Damping adaptive impedance control method based on neural network adjustment parameters

Abstract

The application discloses a damping self-adaptive impedance control method based on a neural network adjustment parameter, a mathematical description of damping compensation is designed based on Lyapunov stability theory, and a damping self-adaptive damping controller is designed.According to the special structure of the mathematical model of the damping self-adaptive damping controller, different excitation functions are designed to reflect the characteristics of the damping coefficient changing under the influence of various factors, a neural network is constructed, and the adaptive adjustment of the damping adjustment parameter in the damping self-adaptive damping controller is realized.Through online learning of the constructed neural network, the optimization of the damping adjustment parameter in the damping self-adaptive damping controller is realized, so that the polishing process environment changes are adapted, the damping control is adapted to the stiffness mutation, the stiffness dynamic change and the expected force dynamic change in different environments such as inclined planes, planes and curved surfaces, and the control precision is effectively improved under the premise of ensuring stability.

Description

Technical Field

[0001] This invention relates to the fields of motor control and robotics, specifically to a damping adaptive impedance control method based on neural network adjustment parameters. Background Technology

[0002] With the development of electronic information technology, robots are widely used in various repetitive work scenarios, such as force-controlled robotic grinding, which features high efficiency, high precision, good stability, and high safety. For robot force control, impedance control is commonly used. Impedance control links the force and position between the robot's end effector and the environment, adjusting the end effector's position through force feedback to achieve force control. However, traditional impedance control is effective in planar environments with fixed stiffness, but its performance is unsatisfactory in situations with varying stiffness and unknown environmental positions.

[0003] To enable impedance control to adapt to complex and unknown environments, scholars both domestically and internationally have been dedicated to improving impedance control. Some literature considers the impact of robot end-effector displacement errors on force and uses model-adaptive methods to compensate for the end-effector position, thereby adjusting the end-effector position in real time to achieve constant force control. However, this requires adjusting too many parameters, and the appropriateness of parameter selection has a significant impact on the system. Other literature introduces adaptive fuzzy sliding mode controllers to compensate for estimation errors caused by time delay estimation, offsetting the interference of nonlinear factors and uncertainties in the dynamic model on the system. Some literature proposes an adaptive impedance control method based on dynamic neural networks for redundant robots under multi-physics constraints. To provide optimal contact performance when the environmental model is unknown, an adaptive impedance learning method is proposed to achieve optimal interaction between the robot and the environment. Some literature designs a model predictive controller based on impedance control methods, uses the Q-learning method to solve the model predictive controller, and then optimizes the impedance parameters online. Some literature proposes an improved active disturbance rejection impedance control strategy. This strategy generates a new desired force through an active disturbance rejection controller, adjusts the position of the robot's end-effector coordinate system, and achieves accurate force tracking. Although the aforementioned literature has improved the traditional impedance control method by addressing issues such as reference position error, time delay error, unsuitable impedance parameters, and desired force error, thus achieving force control, the designed method still needs further improvement in the dynamic performance of the control system. Summary of the Invention

[0004] The present invention addresses the problem that traditional impedance control is insufficient to effectively maintain grinding quality when the environmental stiffness and position of an industrial robot are unknown during the grinding process. It provides a damping adaptive impedance control method based on neural network adjustment parameters.

[0005] To solve the above problems, the present invention is achieved through the following technical solution:

[0006] The damping adaptive impedance control method based on neural network adjustment parameters includes the following steps:

[0007] Step 1, Initialization: Set the contact force error ΔF(1) = 0 at time 1 and the contact force error ΔF(2) = 0 at time 2; set the correction amount e of the reference trajectory at time 1. X (1) = 0, the correction amount e of the reference trajectory at time 2. X (2) = 0; Let the damping compensation amount ΔB(1) = 0 at the first moment and the damping compensation amount ΔB(2) = 0 at the second moment; Let k = 3;

[0008] Step 2: Collect the actual contact force F at time k using the robot's end effector sensor. e (k), and combined with the expected contact force F at time k. d (k) yields the contact force error ΔF(k) at time k, where:

[0009] ΔF(k)=F d (k)-F e (k)

[0010] Step 3: Calculate the correction amount e of the reference trajectory at time k. X (k), where:

[0011]

[0012] In the formula, ΔF(k) is the contact force error at time k, ΔF(k-1) is the contact force error at time k-1, and ΔF(k-2) is the contact force error at time k-2; e X (k) represents the correction amount of the reference trajectory at time k, e X (k-1) is the correction amount for the reference trajectory at time k-1, e X (k-2) is the correction amount for the reference trajectory at time k-2; M d B d and K d These represent the inertia, damping, and stiffness of the target impedance model, respectively; ΔB(k-1) is the damping compensation at time k-1; and T is the sensor sampling period.

[0013] Step 4: Use the correction amount e of the reference trajectory at time k. X (k) The reference trajectory X at time k d (k) is used for compensation to obtain the control quantity X(k) of the reference trajectory at time k, where:

[0014] X(k)=X d (k)+e X (k)

[0015] Step 5: First, subtract the control quantity X(k-1) of the reference trajectory at time k from the control quantity X(k) of the reference trajectory at time k-1 to obtain the increment ΔX(k) of the control quantity X(k) of the reference trajectory at time k; then, subtract the control quantity X(k-1) of the reference trajectory at time k-1 from the increment ΔX(k) of the control quantity of the reference trajectory at time k to obtain the increment ΔX(k) of the control quantity of the reference trajectory at time k.

[0016] Step 6: Combine the increment ΔX(k) of the control quantity X(k) of the reference trajectory at time k with the increment ΔX(k) of the control quantity of the reference trajectory at time k. The input is fed into the neural network to obtain the damping compensation amount ΔB(k) at time k; the above neural network consists of an input layer, an intermediate layer, and an output layer, and the activation function of the intermediate layer is:

[0017]

[0018] In the formula, f1, f2, f3 and f4 are the four excitation functions of the intermediate layer; ΔX(i) is the increment of the control quantity X(i) of the reference trajectory at time i, and ΔX(k) is the increment of the control quantity X(k) of the reference trajectory at time k; Let ΔX(i) be the increment of the control quantity of the reference trajectory at time i. The increment of the control quantity ΔX(k) of the reference trajectory at time k;

[0019] Step 6: Let k = k + 1, and return to step 2.

[0020] Compared with existing technologies, this invention designs a damping adaptive impedance control algorithm based on neural network adjustment parameters, on the basis of adaptive impedance control. By using the force feedback information of the robot end effector and combining it with online learning of the neural network, the optimal damping parameters are determined in real time to adapt to complex and unknown contact environments, thus achieving effective force control during the grinding process. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a traditional impedance control method.

[0022] Figure 2 These are adjustment parameters based on neural networks.

[0023] Figure 3 This is a schematic diagram of a damping adaptive impedance control method based on neural network adjustment parameters. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific examples and the accompanying drawings.

[0025] To study the entire polishing system, the robot and its environment are treated as a dynamic system for modeling and analysis. Generally, the environmental dynamics model of the tool tip and polishing device can be expressed as:

[0026]

[0027] In the formula, F e B represents the force between the workpiece and the robot's end effector. e and K e X and X represent the damping and stiffness parameters of the environment, respectively; e These represent the actual location and the location on the environmental surface, respectively. and These represent the rate of change corresponding to the actual location and the rate of change corresponding to the location on the environmental surface, respectively.

[0028] Because the robot's end effector moves slowly, the environment model can be simplified to a "spring" model, which represents the relationship between the robot's end effector, environmental displacement, and the forces acting on the environmental contact surface.

[0029]

[0030] Impedance control involves establishing a dynamic relationship model between contact force and position, and adjusting the parameters of the impedance model to change its dynamic characteristics, ensuring that the robot exhibits good compliance in the environment. Impedance control can be viewed as a mass-damped-spring model:

[0031]

[0032] In the formula: X d X represents the reference trajectory; M represents the actual position of the robotic arm's end effector; d B d and K d F represents the inertia, damping, and stiffness of the target impedance model, respectively. e For end contact force; F d For the power of expectation, and These represent the velocity and acceleration corresponding to the change in actual position, respectively. and These represent the velocity and acceleration corresponding to the change in the reference trajectory, respectively. The impedance control block diagram is shown in Figure 1.

[0033] To simplify subsequent calculations, equation (3) is transformed using the Laplace transform to obtain:

[0034]

[0035] In the formula, s is the Laplace operator, and e is the position deviation. X (s)=X(s)-X d (s).

[0036] Assuming the robot arm is working and the influence of its inner-loop position control on the system is ignored, calculate the deviation ΔF = F between the actual contact force and the desired contact force at the end of the robot arm. d -F e ,but:

[0037] ΔF=F d -F e =F d -K e (XX e ) = F d +K e X e -K e [X d +h(s)ΔF] (5)

[0038] In the formula, h(s) is the target impedance model. K e Environmental stiffness, where s is the Laplace operator. The time domain is transformed to the frequency domain using the Laplace transform, which is then used to calculate the steady-state error of the system.

[0039] After further simplification of equation (5), we get:

[0040]

[0041] When the robotic arm is operating in a steady state, both its velocity and acceleration approach zero, and the steady-state value ΔF corresponding to the deviation ΔF is... ss for:

[0042]

[0043] In the formula, k eq The target impedance and the equivalent stiffness parameters of the environment.

[0044]

[0045] Therefore, the magnitude of the actual contact force between the robotic arm and the environment can be determined as follows:

[0046]

[0047] As can be seen from the above formula, the actual contact force F at the end of the robotic arm is equal to the reference trajectory X. d and desired contact force F dThe function. When the reference trajectory X d Satisfy the following expression:

[0048]

[0049] From equation (10), it can be seen that when the steady-state error of the contact force ΔF ss When the value is 0, the environmental position X of the contact surface needs to be accurately obtained. e and stiffness magnitude K e Then, the reference trajectory X is calculated. d .

[0050] In actual grinding processes, the workpiece's rigidity and environmental position are difficult to obtain precisely, resulting in the actual contact force not being the desired contact force, thus requiring position adjustment. Considering that the workpiece being processed by the robotic arm generally has high rigidity during actual grinding, even a small positional error can lead to a large steady-state error in the contact force. Furthermore, the processing environment is generally unknown and variable, making it difficult for the actual contact force to accurately track the desired contact force, which directly affects the grinding effect.

[0051] Impedance control allows the robot to adapt to environmental parameters by adjusting inertia, damping, and stiffness parameters. Fixed parameters are only suitable for a single, fixed environment, resulting in large force errors and poor tracking ability in environments with varying stiffness or complex curved surfaces. Dynamically adjusting impedance control parameters allows the robot's dynamic characteristics to adapt to environmental changes, ensuring system stability and reducing steady-state errors. The adaptive target impedance model h′(s) is:

[0052]

[0053] In the formula, M d B d and K d These represent the inertia, damping, and stiffness of the target impedance model, respectively, with ΔB representing the damping compensation.

[0054] To ensure system stability, a Lyapunov function is used to obtain damped adaptive impedance control. The functional relationship between the damping compensation ΔB and ΔX and ΔF is as follows:

[0055]

[0056] In the formula, t is the current continuous time. γ1 and γ2 are compensation coefficients, and in the continuous time domain, ΔX(t) and These are the position increment and velocity increment over the current continuous time t, respectively.

[0057] Formula (12) reveals that the damping coefficient increment ΔB(t) is affected by multiple factors and combinations of multiple factors, showing the relationship between damping and multi-factor characteristics.

[0058] Although damped adaptive impedance control offers improved performance compared to traditional impedance control, its convergence capability in curved environments remains insufficient and it suffers from excessive overshoot. To address the issue of grinding force accuracy caused by changes in environmental parameters under unknown conditions, a neural network is constructed to adaptively adjust parameters, tracking real-time changes in environmental stiffness and position to achieve precise control of the desired force.

[0059] Simplifying formula (12) yields:

[0060]

[0061] In the formula, ω1, ω2, ω3, and ω4 are damping adjustment parameters.

[0062] Based on the unique structure of damping in the damping adaptive impedance control according to equation (13), a neural network is constructed to adaptively adjust the parameters. The damping adjustment parameters in equation (13) are learned online by the neural network to make the damping adjustment parameters reach the optimal level, so that the damping adjustment parameters remain optimal under different grinding environments. The excitation function reflects the multi-factor characteristics of damping change. Multiple excitation functions of the neural network are selected as shown in equation (14):

[0063]

[0064] The neural network designed based on ΔB(t)=ω1f1+ω2f2+ω3f3+ω4f4 is as follows: Figure 2 As shown, the neural network consists of an input layer, an intermediate layer, and an output layer, and multiple activation functions are designed to address multiple factors affecting damping in adaptive impedance control.

[0065] Set the performance metric function of the neural network to:

[0066]

[0067] In the formula, ΔF represents the deviation between the desired force and the contact force. k represents the current moment after discretization of the continuous time t.

[0068] Based on the designed neural network and the gradient descent method, the importance of each weight varies as each weight has a different proportion in the whole system.

[0069] This invention employs a method of independently setting the learning rate, and the neural network is implemented in the discrete domain. A separate learning rate parameter is set for each weight adjustment, and the weight increment is updated according to the steepest descent method:

[0070]

[0071] In the formula: η is the learning rate, α is the momentum factor, and Δω j (k) and ωj (k-1) represent the weight increment at time k and the weight at time k-1, respectively. The increment of X(k) is ΔX(k) = X(k) - X(k-1), and the increment of ΔX(k) is...

[0072] The damping control block diagram of the neural network adjustment parameters is shown in Figure 3. The current position and velocity information are used as the input signals of the neural network. The neural network calculates in real time and adjusts the damping adjustment parameters in the damping adaptive impedance controller, thereby calculating the end position increment. Through the transformation from position to force, the force control is realized.

[0073] The damping adaptive impedance control method based on neural network adjustment parameters designed in this invention includes the following steps:

[0074] Step 1, Initialization: Set the contact force error ΔF(1) = 0 at time 1 and the contact force error ΔF(2) = 0 at time 2; set the correction amount e of the reference trajectory at time 1. X (1) = 0, the correction amount e of the reference trajectory at time 2. X (2) = 0; Let the damping compensation amount ΔB(1) = 0 at the first moment and the damping compensation amount ΔB(2) = 0 at the second moment; Let k = 3;

[0075] Step 2: Collect the actual contact force F at time k using the robot's end effector sensor. e (k), and combined with the expected contact force F at time k. d (k) yields the contact force error ΔF(k) at time k, where:

[0076] ΔF(k)=F d (k)-F e (k)

[0077] Step 3: Calculate the correction amount e of the reference trajectory at time k. X (k), where:

[0078]

[0079] In the formula, ΔF(k) is the contact force error at time k, ΔF(k-1) is the contact force error at time k-1, and ΔF(k-2) is the contact force error at time k-2; e X (k) represents the correction amount of the reference trajectory at time k, e X (k-1) is the correction amount for the reference trajectory at time k-1, e X (k-2) is the correction amount for the reference trajectory at time k-2; M d B d and K dThese represent the inertia, damping, and stiffness of the target impedance model, respectively; ΔB(k-1) is the damping compensation at time k-1; and T is the sensor sampling period.

[0080] Step 4: Use the correction amount e of the reference trajectory at time k. X (k) The reference trajectory X at time k d (k) is used for compensation to obtain the control quantity X(k) of the reference trajectory at time k, where:

[0081] X(k)=X d (k)+e X (k)

[0082] Step 5: First, subtract the control quantity X(k-1) of the reference trajectory at time k from the control quantity X(k) of the reference trajectory at time k-1 to obtain the increment ΔX(k) of the control quantity X(k) of the reference trajectory at time k; then, subtract the control quantity X(k-1) of the reference trajectory at time k-1 from the increment ΔX(k) of the control quantity of the reference trajectory at time k to obtain the increment ΔX(k) of the control quantity of the reference trajectory at time k. in:

[0083] ΔX(k)=X(k)-X(k-1)

[0084]

[0085] Step 6: Combine the increment ΔX(k) of the control quantity X(k) of the reference trajectory at time k with the increment ΔX(k) of the control quantity of the reference trajectory at time k. The input is fed into the neural network to obtain the damping compensation amount ΔB(k) at time k; the above neural network consists of an input layer, an intermediate layer, and an output layer, and the activation function of the intermediate layer is:

[0086]

[0087] In the formula, f1, f2, f3 and f4 are the four excitation functions of the intermediate layer; ΔX(i) is the increment of the control quantity X(i) of the reference trajectory at time i, and ΔX(k) is the increment of the control quantity X(k) of the reference trajectory at time k; Let ΔX(i) be the increment of the control quantity of the reference trajectory at time i. The increment of the control quantity ΔX(k) of the reference trajectory at time k;

[0088] Step 6: Let k = k + 1, and return to step 2.

[0089] To ensure the stability of the control system, this invention designs a mathematical description of damping compensation based on Lyapunov stability theory and designs an adaptive damping controller. Based on the special structure of the adaptive damping controller's mathematical model, different excitation functions are designed to reflect the characteristics of the damping coefficient changes under the influence of various factors. A neural network is constructed for the adaptive adjustment of the damping parameters in the adaptive damping controller. Through online learning of the constructed neural network, the damping parameters in the adaptive damping controller are optimized to adapt to changes in the grinding process environment. This enables the damping control to adapt to sudden changes in stiffness, dynamic changes in stiffness, and dynamic changes in desired force under different environments such as inclined planes, planes, and curved surfaces, effectively improving control accuracy while ensuring stability.

[0090] It should be noted that although the embodiments described above are illustrative, they are not intended to limit the invention. Therefore, the invention is not limited to the specific embodiments described above. Any other embodiments obtained by those skilled in the art under the guidance of this invention without departing from its principles are considered to be within the protection scope of this invention.

Claims

1. A damped adaptive impedance control method based on neural network adjustment parameters, characterized in that, The steps include the following: Step 1, Initialization: Set the contact force error ΔF(1) = 0 at time 1 and the contact force error ΔF(2) = 0 at time 2; set the correction amount e of the reference trajectory at time 1. X (1) = 0, the correction amount e of the reference trajectory at time 2. X (2) = 0; Let the damping compensation amount ΔB(1) = 0 at the first moment and the damping compensation amount ΔB(2) = 0 at the second moment; Let k = 3; Step 2: Collect the actual contact force F at time k using the robot's end effector sensor. e (k), and combined with the expected contact force F at time k. d (k) yields the contact force error ΔF(k) at time k, where: ΔF(k)=F d (k)-F e (k) Step 3: Calculate the correction amount e of the reference trajectory at time k. X (k), where: In the formula, ΔF(k) is the contact force error at time k, ΔF(k-1) is the contact force error at time k-1, and ΔF(k-2) is the contact force error at time k-2; e X (k) represents the correction amount of the reference trajectory at time k, e X (k-1) is the correction amount for the reference trajectory at time k-1, e X (k-2) is the correction amount for the reference trajectory at time k-2; M d B d and K d These represent the inertia, damping, and stiffness of the target impedance model, respectively; ΔB(k-1) is the damping compensation at time k-1; and T is the sensor sampling period. Step 4: Use the correction amount e of the reference trajectory at time k. X (k) The reference trajectory X at time k d (k) is used for compensation to obtain the control quantity X(k) of the reference trajectory at time k, where: X(k)=X d (k)+e X (k) Step 5: First, subtract the control quantity X(k-1) of the reference trajectory at time k from the control quantity X(k) of the reference trajectory at time k-1 to obtain the increment ΔX(k) of the control quantity X(k) of the reference trajectory at time k; then, subtract the control quantity X(k-1) of the reference trajectory at time k-1 from the increment ΔX(k) of the control quantity of the reference trajectory at time k to obtain the increment ΔX(k) of the control quantity of the reference trajectory at time k. Step 6: Combine the increment ΔX(k) of the control quantity X(k) of the reference trajectory at time k with the increment ΔX(k) of the control quantity of the reference trajectory at time k. The input is fed into the neural network to obtain the damping compensation amount ΔB(k) at time k; the above neural network consists of an input layer, an intermediate layer, and an output layer, and the activation function of the intermediate layer is: In the formula, f1, f2, f3 and f4 are the four excitation functions of the intermediate layer; ΔX(i) is the increment of the control quantity X(i) of the reference trajectory at time i, and ΔX(k) is the increment of the control quantity X(k) of the reference trajectory at time k; Let ΔX(i) be the increment of the control quantity of the reference trajectory at time i. The increment of the control quantity ΔX(k) of the reference trajectory at time k; Step 6: Let k = k + 1, and return to step 2.

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