Robot nonlinear contact force control method and system based on Maxwell-fractional impedance model

Abstract

The invention belongs to the related technical field of robot force control, and discloses a robot nonlinear contact force control method and system based on a Maxwell-fractional impedance model. The method comprises the following steps that a force position controller based on a Maxwell-fractional order impedance model is adopted to control a robot end tool to scan the surface of a soft material to be scanned in a horizontal plane according to a preset scanning track, and constant force contact between the robot end tool and the soft material to be scanned is kept in the height direction; the constant force contact is realized according to the following mode: presetting an initial position where a robot tail end tool is contacted with a soft material to be scanned, and calculating an optimal position of the robot tail end tool in a height direction in real time when a contact force tracking steady-state error of the robot tail end is zero in a scanning process; and the position of the robot end tool in the height direction is adjusted in real time according to the optimal position. According to the invention, the problem of force safety control during scanning of the soft material watchcase is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to robotic force control, and more specifically, relates to a method and system for non-linear contact force control of a robot based on a Maxwell-fractional impedance model. Background Art

[0002] In order to achieve the stability of a robot's scanning task in a soft material environment (such as silicone, human tissue, and foam), a more stable and precise force control method is required at the robot's end effector. Considering the safety of robot control, most robots do not open the underlying force / torque control interface. Therefore, a position-based control method needs to be selected to design the force controller. Position-based impedance control is widely used in the compliant control tasks of collaborative robots, but traditional impedance control methods have disadvantages such as large position fluctuations, poor disturbance resistance, low force tracking accuracy, and easy occurrence of force shocks. When the robot's end effector makes contact with the environment, it is difficult to simultaneously achieve rapid contact establishment and safety.

[0003] For interaction tasks in a soft material environment, it is necessary to have a certain understanding of the characteristics of the environment, and generally, it needs to be described in the form of model representation. Therefore, the parameters of the environment model also need to be identified. Inaccurately estimated environment parameters cannot accurately describe the characteristics of the environment, which will affect the effect of contact force control in the robot's interaction task. The force control effect of an impedance controller is highly correlated with the input reference position. Therefore, the method of online real-time updating of the reference position can significantly improve the force tracking accuracy. Moreover, in the case of environmental changes, real-time updating of the reference position can ensure the safety of the robot's interaction with the environment.

[0004] Therefore, in order to improve the force control accuracy and safety of a robot's scanning task in a soft material environment, it is necessary to improve the traditional impedance controller model and propose a force control method suitable for a soft silicone material environment. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement requirements of the prior art, the present invention provides a method and system for non-linear contact force control of a robot based on a Maxwell-fractional impedance model, which solves the problem of safe force control during the scanning of a soft material shell.

[0006] To achieve the above object, according to one aspect of the present invention, a method for non-linear contact force control of a robot based on a Maxwell-fractional impedance model is provided. The method includes the following steps:

[0007] A force-position controller based on the Maxwell-fractional impedance model is used to control the end-effector of the robot to scan the surface of the soft material to be scanned along a preset scanning trajectory in the horizontal plane, and a constant force contact between the end-effector of the robot and the soft material to be scanned is maintained in the height direction. The constant force contact is achieved in the following manner:

[0008] The initial position of the contact between the end-effector of the robot and the soft material to be scanned is preset, and the optimal position of the end-effector of the robot in the height direction is calculated in real time when the steady-state error of the contact force tracking at the end of the robot during the scanning process is zero. The position of the end-effector of the robot in the height direction is adjusted in real time according to the optimal position.

[0009] Further preferably, the calculation of the steady-state error of the contact force tracking is carried out in the following manner:

[0010] The actual position of the end-effector of the robot in the height direction is calculated by using the force-position controller;

[0011] The non-linear contact force model of the soft material to be scanned is transformed into a linear contact force model, and the contact force deviation between the end-effector of the robot and the soft material to be scanned is calculated by using the linear contact force model;

[0012] A contact force steady-state error relationship is established by combining the actual position of the end-effector of the robot in the height direction and the contact force deviation.

[0013] Further preferably, the formula for the actual position of the end-effector of the robot in the height direction is as follows:

[0014]

[0015] where x a is the calculated actual height position, x r is the reference position in the height direction, is the position deviation amount, Δf is the difference between the actually measured force and the preset desired contact force, and Φ(s) is the transfer function of the force-position controller.

[0016] Further preferably, the linear contact force model of the soft material to be scanned is as follows:

[0017]

[0018] where F z is the contact force in the height direction, are the penetration amount and penetration speed of the end-effector on the soft material respectively, F d is the preset desired contact force, and K e , λ, and β are the stiffness coefficient, damping coefficient, and exponential term coefficient identified from the non-linear contact force model of the soft material respectively.

[0019] Further preferably, the formula for the contact force deviation is as follows:

[0020] Wherein, F z is the contact force in the height direction, and F d is the preset desired contact force. are respectively the environmental stiffness and damping parameters after linearization of the soft material nonlinear contact force model, x e and are respectively the surface position and change speed of the soft material, x a and are respectively the actual spatial position and speed of the center point of the end tool.

[0021] Further preferably, the steady-state error of the contact force tracking is calculated in the following manner:

[0022]

[0023] Wherein, B is the control damping gain of the force-position controller, and are respectively the environmental stiffness and damping parameters after linearization of the soft material nonlinear contact force model, x r and are respectively the desired position and desired speed of the center of the end tool.

[0024] Further preferably, the calculation formula for the optimal position is as follows:

[0025]

[0026] Wherein, and are respectively the environmental stiffness and damping parameters after linearization of the soft material nonlinear contact force model, x e is the surface position of the soft material, is the speed of the center point of the end tool, and F d is the preset desired contact force.

[0027] Further preferably, the formulas for and β are as follows:

[0028]

[0029]

[0030] Wherein, K e , λ, and β are respectively the stiffness coefficient, damping coefficient, and exponential term coefficient identified by the soft material nonlinear contact force model, and F d is the preset desired contact force, is the iteration parameter in the identification process.

[0031] Further preferably, the formula of the force-position controller is as follows:

[0032]

[0033] where M, B, and K are the desired mass, damping, and stiffness coefficients of the controller, β D is the fractional differential operator, λ I is the fractional integral operator, s is the Laplace operator that transforms the control law from the time domain to the complex frequency domain, E x (s) and E f (s) are the Laplace transforms of the position error and the force error, respectively.

[0034] According to another aspect of the present invention, there is provided a system for robot non-linear contact force control based on the Maxwell-fractional impedance model. The system includes an actuator for performing the above-mentioned method for robot non-linear contact force control based on the Maxwell-fractional impedance model.

[0035] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following beneficial effects are achieved:

[0036] 1. By using the force-position controller based on the Maxwell-fractional impedance model, the present invention makes the contact force tracking steady-state error at the end of the robot zero during the scanning process, realizes the constant-force contact between the end tool of the robot and the soft material to be scanned during scanning, and solves the problem of safe force control during the scanning of the soft material surface.

[0037] 2. On the one hand, the present invention controls the robot to move along a preset trajectory in the horizontal plane through the force-position controller, and on the other hand, makes a constant-force contact with the soft material to be scanned in the height direction, realizing the control in two dimensions during the movement of the robot, with high control precision.

[0038] 3. The present invention calculates the contact force deviation between the end tool of the robot and the soft material to be scanned by using the non-linear contact force model of the soft material to be scanned, fully considers the physical properties of the material itself, and the deviation calculated by the force model includes the contact characteristics of the soft material, describes the relationship between the contact force change caused by the scanning position of the end tool and the deformation of the soft material, and based on this, the control position output by the force-position control can be adjusted in time.

[0039] 4. The contact force tracking steady-state error established by the present invention is analyzed by combining the end control position output by the force-position controller and the contact force model of the soft material. To ensure that the force tracking steady-state error is as close to zero as possible, the optimal position of the robot end in the height direction is obtained in real time as the reference trajectory and adjusted online in real time. The robot can improve the force tracking accuracy by tracking this trajectory. Description of the Drawings

[0040] Figure 1 It is a flowchart of a robot non - linear contact force control method based on the Maxwell - fractional - order impedance model constructed according to the preferred embodiment of the present invention.

[0041] Figure 2 It is a schematic diagram of calibrating the end TCP coordinate system according to the preferred embodiment of the present invention.

[0042] Figure 3 It is a schematic diagram of the initial reference trajectory generated by teaching points according to the preferred embodiment of the present invention. Among them, (a) is the trajectory schematic diagram when the initial reference trajectory is a straight line, and (b) is the trajectory schematic diagram when the initial reference trajectory is a curve.

[0043] Figure 4 It is a robot control framework diagram based on the Maxwell - fractional - order impedance model according to the preferred embodiment of the present invention.

[0044] Figure 5 It is a robot excitation trajectory diagram for estimating the parameters of the non - linear environmental force HC model according to the preferred embodiment of the present invention.

[0045] Figure 6 It is the environmental parameters obtained based on the exponentially weighted least - squares method according to the preferred embodiment of the present invention. Among them, (a) is the estimated environmental stiffness, (b) is the estimated environmental damping, and (c) is the exponential term coefficient.

[0046] Figure 7 It is a diagram of the actual trajectory position at the end of the robot soft silicone material scanning experiment according to the preferred embodiment of the present invention. Among them, (a) is the actual trajectory under the straight - line reference trajectory, and (b) is the actual trajectory under the circular reference trajectory.

[0047] Figure 8 It is a schematic diagram of the experimental device for the robot soft silicone material scanning experiment according to the preferred embodiment of the present invention.

[0048] Figure 9 It is a diagram of the actual force tracking effect of the robot according to the preferred embodiment of the present invention. Among them, (a) is the contact force under the straight - line reference trajectory, and (b) is the contact force under the circular reference trajectory. Detailed Implementation Manner

[0049] To make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0050] As Figure 1 shown, a robot non-linear contact force control method based on the Maxwell-fractional impedance model specifically includes the following steps:

[0051] (a) Perform end-effector calibration and real-time gravity compensation of the force sensor, and generate the initial motion trajectory of the robot according to the taught points.

[0052] Connect the robot and the computer controller, and use the UR robot teach pendant to perform TCP calibration on the end-effector to determine the coordinates of the center point of the end-effector. In the embodiments of the present invention, the transformation matrix of the end-effector center relative to the robot flange is:

[0053]

[0054] As Figure 2 shown, this figure is a schematic diagram of the coordinate system of the TCP after calibration. Perform gravity compensation on the end-effector, and generate the initial robot scanning trajectory according to the position of the soft silicone surface, Figure 3 which is the initial reference trajectory generated by the trajectory generator.

[0055] (b) Design a robot force-position controller based on the Maxwell-fractional impedance model, and simultaneously control the scanning trajectory and the contact force to ensure accurate and stable scanning on the soft silicone material.

[0056] Based on the idea of the Maxwell model, modify the classical impedance controller to design a control law that simultaneously realizes robot contact force and position tracking. The control equation is as follows:

[0057]

[0058] where X a , X r are the actual position and the input reference position of the robot respectively, and the difference between the two is defined as the disturbance amount of the position E = X a - X r ; ΔF = F d - F e is the difference between the desired contact force and the actual contact force; M, B, and K are the inertia coefficient, damping coefficient, and stiffness coefficient respectively.

[0059] Based on the modified Maxwell impedance control equation, since fractional calculus has the characteristics of memory and heredity in describing nonlinear systems and can better describe the dynamic characteristics of soft material interactions, the force error integrator is changed to a fractional integrator. The controller equation is as follows:

[0060]

[0061] In the above equation, is the output of the fractional integrator of the force error. According to the Grünwald-Letnikov definition of the fractional order, we have:

[0062]

[0063] When choosing a sufficiently small step size h during control, we have

[0064] where t 0 is the starting memory time of the fractional integrator, t is the current time, λ I is the integration coefficient, h is the step size value, should take the closest integer, and φ j is the binomial coefficient. Since Γ(x + 1) = xΓ(x), where Γ(·) is the Gamma function, the recurrence relation of the binomial coefficient φ j is as follows:

[0065]

[0066] The binomial coefficient calculated through the recurrence relation has higher calculation accuracy and can avoid large errors caused by direct calculation of the Gamma function. Therefore, the binomial coefficient φ j is calculated according to the following rules:

[0067]

[0068] Analyzing the impedance control equation for the position quantity, the position error differential is changed to a fractional differentiator. Due to the influence of real-time performance and complexity in practical applications on the effect of the fractional differentiator, a superimposer of the spring-damping and mass-spring-damping models is designed for approximation. Using the method of the superimposer for equivalent processing can achieve the same effect and has better real-time performance. Based on the Maxwell-fractional control approximation model as follows

[0069]

[0070] where β D is the differential operator of the fractional differentiator, E x (s), E f(s) are the Laplace transforms of the position error and the force error respectively. The schematic diagram of the control framework in step (b) is as Figure 4 shown.

[0071] (c) Construct a non-linear environmental force model and use the exponentially weighted least squares method to identify the model parameters online.

[0072] The weighted least squares method is used to identify the environmental modeling parameters, and a time-varying forgetting factor θ k = 1 - γ k is adopted during the identification process, where u is the forgetting factor change speed factor, u = 2 is taken during the identification process, and the sensor data output rate is 500 HZ. The time-varying forgetting factor can improve the rapidity and stability of the identification process.

[0073] The dynamic modeling of the robot-environment interaction is the Hunt–Crossley (HC) model, and the contact force is characterized as where δx(t) = x(t) - x e (t). The input robot excitation trajectory during the experiment is as Figure 5 shown. After logarithmic linearization and discretization, we can obtain where the meanings of the various parameters are:

[0074]

[0075] The intermediate quantities calculated using the EWRLS method for identification are as follows, L k+1 , P k+1 are the adaptive gain vector and the covariance matrix respectively.

[0076]

[0077] The parameters estimated by the EWRLS method are iteratively updated, and the update equations are as follows.

[0078]

[0079] Finally, the parameters of the HC model are as follows, and the parameter estimation results are as Figure 6 shown.

[0080]

[0081] (d) Analyze the force tracking steady-state error of the robot force-position controller and design an online trajectory generator based on the non-linear environmental force model.

[0082] Analyze the interaction relationship between the end normal and the environment. Assume that when the interaction between the robot end and the environment tends to be balanced, δx = δx sThe condition is that the HC model is approximately linearized using the Taylor expansion.

[0083]

[0084] At the equilibrium position, it satisfies By calculating F e The partial derivative terms can be used to obtain that the contact force between the robot end and the environment approximately satisfies a linear relationship, and the linear relationship formula is as follows.

[0085]

[0086] The steady-state error of contact force tracking is obtained in the following way:

[0087] Use the force-position controller to calculate the actual position of the robot end tool in the height direction;

[0088]

[0089] where x a is the calculated actual height position, x r is the reference position in the height direction, is the position deviation, Δf is the difference between the actual measured force and the preset desired contact force, and Φ(s) is the transfer function of the control law of the designed force-position controller. Establish a non-linear contact force model of the soft material to be scanned, and use the force model to calculate the contact force deviation between the robot end tool and the soft material to be scanned;

[0090]

[0091] where, F z represents the contact force in the height direction, F d is the preset desired contact force, are the environmental stiffness and damping parameters after linearizing the non-linear contact force model of the above soft material, respectively represent the surface position and change speed of the soft material, x a and are respectively the actual spatial position and speed of the center point of the end tool.

[0092] Combine the actual position of the robot end tool in the height direction and the contact force deviation to establish a contact force steady-state error relationship.

[0093] Regarding the impedance controller as an adjustment of the position deviation on the reference trajectory, combined with the approximate linear relationship of the environmental force, the force tracking steady-state error of the Maxwell-fractional impedance controller can be obtained as follows.

[0094]

[0095] To ensure that the force tracking error of the robot end-effector in the soft silicone material environment scanning task is zero, it is necessary to satisfy lim t→∞ Δf(t) = 0, then the calculation of the reference trajectory satisfies Approximate the reference trajectory velocity as the actual end-effector velocity at the previous moment to avoid sudden changes in contact force caused by drastic changes in velocity. Construct an online robot reference trajectory generator Input the reference position into the robot Maxwell-fractional order impedance controller in real time. The running trajectory of the robot end-effector is as Figure 7 shown.

[0096] In a specific embodiment of the present invention, the soft material used in the experiment is silicone, with the model number of Blue Butterfly LDX / V6. Apply a coupling agent evenly on the surface area to be scanned for lubrication and close fitting. Drag the end-effector above the silicone plate by hand and record the initial environmental position x e . Conduct parameter identification of the non-linear HC model, and the online reference trajectory generator outputs the reference trajectory in real time Input the updated reference trajectory into the Maxwell-fractional order impedance controller, and output the pose information of the trajectory points where the robot is about to move. Use inverse kinematics to calculate the robot joint angle q from the pose information, and send the target joint angle to the robot motion controller to control the motion of the robot. As Figure 8 shown, it is a schematic diagram of the experimental device.

[0097] The specific parameters used in the actual experiment are as follows. The impedance control parameters are:

[0098] M = 20, B = 1000, K = 4000

[0099] The parameters of the fractional order controller are:

[0100] λ I = β D = 0.7, h = 0.02, L = 2000

[0101] The desired force is set to 10N, and the maximum safety threshold of the force is 30N. As Figure 9 shown, this figure is the graph of the change in the non-linear environmental scanning contact force of the robot based on the Maxwell-fractional order impedance model. MFO-IC (Maxwell-Fractional Order Impedance Control) represents the method proposed in the present invention.

[0102] It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robot nonlinear contact force control method based on Maxwell-fractional impedance model, characterized in that: The method comprises the following steps: A force position controller based on the Maxwell-fractional impedance model is used to control the robot end tool to scan the surface of the soft material to be scanned according to a preset scanning trajectory in the horizontal plane, and to maintain a constant force contact between the robot end tool and the soft material to be scanned in the height direction. The constant force contact is achieved in the following way: The initial position of the robot end tool in contact with the soft material to be scanned is preset, and the optimal position of the robot end tool in the height direction when the contact force tracking steady-state error of the robot end is zero during the scanning process is calculated in real time. The position of the robot end tool in the height direction is adjusted in real time according to the optimal position.

2. A robot nonlinear contact force control method based on Maxwell-fractional impedance model as claimed in claim 1, characterized in that: The contact force tracking steady-state error is calculated as follows: Utilizing the force position controller to calculate the actual position of the robot end tool in the height direction; The nonlinear contact force model for scanning soft materials is converted into a linear contact force model, and the contact force deviation between the robot end tool and the soft material to be scanned is calculated using the linear contact force model; A contact force steady-state error relationship is established by combining the actual position of the robot end tool in the height direction and the contact force deviation.

3. The robot nonlinear contact force control method based on the Maxwell-fractional impedance model as claimed in claim 2, characterized in that: The formula for the actual position of the robot end tool in the height direction is as follows: Among them, x a is the calculated actual height position, x r is the reference position in the height direction, is the position deviation, Δf is the difference between the actual measured force and the preset expected contact force, and φ(s) is the transfer function of the force position controller.

4. A robot nonlinear contact force control method based on Maxwell-fractional impedance model as claimed in claim 2 or 3, characterized in that: The linear contact force model of the soft material to be scanned is as follows: Among them, F z is the contact force in the height direction, are the penetration amount and penetration speed of the end tool on the soft material, F d is the preset expected contact force, K e , λ, β are the stiffness coefficient, damping coefficient and exponential term coefficient for the identification of nonlinear contact force model of soft materials respectively.

5. The robot nonlinear contact force control method based on the Maxwell-fractional impedance model as claimed in claim 4, characterized in that: The formula for the contact force deviation is as follows: Among them, F z is the contact force in the height direction, F d is the preset expected contact force, are the environmental stiffness and damping parameters of the linearized nonlinear contact force model of soft materials, x e and are the surface position and speed of change of the soft material, x a and are the actual spatial position and velocity of the center point of the end tool, respectively.

6. A robot nonlinear contact force control method based on Maxwell-fractional impedance model as claimed in claim 1 or 5, characterized in that: The contact force tracking steady-state error is calculated as follows: Where B is the control damping gain of the force position controller, and are the environmental stiffness and damping parameters of the linearized nonlinear contact force model of soft materials, respectively. r and are the desired position and velocity of the end tool center respectively.

7. A robot nonlinear contact force control method based on Maxwell-fractional impedance model as claimed in claim 1 or 5, characterized in that: The calculation formula of the optimal position is as follows: in, and They are the environmental stiffness and damping parameters of the linearized nonlinear contact force model of soft materials, and x e is the surface position of the soft material, is the speed of the tool center point at the end, F d is the preset desired contact force.

8. The robot nonlinear contact force control method based on the Maxwell-fractional impedance model as claimed in claim 7, characterized in that: Said The formulas for and β are as follows: Among them, K e ,λ,β are the stiffness coefficient, damping coefficient and exponential term coefficient for the identification of nonlinear contact force model of soft materials, F d is the preset expected contact force, is the iteration parameter in the identification process.

9. A robot nonlinear contact force control method based on Maxwell-fractional impedance model as claimed in claim 1 or 5, characterized in that: The formula of the force position controller is as follows: Among them, M, B, K are the desired mass, damping, and stiffness coefficients of the controller, β D is a fractional differential operator, λ I is a fractional-order integral operator, s is the Laplace operator that converts the control law from the time domain to the complex frequency domain, and E x (s) and E f (s) are the Laplace transforms of position error and force error, respectively.

10. A robot nonlinear contact force control system based on Maxwell-fractional impedance model, characterized in that: The system includes an actuator, which is used to execute the robot nonlinear contact force control method based on the Maxwell-fractional impedance model described in claims 1-9.

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