A robot motion solution method based on nonlinear friction

Abstract

The present invention proposes a method for solving robot motion based on nonlinear friction, including: step S1, establishing a basic friction model; step S2, fixing the excitation frequency, and solving the time domain equation by step-by-step integration; step S3, traversing all the excitation frequencies, repeating step S2, and performing full frequency domain analysis. The force change corresponding to the displacement, velocity, and acceleration in the step-by-step integration will be used as the calculation intermediate quantity to participate in the calculation of the next iteration, and the current acceleration will be updated according to the intermediate value of the force value change; the current velocity term will be updated according to the new acceleration and the intermediate value of the force value change; the current displacement term will be updated according to the new acceleration, velocity, and the intermediate value of the force value; the error in the time domain will be controlled, and the physical quantity scaling coefficient q will be introduced as the target equation in the time domain analysis; the solution of the equation is the vector composed of displacement and velocity in the time domain analysis; if there is no optimal solution or the result diverges, the optimal solution will be inherited from the initial value, and the next frequency domain analysis will continue.

Description

Technical Field

[0001] The invention relates to the technical field of robots, and in particular to a robot motion solving method based on nonlinear friction force. Background Art

[0002] The traditional robot modeling method uses the superposition of static friction and Coulomb friction to model the friction part. Due to the complexity of the actual movement process of the robot, the contact surface between the components will change in real time with different working conditions. The use of a constant contact surface friction model will cause the robot dynamic model to be unable to maintain accuracy. In recent years, with the improvement of computer performance, more and more complex friction models have been proposed: Stribeck exponential friction model, Dahl dynamic friction model, and LuGre dynamic friction model. With the introduction of more and more parameters, the difficulty of parameter identification and the complexity of calculation are greatly increased.

[0003] On the other hand, experimental measurements of friction forces of a single joint, the smallest component of a robot, often cannot accurately fit the actual working conditions, resulting in huge differences between theoretical calculated values, measured values, and actual working conditions, and the confidence level of the test results is not high. Summary of the invention

[0004] The object of the present invention is to solve at least one of the technical drawbacks.

[0005] Therefore, the object of the present invention is to provide a robot motion solving method based on nonlinear friction force.

[0006] In order to achieve the above object, an embodiment of the present invention provides a robot motion solution method based on nonlinear friction force, comprising the following steps:

[0007] Step S1, establishing a basic friction model;

[0008] Step S2, fixing the excitation frequency and solving the time domain equation by step-by-step integration;

[0009] Among them, the corresponding displacement x, velocity x, acceleration in the step-by-step integration The force change It will be used as an intermediate quantity in the calculation and participate in the next iteration calculation, where m is mass, d is damping, k is stiffness,

[0010]

[0011] Update the current acceleration according to the intermediate value of the force change:

[0012]

[0013] in, is the intermediate value of force change, t is the time variable in the time domain equation;

[0014] Update the current velocity term based on the new acceleration and force value changes: ;

[0015] Update the current displacement term based on the new acceleration, velocity, and intermediate force values:

[0016]

[0017] For a fixed-length time-invariant system, each time a time domain integration is performed, the frequency domain image is updated n times until the maximum excitation frequency exceeds twice the system natural frequency, and the next time domain analysis calculation is performed, where n is the specified maximum number of frequency analysis iterations;

[0018] Control the error in the time domain and introduce the physical quantity scaling factor , as the target equation in time domain analysis;

[0019]

[0020] The solution of the equation is the vector composed of displacement and velocity in time domain analysis;

[0021]

[0022] in, is the time variable of the time domain function; The displacement calculated for this time domain analysis; is the speed of this time domain analysis calculation; the physical quantity scaling factor , used to adjust the allowable error of displacement and velocity;

[0023] If there is no optimum or the result diverges, the optimal solution is inherited from the initial value and the next step of frequency domain analysis is continued;

[0024] Step S3, traverse all excitation frequencies, repeat step S2, and perform full frequency domain analysis.

[0025] Furthermore, after step S2, the method further includes the following steps: performing parallel experiments on the friction force test of a single joint.

[0026] Furthermore, the friction force test for a single joint is conducted in parallel in the following three environments:

[0027] Test 1: Lock the joint motor to create a pure static friction environment test condition;

[0028] Test 2: Make the joint axis perpendicular to the ground to create a pure dynamic friction test condition that balances gravity;

[0029] Test 3: Keep the joints moving at a constant speed to create constant inertial force and Coriolis force testing conditions.

[0030] Further, the pure static friction environment test conditions are: static friction test environment: the contact surface does not have relative displacement, there is only a small force at the motor output end, there is no displacement, and the encoder cannot read the changed angle;

[0031] The pure dynamic friction test conditions for balancing gravity are: Pure dynamic friction: the joint and the motor rotate in the horizontal plane;

[0032] The constant inertial force and Coriolis force test conditions are uniform motion.

[0033] According to the robot motion solution method based on nonlinear friction force in the embodiment of the present invention, a nonlinear friction force model is proposed, and the high-order system is modeled and solved in combination with the alternating time-frequency analysis method (AFT). In order to verify the effectiveness of the model, a single joint measurement method is proposed for a robotic arm robot. The mathematical model of the present invention is simple, and the accuracy is determined by the order of the theoretical solution and the number of small quantities, and the calculation complexity is not high; secondly, an iterative method of alternating time-frequency solution is adopted, and the time domain solution error is used as the target equation, and no additional constraints are required; finally, the test method proposed in the patent can control variables to the greatest extent, reduce errors caused by coupling factors, reduce model misjudgment, and improve test accuracy.

[0034] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0036] Figure 1 is a flow chart of a robot motion solving method based on nonlinear friction according to an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of a friction force basic model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0039] like Figure 1 and Figure 2 As shown, the robot motion solution method based on nonlinear friction force in an embodiment of the present invention includes the following steps:

[0040] Step S1, establishing a basic friction model;

[0041] Step S2, fixing the excitation frequency and solving the time domain equation by step-by-step integration;

[0042] Among them, the corresponding displacement x, velocity x, acceleration in the step-by-step integration The force change It will be used as an intermediate quantity in the calculation and participate in the next iteration calculation, where m is mass, d is damping, k is stiffness,

[0043]

[0044] Update the current acceleration according to the intermediate value of the force change:

[0045]

[0046] in, is the intermediate value of force change, t is the time variable in the time domain equation;

[0047] Update the current velocity term based on the new acceleration and force value changes:

[0048] ;

[0049] Update the current displacement term based on the new acceleration, velocity, and intermediate force values:

[0050]

[0051] For a fixed-length time-invariant system, each time a time domain integration is performed, the frequency domain image is updated n times until the maximum excitation frequency exceeds twice the system natural frequency, and the next time domain analysis calculation is performed, where n is the specified maximum number of frequency analysis iterations;

[0052] Control the error in the time domain and introduce the physical quantity scaling factor , as the target equation in time domain analysis;

[0053]

[0054] The solution of the equation is the vector composed of displacement and velocity in time domain analysis;

[0055]

[0056] in, is the time variable of the time domain function; The displacement calculated for this time domain analysis; is the speed of this time domain analysis calculation; the physical quantity scaling factor , used to adjust the allowable error of displacement and velocity;

[0057] If there is no optimum or the result diverges, the optimal solution is inherited from the initial value and the next step of frequency domain analysis is continued.

[0058] In an embodiment of the present invention, after step S2, the following step is also included: a parallel experiment is performed on the friction force test of a single joint to verify the accuracy of the above model in practice.

[0059] Step S3, traverse all excitation frequencies, repeat step S2, and perform full frequency domain analysis.

[0060] Among them, parallel experiments were conducted on the friction force test of a single joint in the following three environments:

[0061] Test 1: Lock the joint motor to create a pure static friction environment test condition. The pure static friction environment test conditions are: static friction test environment: no relative displacement occurs on the contact surface, there is only a small force at the motor output end, no displacement, and the encoder cannot read the changing angle.

[0062] Test 2: Make the joint axis perpendicular to the ground to create a pure dynamic friction test condition that balances gravity. The pure dynamic friction test condition that balances gravity is as follows: Pure dynamic friction: The joint and motor rotate in the horizontal plane.

[0063] Test 3: Keep the joints moving at a constant speed to create constant inertia and Coriolis force test conditions. The constant inertia and Coriolis force test conditions are uniform motion.

[0064] The robot motion solving method based on nonlinear friction in the embodiment of the present invention first takes a multi-degree-of-freedom spring damping system as an example, establishes a mathematical model, and solves the time domain equation by step-by-step integration.

[0065] According to the robot motion solution method based on nonlinear friction force in the embodiment of the present invention, a nonlinear friction force model is proposed, and the high-order system is modeled and solved in combination with the alternating time-frequency analysis method (AFT). In order to verify the effectiveness of the model, a single joint measurement method is proposed for a robotic arm robot. The mathematical model of the present invention is simple, and the accuracy is determined by the order of the theoretical solution and the number of small quantities, and the calculation complexity is not high; secondly, an iterative method of alternating time-frequency solution is adopted, and the time domain solution error is used as the target equation, and no additional constraints are required; finally, the test method proposed in the patent can control variables to the greatest extent, reduce errors caused by coupling factors, reduce model misjudgment, and improve test accuracy.

[0066] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0067] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A robot motion solution method based on nonlinear friction, characterized in that: The steps include: Step S1, establishing a basic friction model; Step S2, fixing the excitation frequency and solving the time domain equation by step-by-step integration; Among them, the corresponding displacement x and velocity in the step-by-step integration are , acceleration The force change It will be used as an intermediate quantity in the calculation and participate in the next iteration calculation, where m is mass, d is damping, k is stiffness, ； Update the current acceleration according to the intermediate value of the force change: ； in, is the intermediate value of force change, t is the time variable in the time domain equation; Update the current velocity term based on the new acceleration and force value changes: ； Update the current displacement term based on the new acceleration, velocity, and intermediate force values: ； For a fixed-length time-invariant system, each time a time domain integration is performed, the frequency domain image is updated n times until the maximum excitation frequency exceeds twice the system natural frequency, and the next time domain analysis calculation is performed, where n is the specified maximum number of frequency analysis iterations; Control the error in the time domain and introduce the physical quantity scaling factor , as the target equation in time domain analysis; ； The solution of the equation is the vector composed of displacement and velocity in time domain analysis; ； in, is the time variable of the time domain function; The displacement calculated for this time domain analysis; is the speed of this time domain analysis calculation; the physical quantity scaling factor , used to adjust the allowable error of displacement and velocity; If there is no optimum or the result diverges, the optimal solution is inherited from the initial value and the next step of frequency domain analysis is continued; Step S3, traverse all excitation frequencies, repeat step S2, and perform full frequency domain analysis.

2. The robot motion solving method based on nonlinear friction force as claimed in claim 1, characterized in that: After step S2, the following step is also included: performing parallel experiments on the friction force test of a single joint.

3. The robot motion solving method based on nonlinear friction force as claimed in claim 2, characterized in that: The friction force test for a single joint was conducted in parallel in the following three environments: Test 1: Lock the joint motor to create a pure static friction environment test condition; Test 2: Make the joint axis perpendicular to the ground to create a pure dynamic friction test condition that balances gravity; Test 3: Keep the joints moving at a constant speed to create constant inertial force and Coriolis force testing conditions.

4. The robot motion solving method based on nonlinear friction force as claimed in claim 3, characterized in that: The pure static friction environment test conditions are as follows: static friction test environment: the contact surface does not have relative displacement, there is only a small force at the motor output end, there is no displacement, and the encoder cannot read the changing angle; The pure dynamic friction test conditions for balancing gravity are: Pure dynamic friction: the joint and the motor rotate in the horizontal plane; The constant inertial force and Coriolis force test conditions are uniform motion.

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