An adaptive admittance method and system based on optimal control LQR theory

Abstract

This invention provides an adaptive admittance method and system based on the optimal control LQR theory, including constructing an environmental dynamics model and a robotic arm admittance control model, and deriving their interactive dynamics model; defining state variables and control inputs, and establishing a standard form state-space equation; constructing a quadratic performance index function, transforming admittance parameter optimization into an LQR problem; substituting the linear quadratic regulator framework into the quadratic performance index function, transforming the LQR problem into solving the Riccati matrix differential equation, and deriving analytical expressions for virtual optimal stiffness and virtual optimal damping; within the robotic arm control sampling frequency, inputting real-time collected environmental contact forces and the actual pose of the robotic arm end effector, along with set weighting coefficients, into the analytical expressions to calculate optimal virtual stiffness and damping; and then calculating pose corrections based on the admittance control model to correct the robotic arm's motion trajectory.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and specifically to an adaptive admittance method and system based on the optimal control LQR theory. Background Technology

[0002] When robots perform tasks requiring physical interaction with the external environment, such as assembly, grinding, polishing, and medical surgery, simple displacement or force control is often insufficient. Tiny positional errors can lead to enormous contact forces, damaging the workpiece or the robot; conversely, excessive external forces can cause the robot to deviate from its intended trajectory. Therefore, compliant control technology has emerged. Its core principle is to establish a dynamic relationship between the robot's position and contact forces, enabling the robot's end effector to exhibit impedance or admittance characteristics similar to a spring-damped mass.

[0003] Admittance control, as a mainstream indirect force control method, uses contact forces detected by force sensors to calculate pose corrections via a second-order admittance model (virtual mass, damping, and stiffness), which are then input into the inner-loop position controller. Its performance is highly dependent on the selection of virtual damping and virtual stiffness. Traditional admittance control often uses fixed parameters, making it difficult to balance steady-state accuracy, dynamic response, and system energy consumption when facing environments with varying stiffness (such as transitioning from air contact to rigid workpieces) or time-varying tasks. If the parameters are set too softly, the response is slow and the steady-state error is large; if they are set too stiffly, force overshoot, oscillation, or even instability can easily occur.

[0004] To address environmental uncertainties, existing research has proposed various adaptive methods. CN119897853B discloses a robust adaptive variable admittance control method based on different intentions in feature space. This method establishes a mapping relationship between actual contact force and virtual contact force, designs an adaptive damping coefficient for direct intention based on the virtual motion velocity of feature points, and combines trajectory curvature information to achieve force guidance for indirect intention, thus improving compliance and robustness to some extent. However, the adjustment of its adaptive parameters relies on a preset fixed threshold and empirical formula. When the environmental stiffness changes abruptly, the parameter update speed lags behind the environmental change, easily leading to dynamic response delay or overshoot, which reduces system stability. CN115741668B discloses another adaptive admittance control scheme, which detects the oscillation amplitude of the contact force signal through an observer. When the oscillation exceeds a threshold, the initial environmental stiffness is adjusted and the admittance parameters are dynamically updated. Although this method can alleviate the oscillation problem caused by abrupt changes to some extent, it only relies on single-mode information of the contact force.

[0005] In summary, existing admittance control technologies generally suffer from the following problems: parameter adjustment lags when environmental stiffness changes abruptly, making it difficult to balance dynamic response and stability; intent recognition relies on single-modal information (force only or vision only), resulting in incomplete capture of complex human intent; and visual and force information are not effectively coupled, making it difficult to achieve precise coordinated control in dynamic environments.

[0006] Therefore, there is an urgent need for a robust adaptive variable admittance control method that can integrate visual and force information in the feature space, quickly respond to sudden changes in environmental stiffness, and accurately identify multimodal human intentions. Summary of the Invention

[0007] This invention addresses the shortcomings of existing technologies by providing an adaptive admittance method and system based on the optimal control LQR theory. The adaptive admittance method constructs the admittance parameter optimization problem as an LQR problem, analytically solving for the optimal parameter expression, thereby achieving optimal online self-tuning of the parameters and effectively balancing force tracking accuracy, dynamic overshoot, and system energy consumption.

[0008] The first aspect of this invention is to provide an adaptive admittance method based on optimal control LQR theory, comprising: Step 1: Construct the environmental dynamics model and the robotic arm admittance control model, and derive the interaction dynamics model between the two; Step 2: Based on the interactive dynamics model constructed in Step 1, define the state variables and control inputs, and establish the standard form of the state-space equations; define the state variables as including the pose tracking error of the robotic arm end effector and its time derivative, wherein the pose tracking error is the difference between the desired pose and the actual pose, and the time derivative is the difference between the desired velocity and the actual velocity; define the control input as the force deviation, that is, the difference between the desired force exerted by the robotic arm end effector on the environment and the actual contact force. Step 3: Transform the state-space equation obtained in Step 2 into a general matrix state equation suitable for optimal control, define the state vector to include the pose tracking error and its time derivative; and construct a quadratic performance index function to transform the admittance parameter optimization into an LQR problem; wherein, the integral term of the quadratic performance index function includes the weighted sum of squares of the state error and the weighted sum of squares of the control input. Step 4: Substitute the linear quadratic regulator framework established in Step 3 into the quadratic performance index function to transform the LQR problem into solving the Riccati matrix differential equation to obtain the positive definite symmetric matrix P; based on the matrix P, the state space equation obtained in Step 2, and the preset input energy consumption penalty weight matrix, derive the analytical expressions for the virtual optimal stiffness and virtual optimal damping. Step 5: Within the robotic arm's controlled sampling frequency, collect the environmental contact force and the actual pose of the robotic arm's end effector in real time, and set weighting coefficients based on task requirements; input the estimated values ​​of the current environmental stiffness and damping, along with the weighting coefficients, into the analytical expression obtained in Step 4 to calculate the optimal virtual stiffness and optimal virtual damping for the current period; based on the calculated optimal virtual stiffness and optimal virtual damping, and the expected force exerted by the robotic arm's end effector on the environment... Environmental forces The pose correction amount is calculated based on the admittance control model to correct the motion trajectory of the robotic arm.

[0009] Furthermore, step two specifically includes: S21: Define state variables and control inputs: where the state variable is selected as pose tracking error. and pose tracking error speed The control input is selected as the desired force exerted by the robotic arm's end effector on the environment. and the forces exerted by the end effector on the environment The difference between the two is defined as the force deviation u, which is used as the control input. S22: Based on the force deviation u As the core control input of the state-space model, a linear time-invariant state-space equation is constructed: ; in, To represent the first-order differential, It is the difference between the desired pose and the actual pose, i.e. ; It is the difference between the expected speed and the actual speed, that is... ; It refers to the surface quality of the environment; Here is the surface stiffness matrix of the environment. The environmental surface damping matrix; S23: Transform the state-space equations into a mathematical framework for linear optimal control design: ; Where A is the system matrix, determined by the environmental surface quality, damping, and stiffness, and B is the input matrix, which correlates the gain of the control input.

[0010] Furthermore, the quadratic performance index function in step three is specifically defined as follows: ; in, It is a positive weight matrix, representing the weight of the steady-state error in the cost function; It is a positive weight matrix, representing the weight of the free overshoot in the cost function; It is a positive weight matrix, representing the weight of the input energy consumption in the cost function.

[0011] Furthermore, the analytical expressions for the virtual optimal stiffness and virtual optimal damping in step four further include: against And the robotic arm admittance model constructed in step one ,for In this case, the optimal stiffness and optimal damping are calculated. for: ; .

[0012] Furthermore, the analytical expressions for the virtual optimal stiffness and virtual optimal damping in step four further include: For grinding operations where the environmental equivalent quality is negligible, ignore The calculation, Optimal virtual damping for: .

[0013] This simplified form eliminates matrix operations, requiring only a single algebraic calculation to obtain the optimal parameters, making it suitable for millisecond-level real-time control scenarios.

[0014] Furthermore, in step five, the pose correction amount is superimposed on the original desired trajectory generation control command and sent to the robotic arm's underlying controller for execution, thereby realizing the dynamic adaptive update of the admittance parameters.

[0015] Furthermore, in step five, the estimated values ​​of the current environmental stiffness and damping are determined based on a lookup table method or an online estimation algorithm.

[0016] A second aspect of this invention is to provide an adaptive admittance system for a robotic arm based on the optimal control LQR theory, comprising: The parameter acquisition submodule is used to input the preset desired trajectory, acquire the environmental contact force and the actual pose of the robotic arm end effector in real time, obtain the estimated values ​​of the current environmental stiffness and damping, and receive the set weight coefficients. The optimal impedance planning module stores closed-form analytical expressions for virtual stiffness and virtual damping derived from linear quadratic optimal control theory. The optimal impedance planner is configured to receive data from the parameter acquisition submodule and execute steps one to four above to generate analytical expressions for virtual optimal stiffness and virtual optimal damping. The pose correction module is used to determine the virtual optimal stiffness and virtual optimal damping obtained from the optimal impedance planning module, as well as the environmental forces from the force sensor. And the pre-defined desired force of the robotic arm end effector on the environment. The pose correction is calculated based on the admittance control model.

[0017] The beneficial effects of this invention are as follows: This invention integrates force tracking accuracy, dynamic overshoot suppression, and system energy consumption into a unified quadratic optimization framework using LQR theory. Simulation results show that, compared to traditional constant impedance control, it can completely suppress overshoot. Moreover, compared with existing adaptive admittance methods that rely on iterative search or gradient descent and have a large computational load, this invention derives the closed analytical expression of the optimal parameters through the Riccati equation, which does not require iterative calculation and can run in real time in embedded systems with only simple algebraic operations, thus significantly improving computational efficiency. Moreover, it has the ability to adapt to sudden changes in environmental stiffness, and can instantly adjust virtual parameters based on analytical expressions, with a fast response speed; and the weight coefficients can intuitively reflect task preferences, and can adapt to different task requirements without modifying the algorithm structure. Attached Figure Description

[0018] Figure 1 This is a flowchart of an adaptive admittance method based on optimal control LQR theory as described in this invention; Figure 2 The results of virtual stiffness adaptive variation using the method described in this invention are shown; Figure 3 The results of virtual damping adaptive change using the method described in this invention are shown. Detailed Implementation

[0019] To make the objectives, technical solutions, beneficial effects, and significant advancements of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings provided in the examples of the present invention. Obviously, all 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.

[0020] In the description of this application, unless otherwise expressly specified and limited, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more; unless otherwise specified or explained, the terms "connected," "fixed," etc., should be interpreted broadly. For example, "connected" can be a fixed connection, a detachable connection, an integral connection, or an electrical connection; "connected" can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0021] like Figure 1 As shown, an adaptive admittance method based on optimal control LQR theory includes: Step 1: Construct the environmental dynamics model and the robotic arm admittance control model, and derive the interaction dynamics model between the two.

[0022] S11: Construct an environmental dynamics model.

[0023] Assume the interaction environment is a passive system with linear stiffness-damping characteristics, and neglect its mass. Its dynamic behavior is dominated only by elastic restoring force and viscous damping force, and the environmental dynamic model is expressed as follows: (1) in, It is environmental contact force. This is the pose of the robotic arm's end effector. The pose in contact with the environment is calculated using a unified base coordinate system. It represents the surface quality of the environment and is a diagonal matrix. Here is the surface stiffness matrix of the environment. Let be the environmental surface damping matrix, and , These are obtained using a lookup table method, and all are diagonal matrices.

[0024] S12: Admittance control achieves compliant interaction of the robotic arm by converting contact force deviation into pose correction. Therefore, a robotic arm admittance control model is constructed: (2) in, The virtual quality is preset based on empirical values. For the virtual damping to be optimized, Virtual stiffness to be optimized; It is the preset expected contact force of the robotic arm end effector with the environment; It is the difference between the desired pose and the actual pose of the robotic arm, i.e., the pose tracking error. ,in It is the preset desired pose of the robotic arm end effector.

[0025] S13: When the robot interacts with the environment, the force sensor value of the robotic arm is the contact force with the environment. Therefore, based on the constructed environmental dynamics model and the robotic arm admittance control model, an interaction dynamics model between the robotic arm and the environment is constructed, as shown in the following equation: (3) By constructing an environmental dynamics model and a robotic arm admittance control model, the physical constraints of environmental interaction and the adjustment mechanism of admittance control are clarified, providing a clear input-output relationship for subsequent optimal parameter solving based on LQR theory.

[0026] Step 2: To transform the admittance control parameter optimization problem into an optimal control problem, it is necessary to construct state-space equations. Therefore, based on the interactive dynamics model of the robotic arm and environment constructed in Step 1, state variables and control inputs are defined, and the standard form of the state-space equations is derived.

[0027] S21: Define state variables and control inputs.

[0028] The state variable is selected as pose tracking error. and pose tracking error speed Define state variables .

[0029] The control input is selected as the desired force exerted by the robotic arm end effector on the environment. and the forces exerted by the end effector on the environment The difference between the two is defined as the force deviation u, which is used as the control input, i.e.: (4) S22: The force deviation u As the core control input of the state-space model, the linearized state-space equations are constructed as follows: (5) in, To represent the first-order differential, It is the difference between the desired pose and the actual pose, i.e. ; It is the difference between the expected speed and the actual speed, that is... .

[0030] S23: Let in the general equation The state-space equations are transformed into a mathematical framework for linear optimal control design: (6) Step 3: Define performance metrics. After establishing the interaction model between the robotic arm and the environment as a general state equation, the optimal admittance parameters of the robotic arm can be obtained by solving the linear quadratic regulator (LQR). In optimal control theory, the LQR is designed to minimize the sum of system state and energy consumption. This paper uses the infinite time domain Raccati recursive method for detailed solution.

[0031] S31: Construct a linear quadratic regulator (LQR) framework, and transform the mathematical carrier formula (6) of the state-space equation obtained in step two into a general matrix state equation: (7) In the formula, Z represents the element. The vector.

[0032] S32: Constructing a quadratic performance index function J : (8) in: It is a positive weight matrix, representing the weight of the steady-state error in the cost function; It is a positive weight matrix, representing the weight of the free overshoot in the cost function; It is a positive weight matrix, representing the weight of the input energy consumption in the cost function.

[0033] During the experiment, values ​​were assigned to the three factors respectively; the larger the value, the heavier the penalty and the closer it is to the expected value. In this embodiment, we set... This represents the balance accuracy and overshoot suppression while ensuring a certain level of energy efficiency. These three coefficients are selected as needed.

[0034] The integral term of the quadratic performance index function includes the weighted sum of squares of the state error and the weighted sum of squares of the control input. The weighted sum of squares of the state error reflects steady-state error and dynamic overshoot, while the weighted sum of squares of the control input reflects energy consumption.

[0035] Step 4: Substitute the linear quadratic regulator framework established in Step 3 into the quadratic performance index function to transform the LQR problem into solving the Riccati matrix differential equation to obtain the positive definite symmetric matrix P; based on the matrix P, the state-space equation obtained in Step 2, and the preset input energy consumption penalty weight matrix, derive the analytical expressions for the virtual optimal stiffness and virtual optimal damping.

[0036] Substituting the linear quadratic regulator (LQR) framework obtained in step three into the quadratic performance index function, we can find the virtual damper to be optimized. and virtual stiffness to be optimized (i.e., optimal admittance parameter) , The problem is transformed into a linear quadratic regulator problem that minimizes the performance index function J.

[0037] S41: First, establish the Riccati matrix differential equation to solve for the positive definite symmetric matrix P; the matrix P is a real-time positive definite symmetric matrix. In the finite time domain, if the upper limit of the cost integral of the quadratic performance index function is finite, it will only be a time-varying value P(t). When the upper limit approaches infinity, it approaches a constant value, which can be obtained from the Riccati matrix differential equation: (9) in, P(t) It is a time-varying value. Q It is the system state penalty weight matrix; in the penalty function of the equation ; R This is the input energy consumption penalty weight matrix, which is used in this penalty function. A and B are shown in equation (6).

[0038] Assumption and will Substituting the values, we can calculate: (10) S42: Mapping of optimal solution set and admittance parameter.

[0039] According to the Rittati formula, we will not delve into the solution process, but the final solution can be derived as follows: (11) Combined formula (6), Substituting the definition of R in equation (9) into equation (11), we obtain the final solution: (12) Combination And the robotic arm admittance model constructed in step one For displaying assembly conditions, In this case, the optimal stiffness and optimal damping are calculated. for: (13) (14) For a six-dimensional matrix, the virtual stiffness and virtual damping parameters are calculated independently in each direction under three-dimensional translational and three-dimensional rotational degrees of freedom.

[0040] If the surface quality of the environment is relatively small, this factor can be appropriately ignored to simplify calculations while ensuring overall accuracy. Although this will introduce minor errors, it can usually significantly improve computational efficiency and is suitable for engineering scenarios with high real-time requirements. In real-world environments, for grinding conditions where the equivalent environmental quality is negligible... That is, in the optimal virtual impedance, it can be ignored. The calculation of optimal stiffness and The results are the same, optimal virtual damping for: (15) This simplified form eliminates matrix operations, requiring only a single algebraic calculation to obtain the optimal parameters, making it suitable for millisecond-level real-time control scenarios.

[0041] Step 5: Adaptive control.

[0042] Steps for parameter acquisition: Real-time detection of environmental forces using a force sensor. The actual pose of the robotic arm's end effector is obtained through a pose sensor. X Estimates of current environmental stiffness and damping are obtained using a lookup table method. The operator or the upper-level task planner sets the weighting coefficients α1, α2, α3 according to the low overshoot requirement of the polishing task. The steps of optimal impedance planning are: ... The weighting coefficients α1, α2, and α3 are input into the analytical expressions (14) and (15) obtained in step four to calculate the optimal virtual stiffness in real time. and optimal virtual damping ; The steps of pose correction are: using the calculated optimal virtual stiffness. and optimal virtual damping And the preset expected contact force of the robotic arm end effector with the environment. and the environmental contact force fed back by the force sensor Calculate the pose correction ΔX: (16) Compare the pose correction ΔX with the original desired trajectory Superimposed, a new desired pose command Xr is obtained. +ΔX, sent to the robotic arm's underlying position controller for execution.

[0043] The steps described in step five are repeated in each control cycle to achieve online adaptive updates.

[0044] Through the above steps, the present invention can quickly adjust the admittance parameter when environmental parameters change, and always maintain optimal force tracking performance, dynamic response and energy consumption balance.

[0045] To further verify the dynamic and static performance of the admittance adaptive control method based on optimal control LQR theory described in this invention, this embodiment builds a full closed-loop simulation platform in a mathematical simulation environment, encapsulates the method as an adaptive admittance controller, and conducts comparative experiments with traditional constant impedance control and Gan Yahui's variable impedance control to quantitatively evaluate the force tracking accuracy, overshoot suppression capability, and adaptability to environmental changes.

[0046] Based on typical industrial grinding conditions, the simulation parameters are set as follows: Environmental parameters: In this experiment, the environmental impedance parameters are time-varying stiffness parameters used to analyze the admittance control results. The environmental mass and environmental damping are respectively set as... Surface stiffness matrix For time-varying parameters, the variation curve is defined by the following formula:

[0047] Robotic arm parameters and LQR weighting coefficients: when setting the contact environment pose The desired pose of the robotic arm is 5m. The distance is 5m, and the desired velocity and acceleration are respectively Expectation power is weighted as At that time, the desired force exerted by the robotic arm end effector on the environment is set. The curve showing how it changes over time is shown in the following formula:

[0048] The method described in this invention does not require iterative calculations, and its virtual stiffness adaptive variation result is as follows: Figure 2 As shown, when the environmental stiffness is 200 N / m in the first 20 seconds, the adaptive virtual stiffness is 2.5e-3 N / m. When the environmental stiffness changes to 300 N / m, the adaptive calculation result is 1.667e-3 N / m, and there are no obvious fluctuations or abrupt changes. Figure 3 The figure shows the results of virtual stiffness adaptive variation using the method described in this invention. It can be seen from the figure that the virtual damping remains unchanged before and after, and the calculated result is 42.64 N. In this simulation analysis and experimental test, the virtual damping parameter acting on the robotic arm is composed of environmental damping and... The weighting ratio determines the optimal virtual damping, since the damping in this experimental environment remains unchanged. It remains unchanged.

[0049] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style of the specification is merely for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in the embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An adaptive admittance method based on optimal control LQR theory, characterized in that, include: Step 1: Construct the environmental dynamics model and the robotic arm admittance control model, and derive the interaction dynamics model between the two; Step 2: Based on the interactive dynamics model constructed in Step 1, define the state variables and control inputs, and establish the standard form of the state-space equations; The state variables are defined as the pose tracking error of the robotic arm end effector and its time derivative, wherein the pose tracking error is the difference between the desired pose and the actual pose, and the time derivative is the difference between the desired velocity and the actual velocity; the control input is defined as the force deviation, which is the difference between the desired force exerted by the robotic arm end effector on the environment and the actual contact force. Step 3: Transform the state-space equations obtained in Step 2 into general matrix state equations suitable for optimal control, and define the state vector to include the pose tracking error and its time derivative. Furthermore, a quadratic performance index function is constructed to transform the admittance parameter optimization into an LQR problem; wherein, the integral term of the quadratic performance index function includes the weighted sum of squares of the state error and the weighted sum of squares of the control input; Step 4: Substitute the linear quadratic regulator framework established in Step 3 into the quadratic performance index function to transform the LQR problem into solving the Riccati matrix differential equation to obtain the positive definite symmetric matrix P. Based on the matrix P, the state-space equation obtained in step two, and the preset input energy consumption penalty weight matrix, the analytical expressions for virtual optimal stiffness and virtual optimal damping are derived. Step 5: Within the robotic arm's controlled sampling frequency, collect the environmental contact force and the actual pose of the robotic arm's end effector in real time, and set weighting coefficients based on task requirements; input the estimated values ​​of the current environmental stiffness and damping, along with the weighting coefficients, into the analytical expression obtained in Step 4 to calculate the optimal virtual stiffness and optimal virtual damping for the current period; based on the calculated optimal virtual stiffness and optimal virtual damping, and the expected force exerted by the robotic arm's end effector on the environment... Environmental forces The pose correction amount is calculated based on the admittance control model to correct the motion trajectory of the robotic arm.

2. The adaptive admittance method based on optimal control LQR theory according to claim 1, characterized in that, Step two specifically includes: S21: Define state variables and control inputs: where the state variable is selected as pose tracking error. and pose tracking error speed The control input is selected as the desired force exerted by the robotic arm's end effector on the environment. and the forces exerted by the end effector on the environment The difference between the two is defined as the force deviation u, which is used as the control input. S22: Based on the force deviation u As the core control input of the state-space model, a linear time-invariant state-space equation is constructed: ； in, To represent the first-order differential, It is the difference between the desired pose and the actual pose, i.e. ; It is the difference between the expected speed and the actual speed, that is... ; It refers to the surface quality of the environment; Here is the surface stiffness matrix of the environment. The environmental surface damping matrix; S23: Transform the state-space equations into a mathematical framework for linear optimal control design: ； Where A is the system matrix, determined by the environmental surface quality, damping, and stiffness, and B is the input matrix, which correlates the gain of the control input.

3. The adaptive admittance method based on optimal control LQR theory according to claim 1, characterized in that, The quadratic performance index function in step three is specifically defined as follows: ； in, It is a positive weight matrix, representing the weight of the steady-state error in the cost function; It is a positive weight matrix, representing the weight of the free overshoot in the cost function; It is a positive weight matrix, representing the weight of the input energy consumption in the cost function.

4. The adaptive admittance method based on optimal control LQR theory according to claim 1, characterized in that, The analytical expressions for the virtual optimal stiffness and virtual optimal damping in step four further include: against The robotic arm admittance model constructed in step one ,for In this case, the optimal stiffness and optimal damping are calculated. for: ； 。 5. The adaptive admittance method based on optimal control LQR theory according to claim 1, characterized in that, The analytical expressions for the virtual optimal stiffness and virtual optimal damping in step four further include: For grinding operations where the environmental equivalent quality is negligible, ignore The calculation, Optimal virtual damping for: 。 6. The adaptive admittance method based on optimal control LQR theory according to claim 1, characterized in that, In step five, the pose correction amount is superimposed on the original desired trajectory generation control command and sent to the robot arm's underlying controller for execution, thereby realizing the dynamic adaptive update of the admittance parameters.

7. The adaptive admittance method based on optimal control LQR theory according to claim 1, characterized in that, In step five, the estimated values ​​of the current environmental stiffness and damping are determined based on a lookup table method or an online estimation algorithm.

8. An adaptive admittance system for a robotic arm based on the optimal control LQR theory, characterized in that, include: The parameter acquisition submodule is used to input the preset desired trajectory, acquire the environmental contact force and the actual pose of the robotic arm end effector in real time, obtain the estimated values ​​of the current environmental stiffness and damping, and receive the set weight coefficients. The optimal impedance planning module internally stores closed-form analytical expressions for virtual stiffness and virtual damping derived based on linear quadratic optimal control theory; the optimal impedance planner is configured to receive data from the parameter acquisition submodule and execute steps one to four of the method described in any one of claims 1 to 7 to generate analytical expressions for virtual optimal stiffness and virtual optimal damping. The pose correction module is used to determine the virtual optimal stiffness and virtual optimal damping obtained by the optimal impedance planning module, as well as the environmental contact force output by the force sensor. And the pre-defined desired contact force between the robotic arm end and the environment. Input, and calculate the pose correction based on the admittance control model.

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