems such as random non-repetitive disturbances and uncertainties in the dynamic model during the interaction of the robotic arm with the environment, thereby achieving high-precision trajectory tracking and giving the robotic arm good compliance.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An adaptive admittance control method combining iterative learning control comprises the following steps:

[0008] Step 1: Establish the kinematic model of the robot arm with n degrees of freedom in the Cartesian coordinate system based on the DH rule; establish the dynamic model of the robot arm with n degrees of freedom in the Cartesian coordinate system based on the Lagrange method;

[0009] Step 2: Design inner and outer loop control strategies. The outer loop adopts an adaptive admittance control strategy to dynamically adjust the admittance controller parameters, compensate for environmental uncertainties and dynamic changes, and achieve force tracking.

[0010] Step 3: The inner loop adopts adaptive iterative learning control, which uses prior data from iterative learning control to update the current control input until complete compensation is achieved. This addresses the random non-repetitive disturbances and uncertainties in the dynamic model during the robot arm's interaction with the environment, thus enabling position tracking.

[0011] Step 4: Adopt an improved whale predation algorithm, optimize the iterative learning parameters, improve the convergence speed and tracking accuracy of the algorithm, and enable the system to achieve better position tracking results.

[0012] In step 1, to achieve compliant interaction between the robotic arm and the unstructured environment and to describe the physical information such as the dynamic model and control variables of the interaction system, the kinematic and dynamic equations of the n-degree-of-freedom robotic arm in Cartesian space are established based on the DH rule and the Lagrange method, as follows:

[0013]

[0014] Where, x(t), and Let ψ(q) represent the position, velocity, and acceleration of the robotic arm's end effector in Cartesian coordinates; ψ(q) is the kinematic model of the robotic arm; q∈R n×n The angle vector in the joint space of the robotic arm. and Let J(q) represent the angular velocity and angular acceleration of the robotic arm in joint space, respectively; J(q)∈R m×n Let be the Jacobian matrix of the robotic arm, obtained by taking the partial derivative of ψ(q);

[0015] The dynamics formula for the robotic arm is as follows:

[0016]

[0017] Where M(q)∈R n×n It is an inertial diagonal matrix. Let G(q) ∈ R be the Coriolis and Oswald force matrices. n ×n Let R be the gravity vector matrix, τ∈R n×n The torque vector is the input for the control of the robotic arm;

[0018] In step 2, to ensure the tracking error of the interactive force converges to zero, a dynamic compensation term is designed in the outer loop to adaptively adjust the impedance parameter to compensate for the time-varying error in the dynamic compensation system. When the interactive force increases, it indicates a larger intention error. The robotic arm can increase its compliance by reducing its own impedance parameter and compensating for the position error. The controller is as follows:

[0019]

[0020] Where Δb(t) is the damping parameter compensation; φ(t) is the adaptive law of the admittance controller; T is the sampling period; and α is the adaptive law coefficient.

[0021] The outer loop input is the desired position, and the output serves as the ideal input for the inner loop intelligent iterative learning control. The inner loop involves inverse kinematics of the robotic arm, iterative learning controller, and robotic arm model. Position feedback is used to convert the error e = q... d -q k The input is an iterative learning controller. Through continuous iteration, the error tends to zero, resulting in good compliance of the robotic arm when interacting with the environment.

[0022] In step 3, to ensure position tracking when the robotic arm interacts with the environment, considering the random non-repetitive disturbances and uncertainties in the dynamic model when the robotic arm interacts with the environment, the inner loop is designed to adopt adaptive iterative learning control, which updates the current control input by referencing prior data, and achieves high-precision tracking of the given desired trajectory of the unknown object's actual running trajectory within a given time range.

[0023] Consider the dynamics model of an n-DOF robotic arm with random non-repetitive disturbances and uncertainties, as shown in the following formula:

[0024]

[0025] Where t is time, t∈[0,T]; k is the number of iterations; ΔM, ΔC, and ΔG are the compensation terms for the uncertain parts of M, C, and G, respectively; τ k ∈R n To control the torque; τ dk ∈R n This refers to random, non-repeating disturbances in the system.

[0026] The following conditions must be met during the iteration process:

[0027] During the iteration process, the initial state of the system at each run is on the initial state corresponding to the desired trajectory, i.e., the initial condition is satisfied:

[0028] x k (0)=x d (0), k = 0, 1, 2, ...

[0029] The adaptive iterative learning control law is designed as follows:

[0030]

[0031] Among them, K P K D ∈R n×n For PID parameters; δ k The independent variable of the iteration term is a function of time; γ is the gain coefficient of the nonlinear control term. The hyperbolic tangent function is used to limit the amplitude of the control input; λ is the adaptive parameter; sgn is the floor function.

[0032] Consider the dynamic coupling relationship between the damping parameter compensation Δb of the outer loop admittance control and the gain coefficient γ of the inner loop iterative learning. When the outer loop detects an increase in force tracking error, it not only adjusts the admittance parameter but also adjusts the learning rate of the inner loop in real time through the coupling factor to enhance the system's responsiveness to dynamic environments. The formula is as follows:

[0033] Δb(k)=α*γ(k)+β*(F d -F e )

[0034] γ(k+1)=γ(k)+η*((X r -X d )+λ*Δb(k));

[0035] Where α, β, η, and λ are coupling coefficients, which can be calibrated experimentally.

[0036] In step 4, for the n-DOF robotic arm, an adaptive iterative learning control algorithm based on intelligent algorithm optimization is adopted, and the steps are as follows:

[0037] Step A1: Set the optimization variable dimensions, parameter upper and lower limits, population size, and maximum number of iterations. Generate an initial population within the feasible region through uniform random sampling, and call the fitness function to calculate the error corresponding to each solution, recording the initial optimal solution.

[0038] Step A2: In each iteration, using the current optimal solution as the center, and combining the prey's movement range and the iteration decay factor, multiple candidate solutions are generated through Gaussian perturbation. The Monte Carlo method is used to simulate the prey's escape behavior within its maximum movement range, ensuring sufficient exploration of the local neighborhood. The fitness values ​​of the candidate solutions are calculated, and the optimal candidate solution is selected. If its fitness is better than the historical best value, the global optimal solution is updated. The formula for generating prey candidate positions is as follows:

[0039]

[0040] d = pdist(best, x)

[0041] Where x is the newly generated candidate position of the prey, x best represents the current optimal position of the prey, det is the iteration number, ii is the current iteration number, rand represents the random direction; z is the haste coefficient, which decreases as the distance increases, limiting the prey's movement range, and d represents the distance between the calculated current optimal solution and the individual.

[0042] Step A3: Using the current optimal solution as an attractor, update the position using a linear combination; introduce Gaussian noise to enhance global search capability. After the update, truncate out-of-bounds parameters to ensure the solution remains within the feasible region and approximates the optimal solution. Merge the current population with candidate solutions, sort them by fitness value, and retain the best individuals for the next generation to avoid losing high-quality solutions while maintaining population diversity.

[0043] Step A4: Record the optimal fitness value for each generation, and finally output the global optimal parameter combination and minimum error value to complete the automatic tuning of controller parameters.

[0044] In step 2, design the inner and outer loop control strategies for the robotic arm; the admittance control of the outer loop will be based on the environmental force F. d ,F ext Generate position correction amount X r Position correction amount X r The expected input X as the inner loop d The inner loop uses iterative learning control combined with intelligent algorithms to track and correct the position X. d and the actual position X r Feedback is sent to the outer loop, forming a closed loop.

[0045] During step 3, the damping parameter compensation Δb of the outer loop admittance control and the gain coefficient γ of the inner loop iterative learning are correlated through a dynamic coupling factor. When the outer loop detects an increase in force tracking error, it not only adjusts the admittance parameter but also adjusts the learning rate of the inner loop in real time through the coupling factor to enhance the system's responsiveness to dynamic environments. The formula is as follows:

[0046] Δb(k)=α*γ(k)+β*(F d -F e )

[0047] γ(k+1)=γ(k)+η*((X r -X d )+λ*Δb(k))

[0048] Where α, β, η, and λ are coupling coefficients, which can be calibrated experimentally.

[0049] In step 3, an improved whale algorithm is used to optimize the iterative learning control parameters to minimize errors in trajectory tracking. In each iteration, multiple candidate solutions are generated using Gaussian perturbation, centered on the current optimal solution and considering the prey's movement range and iteration decay factor. A Monte Carlo method is used to simulate the prey's escape behavior within its maximum range, ensuring thorough exploration of the local neighborhood. Furthermore, the position is updated using a linear combination with the current optimal solution as an attractor. Gaussian noise is introduced to enhance global search capabilities. After updating, out-of-bounds parameters are truncated to ensure the solution remains within the feasible region and approximates the optimal solution. The current population and candidate solutions are merged, sorted by fitness value, and the best individuals are retained for the next generation to avoid losing high-quality solutions while maintaining population diversity. The optimal fitness value for each generation is recorded, and finally, the globally optimal parameter combination and minimum error value are output, completing the automated tuning of the controller parameters.

[0050] When performing step 4, a prey agitation coefficient and a speed adjustment mechanism are introduced into the algorithm;

[0051] The principle of the impatience coefficient is: the farther the prey is from the hunter, the smaller the coefficient is, and the smaller the range of movement of the prey. This allows the hunter to traverse as much as possible. When the hunter approaches the prey, the range of movement of the prey will also increase. If the optimal point is not found, it can also jump out of the local optimum and reduce the probability of the local optimum.

[0052]

[0053] d = pdist(best, x);

[0054] Where x is the newly generated candidate position of the prey, Mc is the range of movement of the prey; z is the agitation coefficient, which decreases as the distance increases, limiting the range of movement of the prey; and d represents the distance between the calculated current optimal solution and the individual.

[0055] Speed ​​adjustment mechanism: The number of orbits is dynamically adjusted through an adaptive coefficient. When the distance to the optimum is far, the movement speed is limited to avoid skipping the potential optimum region; when the distance is close, the convergence speed is accelerated. The displacement speed is controlled by the number of orbits. The adjustment mechanism of the number of orbits k is as follows:

[0056]

[0057] Where k is the number of revolutions;

[0058] Using polar coordinates and random angle offsets, spiral approximation and multi-directional exploration are achieved.

[0059] The beneficial effects of this invention are as follows:

[0060] This invention discloses an adaptive admittance control method combining iterative learning control. The robotic arm control system is divided into inner and outer loops. The outer loop employs an adaptive admittance control strategy to dynamically adjust the admittance controller parameters, compensate for environmental uncertainties and dynamic changes, and achieve force tracking. The inner loop employs iterative learning control to handle random non-repetitive disturbances and uncertainties in the dynamic model during the robotic arm's interaction with the environment, achieving position tracking. Simultaneously, an improved whale predation algorithm is used to optimize the iterative learning parameters, improving the algorithm's convergence speed and tracking accuracy, enabling the system to achieve better position tracking performance. Ultimately, this method ensures the robotic arm's compliance while achieving safe and efficient control. Attached Figure Description

[0061] Figure 1 The overall block diagram of adaptive admittance control combined with iterative learning control.

[0062] Figure 2 To improve the flowchart of the whale algorithm.

[0063] Figure 3 This is a control block diagram for iterative learning based on the improved whale algorithm.

[0064] Figure 4 This is a diagram showing the results of iterative learning for position and velocity tracking based on the improved whale algorithm. Detailed Implementation Plan

[0065] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0066] like Figure 1-4 An adaptive admittance control method combining iterative learning control is shown, comprising the following steps:

[0067] Step 1: Establish the kinematic model of the robot arm with n degrees of freedom in the Cartesian coordinate system based on the DH rule; establish the dynamic model of the robot arm with n degrees of freedom in the Cartesian coordinate system based on the Lagrange method;

[0068] Step 2: Design inner and outer loop control strategies. The outer loop adopts an adaptive admittance control strategy to dynamically adjust the admittance controller parameters, compensate for environmental uncertainties and dynamic changes, and achieve force tracking.

[0069] Step 3: The inner loop adopts adaptive iterative learning control, which uses prior data from iterative learning control to update the current control input until complete compensation is achieved. This addresses the random non-repetitive disturbances and uncertainties in the dynamic model during the robot arm's interaction with the environment, thus enabling position tracking.

[0070] Step 4: Adopt an improved whale predation algorithm, optimize the iterative learning parameters, improve the convergence speed and tracking accuracy of the algorithm, and enable the system to achieve better position tracking results.

[0071] Preferably, when performing step 1, a kinematic model of the n-degree-of-freedom manipulator in the Cartesian coordinate system is established based on the DH rule, as shown in the following formula:

[0072]

[0073] Where, x(t), and Let ψ(q) represent the position, velocity, and acceleration of the robotic arm's end effector in Cartesian coordinates; ψ(q) is the kinematic model of the robotic arm; q∈R n×n The angle vector in the joint space of the robotic arm. and Let J(q) represent the angular velocity and angular acceleration of the robotic arm in joint space, respectively; J(q)∈R m×n Let be the Jacobian matrix of the robotic arm, obtained by taking the partial derivative of ψ(q).

[0074] Preferably, during step 1, a dynamic model of the robot arm with n degrees of freedom in the Cartesian coordinate system is established based on the Lagrange method, and the joint space dynamics formula is as follows:

[0075]

[0076] Where M(q)∈R n×n It is an inertial diagonal matrix. Let G(q) ∈ R be the Coriolis and Oswald force matrices. n ×n Let R be the gravity vector matrix, τ∈R n×n This is the torque vector input for the robotic arm control.

[0077] Based on the above kinematic equations and joint space dynamics equations, the dynamics equations of the robotic arm in Cartesian coordinates are given as follows:

[0078]

[0079] Among them, there are

[0080] M r (x)=J -T (q)M(q)J -1 (q);

[0081]

[0082] G r (x)=J -T (q)G(q);

[0083] u=J -T (q)τ;

[0084] Where u is the control force of the robotic arm in the Cartesian coordinate system, and f ext It is an interaction force with the external environment.

[0085] Preferably, in step 2, the outer loop employs adaptive admittance control, specifically including the following steps:

[0086] Step A1: Based on the spring-mass-damping model, considering the one-dimensional case, establish the admittance control equation, as shown in the following formula:

[0087]

[0088] e = x d -x;

[0089] Among them, f d Let x be the desired interaction force; m, b, and k be the mass, damping, and stiffness parameters, respectively; x be the desired interaction force. d x and x represent the desired end position and the actual end position, respectively.

[0090] Step A2: Design a dynamic compensation term to adaptively adjust the admittance parameter. When the interaction force increases, reducing the stiffness of the robotic arm can increase compliance, thereby achieving compliance in interaction with the environment. The formula for the adaptive admittance controller is as follows:

[0091]

[0092] Among them, there are

[0093]

[0094] Where Δb(t) is the damping parameter compensation; φ(t) is the adaptive law of the admittance controller; T is the sampling period; and α is the adaptive law coefficient.

[0095] Step A3: Discretize the continuous system. The discretized formula is as follows:

[0096]

[0097] Δf=f e -f d ;

[0098] Where, x r (nT), x d (nT) represent the actual position and the expected position of the robotic arm's end effector during the nth sampling period, respectively.

[0099] Step A4: Verify the stability of the outer loop system: Further simplification of the above formula yields the state-space equation of the discrete system, as follows:

[0100]

[0101] Where, x1(n)=x r (n), y(n) = x1(n).

[0102] The characteristic equation of the system is obtained from the system matrix, and the stability of the system is determined by the Routh criterion.

[0103] Preferably, when performing step 3, the inner loop of the adaptive iterative learning control is designed, specifically including the following steps:

[0104] Step B1: Consider the dynamic model of an n-DOF robotic arm with random non-repetitive disturbances and uncertainties, as shown in the following formula:

[0105]

[0106] Where t is time, t∈[0,T]; k is the number of iterations; ΔM, ΔC, and ΔG are the compensation terms for the uncertain parts of M, C, and G, respectively; τ k ∈R n To control the torque; τ dk ∈R n This represents random, non-repeating disturbances in the system.

[0107] The following conditions must be met during the iteration process:

[0108] During the iteration process, the initial state of the system at each run is on the initial state corresponding to the desired trajectory, i.e., the initial condition is satisfied:

[0109] x k (0)=x d (0), k = 0, 1, 2, ...

[0110] Step B2: Using Taylor's formula, linearize M(q), C(q), and G(q) in B1 respectively. The dynamic model formula for the k-th iteration is as follows:

[0111]

[0112]

[0113] e = q d -q k ;

[0114]

[0115] Where M = M(q) d ),

[0116] Step B3: For the dynamic model in B2, design an adaptive iterative learning control law, as shown in the following formula:

[0117]

[0118] Among them, K P K D ∈R n×n For PID parameters; δ k The independent variable of the iteration term is a function of time; γ is the gain coefficient of the nonlinear control term. The hyperbolic tangent function is used to limit the amplitude of the control input; λ is the adaptive parameter; and sgn is the floor function.

[0119] Step B4: Establish the dynamic coupling relationship between the damping parameter compensation Δb of the outer loop admittance control and the gain coefficient γ of the inner loop iterative learning, as shown in the following formula:

[0120] Δb(k)=α*γ(k)+β*(F d -F e )

[0121] γ(k+1)=γ(k)+η*((X r -X d )+λ*Δb(k));

[0122] Where α, β, η, and λ are coupling coefficients, which can be calibrated experimentally.

[0123] Preferably, in step 4, an improved whale predation algorithm is used to optimize the adaptive iterative learning parameters, specifically including the following steps:

[0124] Step C1: Initialize parameters such as population size, number of iterations, and variable dimensions; in the inner-loop adaptive iterative learning control, the tracking error of each iteration is used as the fitness function, and the goal is to minimize the error; map the parameters Kp1, Kp2, Kd1, and Kd2 that need to be optimized as optimization variables, set upper and lower limits, set the initial solution within the upper and lower limits, and calculate the initial fitness value, as follows:

[0125] up = [K] p1max ,K p2max ,K d1max ,K d2max ];

[0126] sub = [K p1min ,K p2min ,K d1min ,K d2min ];

[0127] M c = (up-sub) / 20;

[0128] Where up is the upper limit, sub is the lower limit, Kp1, Kp2, Kd1, Kd2 are the iterative learning control parameters, and Mc is the prey movement range.

[0129] Step C2: Simulate prey escape behavior using the Monte Carlo method to generate candidate solutions, narrowing the search range of the algorithm. The perturbation amplitude of the candidate solutions is dynamically adjusted based on the number of iterations; as the number of iterations increases, the perturbation amplitude decreases. The formula for generating prey candidate positions is as follows:

[0130]

[0131] d = pdist(best, x);

[0132] Where x is the newly generated candidate position of the prey, x best represents the current optimal position of the prey, det is the iteration number, ii is the current iteration number, rand represents the random direction; z is the haste coefficient, which decreases as the distance increases, limiting the prey's movement range, and d represents the distance between the calculated current optimal solution and the individual.

[0133] Step C3: The whale updates its own position based on the location of its prey, balances global search with local exploitation using adaptive coefficients, and controls its displacement speed by controlling the maximum number of orbits. The adjustment mechanism for the maximum number of orbits is as follows:

[0134]

[0135] Where k is the maximum number of orbits.

[0136] The further away from the current optimal distance, the lower the individual distribution density, so a certain speed limit is imposed. When the distance to the optimal point is close, a certain reward is given. Based on this, the individual's position is updated using the following formula:

[0137]

[0138] θ′=θ0+Δθ=θ0+(k′*rand)*2π

[0139] x=[y*cosθ′,y*sinθ′];

[0140] Where θ′ and θ0 represent the updated movement angle and the initial angle of the current individual, respectively, and y is the radial distance of movement.

[0141] Step C4: The whale circles its prey, gradually decreasing the distance to find the optimal hunting opportunity without disturbing it. Individuals with better fitness values ​​are retained, and the current optimal parameter combination is updated. After reaching the maximum number of iterations or fitness convergence, the optimal parameters are output. When L ≤ R, the whale directly approximates the prey, outputting the optimal solution, where L is the distance between the whale and the prey, and R is the maximum radius of the prey's movement. The parameter combination with the smallest fitness value is recorded, as shown in the following formula:

[0142] (K′ p ,K d ′)=argminFitness(K p ,K d );

[0143] Wherein, K′ p K d ′ represents the optimal parameter output, and Fitness is the fitness function.

[0144] The present invention will now be described in further detail with reference to the accompanying drawings and specific examples.

[0145] In this embodiment, a two-degree-of-freedom robotic arm is used for simulation verification.

[0146] The robotic arm parameters are as follows: link mass m1=m2=1kg; link length l1=l2=0.5m; link center of mass position lc1=lc2=0.25m; link moment of inertia I1=I2=0.1kg*m 2 The acceleration due to gravity is g = 9.8 m / s². 2 Set the desired trajectory tracking command for the robotic arm: q 1d =sin(2πt),q 2d =cos(2πt); This satisfies the assumptions made in step 3, and the initial state of the robotic arm is: x(0) = [0, 2π, 1, 0] T ;parameter Set the number of iterations to 200.

[0147] Figure 4 The figure shows the tracking results of the robotic arm's position and velocity over time after 200 iterations based on the improved whale algorithm. As can be seen from the figure, the designed controller can track the desired output trajectory with high precision, exhibiting good tracking performance, and the tracking error gradually and stably converges to 0.

Claims

1. An adaptive admittance control method combining iterative learning control, characterized in that, The following steps are adopted: Step 1: Establish the kinematic model of the robot arm with n degrees of freedom in the Cartesian coordinate system based on the DH rule; establish the dynamic model of the robot arm with n degrees of freedom in the Cartesian coordinate system based on the Lagrange method; Step 2: Design inner and outer loop control strategies. The outer loop adopts an adaptive admittance control strategy to dynamically adjust the admittance controller parameters, compensate for environmental uncertainties and dynamic changes, and achieve force tracking. Step 3: The inner loop adopts adaptive iterative learning control, which uses prior data from iterative learning control to update the current control input until complete compensation is achieved. This addresses the random non-repetitive disturbances and uncertainties in the dynamic model during the robot arm's interaction with the environment, thus enabling position tracking. Step 4: Adopt an improved whale predation algorithm, optimize the iterative learning parameters, improve the convergence speed and tracking accuracy of the algorithm, and enable the system to achieve better position tracking results.

2. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: In step 1, to achieve compliant interaction between the robotic arm and the unstructured environment and to describe the physical information such as the dynamic model and control variables of the interaction system, the kinematic and dynamic equations of the n-degree-of-freedom robotic arm in Cartesian space are established based on the DH rule and the Lagrange method, as follows: Where, x(t), and Let ψ(q) represent the position, velocity, and acceleration of the robotic arm's end effector in Cartesian coordinates; ψ(q) is the kinematic model of the robotic arm; q∈R n×n The angle vector in the joint space of the robotic arm. and Let J(q) represent the angular velocity and angular acceleration of the robotic arm in joint space, respectively; J(q)∈R m×n Let be the Jacobian matrix of the robotic arm, obtained by taking the partial derivative of ψ(q); The dynamics formula for the robotic arm is as follows: Where M(q)∈R n×n It is an inertial diagonal matrix. Let G(q) ∈ R be the Coriolis and Oswald force matrices. n×n Let R be the gravity vector matrix, τ∈R n×n This is the torque vector input for the robotic arm control.

3. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: In step 2, to ensure the tracking error of the interactive force converges to zero, a dynamic compensation term is designed in the outer loop to adaptively adjust the impedance parameter to compensate for the time-varying error in the dynamic compensation system. When the interactive force increases, it indicates a larger intention error. The robotic arm can increase its compliance by reducing its own impedance parameter and compensating for the position error. The controller is as follows: Where Δb(t) is the damping parameter compensation; φ(t) is the adaptive law of the admittance controller; T is the sampling period; and α is the adaptive law coefficient. The outer loop input is the desired position, and the output serves as the ideal input for the inner loop intelligent iterative learning control. The inner loop involves inverse kinematics of the robotic arm, iterative learning controller, and robotic arm model. Position feedback is used to convert the error e = q... d -q k The input is an iterative learning controller. Through continuous iteration, the error tends to zero, resulting in good compliance of the robotic arm when interacting with the environment.

4. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: In step 3, to ensure position tracking when the robotic arm interacts with the environment, considering the random non-repetitive disturbances and uncertainties in the dynamic model when the robotic arm interacts with the environment, the inner loop is designed to adopt adaptive iterative learning control, which updates the current control input by referencing prior data, and achieves high-precision tracking of the given desired trajectory of the unknown object's actual running trajectory within a given time range. Consider the dynamics model of an n-DOF robotic arm with random non-repetitive disturbances and uncertainties, as shown in the following formula: Where t is time, t∈[0,T]; k is the number of iterations; ΔM, ΔC, and ΔG are the compensation terms for the uncertain parts of M, C, and G, respectively; τ k ∈R n To control the torque; τ dk ∈R n This refers to random, non-repeating disturbances in the system. The following conditions must be met during the iteration process: During the iteration process, the initial state of the system at each run is on the initial state corresponding to the desired trajectory, i.e., the initial condition is satisfied: x k (0)=x d (0),k=0,1,2,... The adaptive iterative learning control law is designed as follows: Among them, K P K D ∈R n×n For PID parameters; δ k The independent variable of the iteration term is a function of time; γ is the gain coefficient of the nonlinear control term. The hyperbolic tangent function is used to limit the amplitude of the control input; λ is the adaptive parameter; sgn is the floor function. Consider the dynamic coupling relationship between the damping parameter compensation Δb of the outer loop admittance control and the gain coefficient γ of the inner loop iterative learning. When the outer loop detects an increase in force tracking error, it not only adjusts the admittance parameter but also adjusts the learning rate of the inner loop in real time through the coupling factor to enhance the system's responsiveness to dynamic environments. The formula is as follows: Δb(k)=α*γ(k)+β*(F d -F e ) γ(k+1)=γ(k)+η*((X r -X d )+λ*Δb(k); Where α, β, η, and λ are coupling coefficients, which can be calibrated experimentally.

5. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: In step 4, for the n-DOF robotic arm, an adaptive iterative learning control algorithm based on intelligent algorithm optimization is adopted, and the steps are as follows: Step A1: Set the optimization variable dimensions, parameter upper and lower limits, population size, and maximum number of iterations. Generate an initial population within the feasible region through uniform random sampling, and call the fitness function to calculate the error corresponding to each solution, recording the initial optimal solution. Step A2: In each iteration, using the current optimal solution as the center, and combining the prey's movement range and the iteration decay factor, multiple candidate solutions are generated through Gaussian perturbation. The Monte Carlo method is used to simulate the prey's escape behavior within its maximum movement range, ensuring sufficient exploration of the local neighborhood. The fitness values ​​of the candidate solutions are calculated, and the optimal candidate solution is selected. If its fitness is better than the historical best value, the global optimal solution is updated. The formula for generating prey candidate positions is as follows: d = pdist(best, x) Where x is the newly generated candidate position of the prey, x best represents the current optimal position of the prey, det is the iteration number, ii is the current iteration number, rand represents the random direction; z is the haste coefficient, which decreases as the distance increases, limiting the prey's movement range, and d represents the distance between the calculated current optimal solution and the individual. Step A3: Using the current optimal solution as an attractor, update the position using a linear combination; introduce Gaussian noise to enhance global search capability. After the update, truncate out-of-bounds parameters to ensure the solution remains within the feasible region and approximates the optimal solution. Merge the current population with candidate solutions, sort them by fitness value, and retain the best individuals for the next generation to avoid losing high-quality solutions while maintaining population diversity. Step A4: Record the optimal fitness value for each generation, and finally output the global optimal parameter combination and minimum error value to complete the automatic tuning of controller parameters.

6. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: In step 2, design the inner and outer loop control strategies for the robotic arm; the admittance control of the outer loop will be based on the environmental force F. d ,F ext Generate position correction amount X r Position correction amount X r The expected input X as the inner loop d The inner loop uses iterative learning control combined with intelligent algorithms to track and correct the position X. d and the actual position X r Feedback is sent to the outer loop, forming a closed loop.

7. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: During step 3, the damping parameter compensation Δb of the outer loop admittance control and the gain coefficient γ of the inner loop iterative learning are correlated through a dynamic coupling factor. When the outer loop detects an increase in force tracking error, it not only adjusts the admittance parameter but also adjusts the learning rate of the inner loop in real time through the coupling factor to enhance the system's responsiveness to dynamic environments. The formula is as follows: Δb(k)=α*γ(k)+β*(F d -F e ) γ(k+1)=γ(k)+η*((X r -X d )+λ*Δb(k)) Where α, β, η, and λ are coupling coefficients, which can be calibrated experimentally.

8. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: In step 3, an improved whale algorithm is used to optimize the iterative learning control parameters to minimize errors in trajectory tracking. In each iteration, multiple candidate solutions are generated using Gaussian perturbation, centered on the current optimal solution and considering the prey's movement range and iteration decay factor. A Monte Carlo method is used to simulate the prey's escape behavior within its maximum range, ensuring thorough exploration of the local neighborhood. Furthermore, the position is updated using a linear combination with the current optimal solution as an attractor. Gaussian noise is introduced to enhance global search capabilities. After updating, out-of-bounds parameters are truncated to ensure the solution remains within the feasible region and approximates the optimal solution. The current population and candidate solutions are merged, sorted by fitness value, and the best individuals are retained for the next generation to avoid losing high-quality solutions while maintaining population diversity. The optimal fitness value for each generation is recorded, and finally, the globally optimal parameter combination and minimum error value are output, completing the automated tuning of the controller parameters.

9. The adaptive admittance control method combining iterative learning control as described in claim 1, characterized in that: When performing step 4, a prey agitation coefficient and a speed adjustment mechanism are introduced into the algorithm; The principle of the impatience coefficient is: the farther the prey is from the hunter, the smaller the coefficient is, and the smaller the range of movement of the prey. This allows the hunter to traverse as much as possible. When the hunter approaches the prey, the range of movement of the prey will also increase. If the optimal point is not found, it can also jump out of the local optimum and reduce the probability of the local optimum. d = pdist(best, x); Where x is the newly generated candidate position of the prey, Mc is the range of movement of the prey; z is the agitation coefficient, which decreases as the distance increases, limiting the range of movement of the prey; and d represents the distance between the calculated current optimal solution and the individual. Speed ​​adjustment mechanism: The number of orbits is dynamically adjusted through an adaptive coefficient. When the distance to the optimum is far, the movement speed is limited to avoid skipping the potential optimum region; when the distance is close, the convergence speed is accelerated. The displacement speed is controlled by the number of orbits. The adjustment mechanism of the number of orbits k is as follows: Where k is the number of revolutions; Using polar coordinates and random angle offsets, spiral approximation and multi-directional exploration are achieved.

Images