Method and system for controlling speed, impact and force by adjusting impedance parameters for casting polishing

Abstract

The invention provides a method for controlling speed, impact and force by adjusting impedance parameters for casting grinding. The method comprises the steps that the actual contact force of a robot end effector and the environment and the actual position of the robot end effector are collected in real time, and an impedance control model is built; impedance parameters of the impedance control model comprise a feedforward parameter, a quality parameter, a damping parameter and a rigidity parameter; second-order quality-spring-damping system stability analysis is conducted on the free motion stage of the robot through the model, and impedance parameters of the model are updated; meanwhile, parameter constraint analysis and energy dissipation principle analysis are conducted on the contact stage of the robot, and impedance parameters of the model are updated; and finally, generating a robot end force control instruction according to the model after parameter updating. According to the method, mechanical impedance parameters are dynamically adjusted, the speed of free movement, impact attenuation and constant force control are achieved, system energy is dissipated to the maximum extent, the impact force peak value is reduced, and therefore contact loss is avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial robot control, in particular to a method and system for adjusting impedance parameters to control speed, impact and force in casting polishing. BACKGROUND

[0002] In the industrial robot casting polishing operation, the interaction control between the robot and the environment is a key problem. The traditional fixed impedance control method performs poorly in dealing with complex uncertain environments, especially in the impact stage of the transition from free motion to constrained motion, which can easily produce a large force peak value, causing damage to the robot, tool and workpiece.

[0003] The existing impedance control method currently needs to accurately know the environmental characteristics (such as environmental stiffness) to achieve good force tracking performance. However, in actual casting polishing applications, there are often problems such as complex workpiece surface shape, uneven material, etc., and the environmental characteristics are often unknown and time-varying, making it difficult for traditional impedance control methods to achieve ideal results.

[0004] Although some researches have proposed adaptive impedance control and control methods based on switching strategies, these methods mostly require complex parameter tuning processes or rely on accurate environmental models. In particular, in the impact stage, due to the short duration, the response speed of conventional adaptive methods is often not enough to effectively suppress the impact force peak value. Therefore, it is necessary to design a method and system for adjusting impedance parameters to control speed, impact and force in casting polishing. SUMMARY

[0005] The purpose of the present application is to provide a method and system for adjusting impedance parameters to control speed, impact and force in casting polishing, based on an impedance control framework, by dynamically adjusting the mechanical impedance parameters to achieve speed, impact attenuation and constant force control of free motion, and maximize the dissipation of system energy and reduce the impact force peak value, thereby avoiding contact loss.

[0006] To achieve the above purpose, the present application provides the following scheme:

[0007] A method for adjusting impedance parameters to control speed, impact and force in casting polishing, comprising the following steps:

[0008] Real-time acquisition of the actual contact force between the robot end effector and the environment and the actual position of the robot end effector;

[0009] Constructing an impedance control model according to the actual contact force and the actual position; the impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters and stiffness parameters;

[0010] The stability of the robot's free motion phase is analyzed using an impedance control model, and the damping and stiffness parameters are updated based on the desired position and velocity obtained from the analysis.

[0011] The contact phase of the robot is analyzed by using an impedance control model to perform parameter constraint analysis and energy dissipation principle analysis, and the impedance parameters are updated based on the analysis results.

[0012] Based on the impedance control law, and combined with the impedance control model after parameter updates, the robot end effector force control command is generated.

[0013] Optionally, an impedance control model is constructed based on the actual contact force and actual location, including:

[0014] Construct the relationship between force and velocity in the robot impedance control process;

[0015] An impedance control model is constructed based on the relationship between force and velocity, actual contact force, and actual position.

[0016] Optionally, a second-order mass-spring-damped system stability analysis is performed on the robot's free motion phase using an impedance control model, and the damping and stiffness parameters are updated based on the desired position and velocity obtained from the analysis, including:

[0017] During the free motion phase, the impedance control equations are constructed based on the impedance control law when the robot is not in contact with the casting.

[0018] Steady-state analysis of the impedance control model is performed based on the impedance control equation, and the desired position and desired velocity are calculated.

[0019] The damping and stiffness parameters are updated according to the desired location and desired velocity, respectively.

[0020] The impedance control equations are solved based on the updated damping and stiffness parameters, and the mass parameters are calculated based on the solution results.

[0021] Optionally, parameter constraint analysis and energy dissipation principle analysis are performed on the robot's contact phase using an impedance control model, and the impedance parameters are updated based on the analysis results, including:

[0022] The stability of the robot's contact phase is analyzed using an impedance control model to obtain the constraint conditions for the impedance parameters.

[0023] By analyzing the energy dissipation principle of the constraints using Lyapunov functions, the switching criterion for impedance parameters is obtained.

[0024] The impedance parameters are updated according to the switching criteria.

[0025] Optionally, based on the impedance control law and combined with the parameter-updated impedance control model, force control commands for the robot's end effector are generated, including:

[0026] Based on the Newton-Euler dynamics equations, the dynamics equations of a robot subjected to external forces are constructed according to the impedance control model after parameter updates.

[0027] By performing a two-way kinematic mapping between joint space and Cartesian space on the robot's dynamic equations using the Jacobian matrix, the mapping relationship between Cartesian position and joint position can be obtained.

[0028] The actual output torque of each joint is calculated based on the impedance control equation and mapping relationship, and the robot end effector force control command is generated based on the actual output torque.

[0029] A system for adjusting impedance parameters to control speed, impact, and force in casting grinding, comprising:

[0030] Force / position sensor module, used to collect in real time the actual contact force between the robot end effector and the environment and the actual position of the robot end effector;

[0031] The impedance parameter calculation module is used to construct an impedance control model based on the actual contact force and actual position. It also performs a second-order mass-spring-damped system stability analysis on the robot's free motion phase using the impedance control model, and updates the damping and stiffness parameters based on the desired position and desired velocity obtained from the analysis. Furthermore, it performs parameter constraint analysis and energy dissipation principle analysis on the robot's contact phase using the impedance control model, and updates the impedance parameters based on the analysis results. The impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters, and stiffness parameters.

[0032] The inner loop position control module is used to generate robot end effector force control commands based on the impedance control law and the impedance control model after parameter updates.

[0033] According to specific embodiments provided by the present invention, the following technical effects are disclosed: The method for adjusting impedance parameters to control speed, impact, and force in casting grinding provided by the present invention includes: real-time acquisition of the actual contact force between the robot end effector and the environment and the actual position of the robot end effector; constructing an impedance control model based on the actual contact force and actual position; the impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters, and stiffness parameters; performing a second-order mass-spring-damped system stability analysis on the robot's free motion phase through the impedance control model, and updating the damping and stiffness parameters according to the desired position and desired speed obtained from the analysis; performing parameter constraint analysis and energy dissipation principle analysis on the robot's contact phase through the impedance control model, and updating the impedance parameters according to the analysis results; generating robot end effector force control commands based on the impedance control law and the updated impedance control model. This method achieves speed, impact attenuation, and constant force control of free motion by dynamically adjusting mechanical impedance parameters, maximizes the dissipation of system energy, and reduces the peak impact force, thereby avoiding contact loss. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a flowchart of a method for adjusting impedance parameters to control speed, impact, and force in casting grinding according to an embodiment of the present invention.

[0036] Figure 2 This is a block diagram of the control method according to an embodiment of the present invention. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] like Figure 1 and Figure 2As shown, the present invention provides a method for adjusting impedance parameters to control speed, impact, and force in casting grinding, comprising the following steps:

[0040] Step 100: Real-time acquisition of the actual contact force between the robot end effector and the environment, and the actual position of the robot end effector;

[0041] Step 200: Construct an impedance control model based on the actual contact force and actual location; the impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters, and stiffness parameters;

[0042] Step 300: Perform a second-order mass-spring-damped system stability analysis on the robot's free motion phase using an impedance control model, and update the damping and stiffness parameters based on the desired position and desired velocity obtained from the analysis.

[0043] Step 400: Perform parameter constraint analysis and energy dissipation principle analysis on the contact phase of the robot using the impedance control model, and update the impedance parameters based on the analysis results;

[0044] Step 500: Based on the impedance control law, generate robot end effector force control commands by combining the impedance control model with updated parameters.

[0045] In this embodiment, step 100 is implemented as follows: during the interaction between the robot and the unknown environment, the robot's end-effector contact force signal F is collected in real time. e and end position signal q d The displacement signal X in Cartesian space is obtained through transformation. d , and F e X d , and As the raw observation data, including the contact force signal F. e Displacement signal X is used to characterize the actual force between the robot's end effector and the environment. d , and Used to characterize changes in the end position, the two together constitute the original input of the closed-loop feedback.

[0046] Specifically, an impedance control model is constructed based on the actual contact force and actual location, including:

[0047] Construct the relationship between force and velocity in the robot impedance control process;

[0048] An impedance control model is constructed based on the relationship between force and velocity, actual contact force, and actual position.

[0049] In this embodiment, the mechanical resistance in step 200 is the relationship between the system's force and velocity, expressed as:

[0050]

[0051] Where Z represents impedance, f represents external force, v represents velocity, M represents system mass, B represents system damping, and K represents system stiffness.

[0052] Impedance control of a robot system involves applying a desired mass parameter M to the system. d Damping parameter B d and stiffness parameter K d Instead of actual mass, damping, and stiffness, the impedance control model is expressed as:

[0053]

[0054] Where F represents the environmental contact force, and X represents the actual position. For actual speed, For actual acceleration, X ref Represents a reference position. Represents reference speed. This represents the reference acceleration. This expression is general; all other expressions can be considered special cases of this expression. The expression can also be expressed as:

[0055]

[0056] Where FF is the feedforward parameter.

[0057] Specifically, a second-order mass-spring-damped system stability analysis is performed on the robot's free motion phase using an impedance control model. Based on the desired position and velocity obtained from the analysis, the damping and stiffness parameters are updated, including:

[0058] During the free motion phase, the impedance control equations are constructed based on the impedance control law when the robot is not in contact with the casting.

[0059] Steady-state analysis of the impedance control model is performed based on the impedance control equation, and the desired position and desired velocity are calculated.

[0060] The damping and stiffness parameters are updated according to the desired location and desired velocity, respectively.

[0061] The impedance control equations are solved based on the updated damping and stiffness parameters, and the mass parameters are calculated based on the solution results.

[0062] In this embodiment, in step 300, lowercase letters are used instead of uppercase letters for one-dimensional variables such as force, position, and velocity. When F = 0, i.e., before the robot contacts the casting, the control equation expression of the system, based on the control law, is as follows: Then the expected position x is calculated. ∞ and expected speed The final value is:

[0063]

[0064] A non-zero stiffness will cause the robot to reach the distance given by the above equations and stop there, corresponding to position control. Zero stiffness will cause the system to reach a constant velocity, corresponding to velocity control. The former is suitable for the free motion phase, while the latter is more practical for impact control after contact. Therefore, the stiffness K should be selected first. d To ensure the robot reaches the desired final position x ref Then select damping to ensure the desired final velocity v. ref The expression is:

[0065]

[0066] Then consider mass M. d And according to M d The roots of the characteristic polynomial of the impedance control equation are:

[0067]

[0068] Where mass M d It is the only parameter that is practically unimportant during free motion, and the value assigned to the quality is very low. During the free motion of the grinding process, the desired position x... ref Expected speed v ref If both the feedforward and the mass parameters are known, then the mass value that causes insufficient damping of the system can be obtained from the above equation, expressed as:

[0069]

[0070] Specifically, the contact phase of the robot is analyzed for parameter constraints and energy dissipation principles using an impedance control model. Based on the analysis results, the impedance parameters are updated, including:

[0071] The stability of the robot's contact phase is analyzed using an impedance control model to obtain the constraint conditions for the impedance parameters.

[0072] By analyzing the energy dissipation principle of the constraints using Lyapunov functions, the switching criterion for impedance parameters is obtained.

[0073] The impedance parameters are updated according to the switching criteria.

[0074] In this embodiment, step 400 analyzes the constraints on the impedance parameters during robot grinding from the perspective of the stability of a second-order mass-spring-damped system. When the robot grinds the casting, the environment is rigid, and the reaction force of the environment is f = -K. e (xx e ), here K e x represents the stiffness of the casting. e The coordinates represent the surface of the environment, with the negative sign indicating direction. Combined with the impedance control law, we can obtain... The roots of the characteristic polynomial are: The final value of the position x ∞ (The system's reference position x can be approximated) ref )for:

[0075]

[0076] The final value of the force f ∞ (The reference force f of the system can be approximated) ref )for:

[0077]

[0078] It should be noted that choosing K... d =0 or K d <<K e This not only allows the system to be underdamped, but also allows the system to reach the reference force value, independent of environmental characteristics. The environmental stiffness K during the grinding process... e It is at the level of 10^5, when K d When the value is very small (below 100), its impact on the entire system is negligible. The feedforward term ff of the impedance parameter during the grinding process is slightly larger than the desired system force f. ref M d Values ​​follow During restricted motion, the system is typically underdamped. When oscillating around the equilibrium point, kinetic energy is converted into potential energy, and vice versa. The total energy of a dissipative system at any given time is the sum of its potential and kinetic energy, expressed as:

[0079]

[0080] Where k is stiffness and m is the mass of the system. The position of the environment is assumed to be on a positive coordinate system; a positive velocity indicates the robot is tilting towards the environment, a negative velocity indicates it is moving away, and vice versa for perfect symmetry.

[0081] Furthermore, step 400 analyzes the impedance parameter switching from the perspective of energy dissipation principles to derive the optimal switching criterion under constraints. Specifically, it uses an energy-like Lyapunov function for analysis, the expression of which is: This function represents the distance x from the equilibrium point in the phase plane. ∞ The Euclidean distance. The term is equivalent to the elastic potential energy of the environment, scaled by a factor that depends on the unit. The term is proportional to the kinetic energy. Therefore, it can be said that V is equivalent to the total energy of the system, and any quadratic function of velocity and distance from the origin will have the same effect, with its derivative expressed as: Combining the impedance control law, we get: Substituting this into the derivative expression, we get:

[0082] It should be noted that, under the constraints, the mass, stiffness, damping, and feedforward terms of the impedance parameters switch between two values, and their values ​​follow the results of the stability analysis based on the second-order system described above.

[0083] The switching criteria for quality parameters as system state changes are as follows: To understand the impact of quality on system behavior, the following is derived: Variations on mass, substituted into the impedance control law, yield:

[0084]

[0085] When the expression is positive, energy dissipates more slowly as mass increases; when the expression is negative, energy dissipates more quickly as mass increases. When the expression results in a negative number, a high value is assigned to the mass, and vice versa, resulting in the expression:

[0086]

[0087] if If positive, the mass-related term indicates that energy is absorbed from the system; otherwise, it indicates that energy is transferred. It is important to note that... The derivative corresponds to the square of the velocity, and therefore to the square of the kinetic energy. Therefore... This indicates that kinetic energy is decreasing, meaning it is being converted into elastic potential energy. Assigning a smaller mass value would mean reducing the amount of kinetic energy to be dissipated. Conversely, when... At that time, kinetic energy is increasing, meaning potential energy is being converted in dynamics. It's important to note the switching criterion for the mass term when... When the quality is used, the value of the previous moment is adopted. This criterion applies to the switching of all impedance parameters.

[0088] The switching criteria for stiffness parameters as a function of system state are as follows: To understand the impact of stiffness on system behavior, Regarding the variation of stiffness:

[0089]

[0090] Considering the environmental stiffness during polishing is on the order of 10^5, therefore the above For K d The second term of the variation can be approximated as 0, and can be rewritten as: Based on the principle of mass switching, and considering that the mass term is positive and its position is always positive in this embodiment, the following stiffness switching law is proposed according to the above formula to maximize energy dissipation:

[0091] The switching criteria for damping parameters as the system state changes are as follows: Regarding the variation of damping: Since this value is always negative, this term is always dissipative. Switching the damping does not improve the performance of shock control. Therefore, this implementation does not design a damping switching criterion.

[0092] The specific switching criteria for feedforward parameters as the system state changes are as follows: Variations of the feedforward term: In this embodiment, during actual polishing, M... d <<K e +K d Therefore, the second term of the above partial derivative can be approximated as 0, and can be rewritten as: Similarly, based on the mass switching principle and considering that the mass term is positive, the following stiffness switching law is proposed according to the above formula to maximize energy dissipation:

[0093]

[0094] When the velocity is positive, the robot is penetrating the environment. A low feedforward will result in a lower penetration depth. When the velocity is negative, the robot is moving away from the environment, and the feedforward should be high to push it back in and prevent bounce. In both cases, the feedforward parameters are chosen to be opposite to the robot's motion and act as a brake.

[0095] The specific steps of step 500 in this implementation include:

[0096] Step 501: Based on the Newton-Euler dynamics equations, construct the robot dynamics equations under external forces according to the impedance control model after parameter updates.

[0097] Specifically, the robot's dynamic equations are expressed as follows: Where τ is the vector of motor torque, J(q) is the Jacobian matrix of the robot, F is the vector of external forces acting on the robot's end effector, and M(q) is the robot's inertia matrix. These are the centrifugal force matrix and Coriolis force matrix of the robot, G(q) is the gravitational torque vector on the motor, and q, and These are vectors representing joint position, velocity, and acceleration, respectively. Solving this expression for acceleration yields:

[0098] Step 502: Perform a two-way kinematic mapping between joint space and Cartesian space on the robot's dynamic equations using the Jacobian matrix to obtain the mapping relationship between Cartesian positions and joint positions.

[0099] Specifically, the velocity in the Cartesian coordinates of the robot's end effector. With joint velocity The mapping formula is:

[0100]

[0101] Solving for velocity by combining the mapping formula and the acceleration solution formula The derivative is obtained as follows:

[0102] It should be noted that the robot system in this embodiment is highly nonlinear. The acceleration depends not only on the motor torque and external force, but also on the inertia matrix, centrifugal force, Corylova force, gravity, and robot Jacobian matrix. The magnitude of these values ​​varies depending on the joint position and velocity.

[0103] Step 503: Calculate the actual output torque of each joint based on the impedance control equation and mapping relationship, and generate robot end effector force control commands based on the actual output torque.

[0104] Specifically, based on the expression of the impedance control model, combined with the position loop x d The relevant input instructions and mapping formulas can calculate the actual output torque τ of each joint of the robot. d This controls the robot to move to a designated position, thus forming a closed-loop force control. The system's acceleration is expressed as: The subscript d represents the actual measured data, and the same expression applies below. The acceleration of the joint is calculated using the mapping formula:

[0105]

[0106] The formula for calculating the actual output torque is:

[0107]

[0108] Where M(q), G(q) is determined by the robot's own parameters, J(q) is known, and the impedance parameter M... d B d K d FF is determined by the parameter update process in the above steps, and F is preset by the user in advance.

[0109] The present invention also provides a system for adjusting impedance parameters to control speed, impact, and force in casting grinding, comprising:

[0110] Force / position sensor module, used to collect in real time the actual contact force between the robot end effector and the environment and the actual position of the robot end effector;

[0111] The impedance parameter calculation module is used to construct an impedance control model based on the actual contact force and actual position. It also performs a second-order mass-spring-damped system stability analysis on the robot's free motion phase using the impedance control model, and updates the damping and stiffness parameters based on the desired position and desired velocity obtained from the analysis. Furthermore, it performs parameter constraint analysis and energy dissipation principle analysis on the robot's contact phase using the impedance control model, and updates the impedance parameters based on the analysis results. The impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters, and stiffness parameters.

[0112] The inner loop position control module is used to generate robot end effector force control commands based on the impedance control law and the impedance control model after parameter updates.

[0113] The beneficial effects of this invention are as follows:

[0114] 1) Full-process control is achieved through a unified impedance control framework, which can seamlessly connect the free motion, impact transition and contact stages, avoiding the instability problem caused by switching multiple controllers in traditional methods.

[0115] 2) The design with zero stiffness significantly improves environmental adaptability, making force tracking accuracy unaffected by environmental stiffness, and is particularly suitable for industrial scenarios with unknown environmental stiffness, such as casting grinding.

[0116] 3) The parameter switching strategy achieves excellent impact control through directional energy dissipation, effectively suppressing the peak impact force and thus avoiding contact loss and multiple rebound phenomena.

[0117] 4) Only the force / position sensor signals built into the robot are required, without the need for additional environmental stiffness recognition or complex learning processes. The computational load is small, which fully meets the needs of industrial real-time control.

[0118] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0119] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for adjusting impedance parameters to control speed, impact, and force in grinding castings, characterized in that, Includes the following steps: Real-time acquisition of the actual contact force between the robot's end effector and the environment, and the actual position of the robot's end effector; An impedance control model is constructed based on the actual contact force and the actual position; the impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters, and stiffness parameters. The stability analysis of the robot's free motion phase is performed using the impedance control model, based on the desired position and desired velocity obtained from the analysis. The damping parameters and stiffness parameters are then updated accordingly. The impedance control model is used to perform parameter constraint analysis and energy dissipation principle analysis on the contact phase of the robot, and the impedance parameters are updated based on the analysis results. Based on the impedance control law, and combined with the impedance control model after parameter updates, the robot end effector force control command is generated.

2. The method for adjusting impedance parameters to control speed, impact, and force for grinding castings according to claim 1, characterized in that, An impedance control model is constructed based on the actual contact force and the actual position, including: Construct the relationship between force and velocity in the robot impedance control process; The impedance control model is constructed based on the relationship between force and velocity, the actual contact force, and the actual position.

3. The method for adjusting impedance parameters to control speed, impact, and force for grinding castings according to claim 1, characterized in that, The stability analysis of the robot's free motion phase is performed using the impedance control model, based on a second-order mass-spring-damped system. The damping and stiffness parameters are then updated according to the desired position and velocity obtained from the analysis, including: During the free motion phase, an impedance control equation is constructed based on the impedance control law when the robot is not in contact with the casting. Based on the impedance control equation, a steady-state analysis is performed on the impedance control model to calculate the desired position and the desired velocity. The damping parameter and the stiffness parameter are updated according to the desired position and the desired velocity, respectively. The impedance control equation is solved based on the updated damping and stiffness parameters, and the mass parameters are calculated based on the solution results.

4. The method for adjusting impedance parameters to control speed, impact, and force for grinding castings according to claim 1, characterized in that, The impedance control model is used to perform parameter constraint analysis and energy dissipation principle analysis on the robot's contact phase, and the impedance parameters are updated based on the analysis results, including: The stability analysis of the robot's contact phase is performed using the impedance control model to obtain the constraint conditions for the impedance parameters. The energy dissipation principle of the constraints is analyzed by Lyapunov function to obtain the switching criterion of impedance parameters; The impedance parameters are updated according to the switching criteria.

5. The method for adjusting impedance parameters to control speed, impact, and force for grinding castings according to claim 3, characterized in that, Based on the impedance control law, and combined with the parameter-updated impedance control model, force control commands for the robot's end effector are generated, including: Based on the Newton-Euler dynamics equations, the dynamics equations of a robot subjected to external forces are constructed according to the impedance control model after parameter updates. By performing a bidirectional kinematic mapping between joint space and Cartesian space on the robot's dynamic equations using the Jacobian matrix, the mapping relationship between Cartesian positions and joint positions is obtained. The actual output torque of each joint is calculated based on the impedance control equation and the mapping relationship, and the robot end effector force control command is generated based on the actual output torque.

6. A system for adjusting impedance parameters to control speed, impact, and force in grinding castings, characterized in that, include: Force / position sensor module, used to collect in real time the actual contact force between the robot end effector and the environment and the actual position of the robot end effector; The impedance parameter calculation module is used to construct an impedance control model based on the actual contact force and the actual position. It also performs a second-order mass-spring-damped system stability analysis on the robot's free motion phase using the impedance control model, and updates the damping parameters and stiffness parameters based on the desired position and desired velocity obtained from the analysis. Furthermore, it performs parameter constraint analysis and energy dissipation principle analysis on the robot's contact phase using the impedance control model, and updates the impedance parameters based on the analysis results. The impedance parameters of the impedance control model include: feedforward parameters, mass parameters, damping parameters, and stiffness parameters. The inner loop position control module is used to generate robot end effector force control commands based on the impedance control law and the impedance control model after parameter updates.

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