Parameter identification method for improving GMS friction model of industrial robot

Abstract

The invention discloses a parameter identification method for an improved GMS friction model of an industrial robot. The method comprises the following steps: step 1, introducing a Sigmoid function to design a GMS friction model meeting a differentiable switching point; step 2, constructing an improved Stribeck effect model of the GMS friction model; 3, designing an excitation track for Stribeck effect identification and identifying parameters based on an SOS algorithm; and step 4, designing a GMS dynamic parameter identification method based on SOS state point determination. According to the method, the switching point can be differentiated, the model is prevented from generating oscillation, and resonance of a servo system can be reduced for robot joint control; the Stribeck effect can be described more accurately, and the precision of the classic GMS model is improved; and state point determination based on experience can be avoided, the model fitting precision is improved, and the identification precision of the GMS friction model can be improved on the whole.

Description

Technical Field

[0001] The invention belongs to the field of industrial robots and relates to a parameter identification method for improving a GMS friction model of an industrial robot. Background Art

[0002] Industrial robots are known as the jewel in the crown of the manufacturing industry. Robots can work continuously without rest, which can improve production efficiency and work speed. Due to the dangers of human operation in some special scenarios and the rising labor costs, robots can be used to replace humans. Robots have been widely used and have produced huge economic and social benefits. With the development of robot technology, the requirements for robot control accuracy are getting higher and higher, and the application scenarios of robots need to be expanded to better promote the development of the robot industry. Current hot research directions include human-machine collaborative operation. For human-machine collaborative operation scenarios, it is necessary to ensure the safety of operators, detect collisions, and avoid harm to people. At the same time, it is necessary to sense the force applied by people to robots for better human-machine collaboration. To achieve these requirements, it is necessary to identify a high-precision robot dynamics model.

[0003] The joint torque of the robot is composed of inertia torque, Coriolis force, centrifugal force, gravity and friction, among which inertia torque, Coriolis force, centrifugal force and gravity can be modeled relatively accurately. The friction part of dynamics accounts for about 25% of the total joint torque, which significantly affects the accuracy of the robot model. The static friction model is currently widely used. It has a simple structure, but the modeling accuracy is low at low speeds. Although the dynamic friction model has relatively high accuracy, the identification process is relatively cumbersome and the accuracy still needs to be improved. The GMS friction model is a typical friction model. Compared with the static friction model, the GMS friction model can better describe the Stribeck effect of friction at normal speed, the hysteresis effect without local memory in the pre-sliding stage, and the friction memory in the sliding stage. However, the current GMS friction model has the problems of low Stribeck effect accuracy, failure to meet the differentiability of the switching point, and low identification accuracy. Summary of the invention

[0004] In order to overcome the problem of low precision of Stribeck effect in GMS friction model, the present invention provides a parameter identification method for improving the GMS friction model of industrial robots, and designs the Stribeck speeds corresponding to the Coulomb friction and static friction of the classic Stribeck model as two parameters to better describe the dynamic characteristics of friction corresponding to the Coulomb friction and static friction; regarding the problem that the switching point in the GMS friction model is not differentiable, Sigmoid is introduced as a switching function to meet the differentiability requirements of the switching point; regarding the problem of low identification precision, when identifying the parameters of the Stribeck friction model, the nonlinear least squares method is introduced to identify the parameter value, and the upper and lower bounds of the symbiotic organism search (SOS) algorithm are determined based on the identification results, and the SOS algorithm is used for identification. Regarding the dynamic parameter identification part, the optimal pre-slip critical point is calculated by the SOS algorithm through a periodic trajectory with extremely small displacement, so as to avoid artificially specifying the critical point and improve the identification precision of the dynamic friction parameters.

[0005] The technical solutions proposed for the above technical problems are as follows:

[0006] A parameter identification method for improving the GMS friction model of an industrial robot comprises the following steps:

[0007] Step 1, introduce the Sigmoid function to design a GMS friction model that satisfies the differentiability of the switching point;

[0008] Step 2, construct an improved Stribeck effect model of the GMS friction model;

[0009] Step 3, design the excitation trajectory for Stribeck effect identification and identify the parameters based on the SOS algorithm;

[0010] Step 4: Design a GMS dynamic parameter identification method based on SOS state point determination.

[0011] Furthermore, in step 1, a GMS friction model is constructed. The GMS model is considered to be composed of multiple single-state friction sub-models in parallel. The total friction force is the sum of each sub-friction. The model is expressed as:

[0012]

[0013] Where l is the number of friction sub-models, τ i represents the friction force of a single friction sub-model, f v is the viscous friction coefficient, is the robot joint velocity, when τ i There are different expressions in different states. When the friction submodel is in a sticky state:

[0014]

[0015] When the friction submodel is in sliding state:

[0016]

[0017] Where C is the convergence coefficient, which determines the speed at which the friction force converges to the Stribeck curve in the sliding state; in formula (3): The representative Stribeck curve is defined as:

[0018]

[0019] Among them, f c ,f s They are Coulomb friction coefficient and static friction coefficient respectively; q s are the Stribeck velocity; δ is the Stribeck factor;

[0020] The Sigmoid function is designed as the switching function to combine the functions of the two stages, namely:

[0021]

[0022] in, The designed Sigmoid function is shown in the following formula:

[0023]

[0024] Among them, ρ is the proportional coefficient, which determines the speed of function switching. At this time, the initial value and final value of the designed switching function are -1 and 1, which can reflect the changes of the two states and meet the differentiability requirements.

[0025] Furthermore, in step 2, for the Coulomb friction coefficient f in formula (4), c and the static friction coefficient f s The corresponding Stribeck speed q s The physical properties of the Stribeck effect model cannot be accurately described. For the Coulomb friction coefficient f c The Stribeck velocity ζ1 is introduced to describe the rate of increase of the joint from starting to the maximum Coulomb friction force; for the static friction coefficient f s The corresponding q s The Stribeck speed ζ2 is introduced to describe the partial friction characteristics of the robot joint friction in the boundary lubrication, partial lubrication and full lubrication stages, as shown in formula (7):

[0026]

[0027] Furthermore, the process of step 3 is as follows:

[0028] 3.1 Excitation trajectory design for Stribeck effect identification

[0029] According to the Newton-Euler theorem, the robot dynamics model is constructed and the expression is sorted as follows:

[0030]

[0031] Where τ is the robot joint torque, M(q) is the moment of inertia, is the centrifugal force and G(q) force matrix, G(q) is gravity. From the above formula, we can see that the inertia moment is related to acceleration, the centrifugal force and G(q) force are only related to speed, and gravity is only related to the joint angle, but not to speed and acceleration. Based on this, the excitation trajectory is designed to overcome the influence of inertia moment, centrifugal force, G(q) force and gravity, and only retain friction. The designed excitation trajectory is shown in the following formula:

[0032]

[0033] Among them, k 11 ,k 12 ,k 21 ,k 22 ,k 31 and k 32 It is the velocity trajectory coefficient in the three switching stages. Multiple sets of experiments are conducted on each joint to set the velocity of each joint.

[0034] 3.2 Identification of Stribeck effect parameters based on SOS algorithm

[0035] According to the principle of SOS algorithm, it is necessary to determine the identification parameters. Let the Coulomb friction coefficient f c , static friction coefficient f s , viscous friction coefficient f v , Stribeck speed ζ2,ζ2, and Stribeck factor δ are the parameters to be identified. The upper and lower bounds of the parameter search are roughly set based on experience, and the fitness function is designed as:

[0036]

[0037] in, At speeds of The friction torque after collection and processing and the friction torque estimated based on the improved Stribeck friction model are collected and processed, σ is the data point, σ=1……μ, and the search goal is to obtain the minimum value of the fitness value.

[0038] Furthermore, in step 4, a set of piecewise functions is designed, which is assumed to be divided into four segments and expressed as:

[0039]

[0040] Wherein, τ(q(γ)) is the friction torque of the γth point, γ = 1…κ, a1, a2, a3, a4, k1, k2, k3, k4 are the initial values ​​and slopes of the torque of each segment respectively, q(1), q(κ), q1, q2, q3 are the designed pre-slip initial point, end point and initial point of each segment;

[0041] In order to use the SOS algorithm to determine the segmentation points and slopes, it is necessary to design a fitness function. Since the first and last values ​​of each segmentation function are the same, the relationship based on this is:

[0042]

[0043] From this we can deduce:

[0044]

[0045] According to the principle of SOS algorithm, let a1, a2, a3, a4, k1, k2, k3, k4 be the search parameters, roughly set the upper and lower bounds of the parameter search based on experience, and design the fitness function according to the designed segmentation points:

[0046]

[0047] in, It is the data after τ(q(γ)) filtering, and the search goal is to obtain the minimum value of the fitness value;

[0048] Design the trajectory of dynamic parameter identification, and design the robot to move back and forth at a constant speed while avoiding the influence of joint gravity. The trajectory relationship is:

[0049]

[0050] Among them, q init is the initial position of the joint, The speed is extremely low.

[0051] The technical concept of the present invention is as follows: for the industrial robot joint friction model, combined with the Sigmoid function, a switching function is designed to combine the functions of the pre-sliding stage and the sliding stage of the GMS friction model to reflect the changes in the two states, the model is differentiable, and oscillation is avoided. Two Stribeck velocity factors are introduced for static friction and Coulomb friction to achieve a more accurate description of the Stribeck effect model. Based on the SOS algorithm and the characteristics of the state points of the GMS dynamic friction model, a fitness function is designed to realize the automatic selection of state points and improve the model fitting accuracy.

[0052] The beneficial effects of the present invention are as follows: compared with the classic GMS friction model, the switching point is differentiable, the model is prevented from oscillating, and the resonance of the servo system can be reduced for robot joint control. The improved Stribeck effect model can more accurately describe the Stribeck effect and improve the accuracy of the classic GMS model. The introduction of SOS to determine the state point and the slope of each sub-model can avoid the empirical determination of the state point, improve the model fitting accuracy, and generally improve the identification accuracy of the GMS friction model. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Schematic diagram of the designed Sigmoid function effect;

[0054] Figure 2 Schematic diagram of the excitation trajectory for the Stribeck effect model identification;

[0055] Figure 3 Schematic diagram of the improved and classic Stribeck effect model fitting effect;

[0056] Figure 4 It is a schematic diagram of the excitation trajectory for GMS dynamic parameter identification;

[0057] Figure 5 Schematic diagram of torque filtering for performing GMS dynamic parameter identification excitation trajectory acquisition for robot joints;

[0058] Figure 6 It is a schematic diagram of the identification and fitting effect of GMS dynamic parameters determined based on the SOS state point;

[0059] Figure 7 It is a schematic diagram of the identification process of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described below in conjunction with the accompanying drawings.

[0061] Reference Figure 1-Figure 7 , a parameter identification method for improving the GMS friction model of an industrial robot comprises the following steps:

[0062] Step 1: Introduce the Sigmoid function to design a GMS friction model that satisfies the differentiability of the switching point

[0063] The GMS friction model is constructed. The GMS model is considered to be composed of multiple single-state friction sub-models in parallel. The total friction force is the sum of each sub-friction. The model is expressed as:

[0064]

[0065] Where l is the number of friction sub-models, τ irepresents the friction force of a single friction sub-model, f v is the viscous friction coefficient, is the robot joint velocity, when τ i There are different expressions in different states. When the friction submodel is in a sticky state:

[0066]

[0067] When the friction submodel is in sliding state:

[0068]

[0069] Where C is the convergence coefficient, which determines the speed at which the friction force converges to the Stribeck curve in the sliding state; in formula (3): The representative Stribeck curve is defined as:

[0070]

[0071] Among them, f c ,f s They are Coulomb friction coefficient and static friction coefficient respectively; q s are the Stribeck velocity; δ is the Stribeck factor, which is an empirical parameter, usually 0.5-2;

[0072] The derivative of the sliding state of the GMS friction model near the switching point is less than zero. Each time the switching point is crossed, the friction force τ of the friction submodel i Because the derivative is less than zero, it will return to the pre-slip state, causing the constructed friction force to change repeatedly at the switching point and produce oscillations. Therefore, it is necessary to satisfy the differentiability at the switching point, design the Sigmoid function as the switching function, and combine the functions of the two stages, that is:

[0073]

[0074] in, The designed Sigmoid function is shown in the following formula:

[0075]

[0076] Among them, ρ is the proportional coefficient, which determines the speed of function switching. At this time, the initial value and final value of the designed switching function are -1 and 1, which can reflect the change of the two states and meet the differentiability requirements.

[0077] Step 2: Construct an improved Stribeck effect model for the GMS friction model

[0078] According to formula (4), the Coulomb friction coefficient f c and the static friction coefficient fs The corresponding Stribeck speed q s The physical properties of the Stribeck effect model cannot be accurately described. For the Coulomb friction coefficient f c The Stribeck velocity ζ1 is introduced to describe the rate of increase of the joint from starting to the maximum Coulomb friction force; for the static friction coefficient f s The corresponding q s The Stribeck speed ζ2 is introduced to describe the partial friction characteristics of the robot joint friction in the boundary lubrication, partial lubrication and full lubrication stages, as shown in formula (7):

[0079]

[0080] Step 3: Design the excitation trajectory for Stribeck effect identification and identify the parameters based on the SOS algorithm. The process is as follows:

[0081] 3.1 Excitation trajectory design for Stribeck effect identification

[0082] According to the Newton-Euler theorem, the robot dynamics model is constructed and the expression is sorted as follows:

[0083]

[0084] Where τ is the robot joint torque, M(q) is the moment of inertia, is the centrifugal force and G(q) force matrix, G(q) is gravity. From the above formula, we can see that the inertia moment is related to acceleration, the centrifugal force and G(q) force are only related to speed, and gravity is only related to the joint angle, but not to speed and acceleration. Based on this, the excitation trajectory is designed to overcome the influence of inertia moment, centrifugal force, G(q) force and gravity, and only retain friction. The designed excitation trajectory is shown in the following formula:

[0085]

[0086] Among them, k 11 ,k 12 ,k 21 ,k 22 ,k 31 and k 32 is the velocity trajectory coefficient during the three switching stages. Multiple sets of experiments were conducted on each joint, and the velocity of each joint q iSet to 0.0001,0.001,0.01,0.05,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.4,1.6,1.8,2,2.3,2.6,2.9,3.2,3.6,4,4.5,5,6,8,10,13,16,20,25,31,38,45 deg / s;

[0087] 3.2 Identification of Stribeck effect parameters based on SOS algorithm

[0088] According to the principle of SOS algorithm, it is necessary to determine the identification parameters. Let the Coulomb friction coefficient f c , static friction coefficient f s , viscous friction coefficient f v , Stribeck speed ζ2,ζ2, and Stribeck factor δ are the parameters to be identified. The upper and lower bounds of the parameter search are roughly set based on experience, and the fitness function is designed as:

[0089]

[0090] in, They are respectively the friction torque collected and processed at the speed q(σ) and the friction torque estimated based on the improved Stribeck friction model, σ is the data point, σ=1……μ, and the search goal is to obtain the minimum value of the fitness value;

[0091] Step 4: Design a GMS dynamic parameter identification method based on SOS state point determination

[0092] The traditional GMS model determines the characteristic state of the pre-slip state. The state point can be determined by selecting the first rising stage and divided into different curves. Traditionally, the state point needs to be determined based on experience, and the slope is determined based on the horizontal and vertical intercepts. It relies on experience and cannot be quantitatively and accurately calculated, resulting in large calculation errors. Therefore, a set of segmented functions is designed, which is assumed to be divided into four segments and expressed as:

[0093]

[0094] Wherein, τ(q(γ)) is the friction torque of the γth point, γ = 1…κ, a1, a2, a3, a4, k1, k2, k3, k4 are the initial values ​​and slopes of the torque of each segment respectively, q(1), q(κ), q1, q2, q3 are the designed pre-slip initial point, end point and initial point of each segment;

[0095] In order to use the SOS algorithm to determine the segmentation points and slopes, it is necessary to design a suitable fitness function. Since the first and last values ​​of each segmentation function are the same, the relationship based on this is:

[0096]

[0097] From this we can deduce that

[0098]

[0099] According to the principle of SOS algorithm, let a1, a2, a3, a4, k1, k2, k3, k4 be the search parameters, roughly set the upper and lower bounds of the parameter search based on experience, and design the fitness function based on the designed segmentation points:

[0100]

[0101] in, It is the data after τ(q(γ)) filtering, and the search goal is to obtain the minimum value of the fitness value;

[0102] Design the trajectory of dynamic parameter identification, and design the robot to move back and forth at a constant speed while avoiding the influence of joint gravity. The trajectory relationship is:

[0103]

[0104] Among them, q init is the initial position of the joint, The speed is extremely low.

[0105] In order to verify the effectiveness of the proposed method, regarding the differentiability of the GMS friction model, the present invention proposes a strategy of using the Sigmoid function to switch the two states of the GMS friction model according to the joint speed. The state switching has a switching process, and the function also meets the differentiability requirements. Figure 1 It can be seen from the figure that the function switches between 0 and 1, which is continuous and differentiable. Regarding the improvement of the Stribeck friction effect, the present invention designs an excitation trajectory, such as Figure 2 As shown in the figure, the influence of non-friction force is overcome and the friction torque is calculated. A comparison between the traditional Stribeck friction effect and the improved friction effect is given. Figure 3 The fitting effect of the traditional Stribeck friction effect and the improved Stribeck friction effect can be seen in the figure. The root mean square error of the traditional Stribeck friction effect is 1.2121Nm, and the root mean square error of the improved Stribeck friction effect is 0.8241Nm. The root mean square error of the improved Stribeck friction effect is smaller, so the improved model has higher accuracy. As for the determination of the dynamic GMS friction state point, a uniform reciprocating motion is designed, such as Figure 4 As shown in Figure 2, the collected torque data has noise, and denoising is used, such as Figure 5The traditional method is to select and determine based on experience, which depends on human choice, is subjective and unpredictable. However, the points are determined based on the designed GMS friction effect, which relies on algorithms and is not affected by human subjective judgment. It has a more scientific basis and the fitting effect is as shown in the specific results. Figure 6 shown.

[0106] In summary, the parameter identification method based on the improved GMS friction model of industrial robots can make the switching point differentiable and avoid oscillation of the friction model at the switching point. The improved Stribeck friction effect has higher accuracy, and the determination of the state switching point avoids judgment based on experience, which improves the model accuracy.

[0107] The above describes the excellent optimization effect shown by an embodiment of the present invention. Obviously, the present invention is not limited to the above embodiment, and various modifications can be made to it without departing from the basic spirit of the present invention and without exceeding the scope of the essential content of the present invention.

Claims

1. A parameter identification method for improving the GMS friction model of an industrial robot, characterized in that: The method comprises the following steps: Step 1, introduce the Sigmoid function to design a GMS friction model that satisfies the differentiability of the switching point; Step 2, construct an improved Stribeck effect model of the GMS friction model; Step 3, design the excitation trajectory for Stribeck effect identification and identify the parameters based on the SOS algorithm; Step 4: Design a GMS dynamic parameter identification method based on SOS state point determination.

2. A parameter identification method for improving the GMS friction model of an industrial robot as claimed in claim 1, characterized in that: In step 1, a GMS friction model is constructed. The GMS model is considered to be composed of multiple single-state friction sub-models in parallel. The total friction force is the sum of each sub-friction. The model is expressed as: Where l is the number of friction sub-models, τ i represents the friction force of a single friction sub-model, f v is the viscous friction coefficient, is the robot joint velocity, when τ i There are different expressions in different states. When the friction submodel is in a sticky state: When the friction submodel is in sliding state: Where C is the convergence coefficient, which determines the speed at which the friction force converges to the Stribeck curve in the sliding state; in formula (3): The representative Stribeck curve is defined as: Among them, f c ,f s They are Coulomb friction coefficient and static friction coefficient respectively; q s are the Stribeck velocity; δ is the Stribeck factor; The Sigmoid function is designed as the switching function to combine the functions of the two stages, namely: in The designed Sigmoid function is shown in the following formula: Among them, ρ is the proportional coefficient, which determines the speed of function switching. At this time, the initial value and final value of the designed switching function are -1 and 1, which can reflect the changes of the two states and meet the differentiability requirements.

3. A parameter identification method for improving the GMS friction model of an industrial robot as claimed in claim 2, characterized in that: In step 2, for the Coulomb friction coefficient f in formula (4), c and the static friction coefficient f s The corresponding Stribeck speed q s The physical properties of the Stribeck effect model cannot be accurately described. For the Coulomb friction coefficient f c The Stribeck velocity ζ1 is introduced to describe the rate of increase of the joint from starting to the maximum Coulomb friction force; for the static friction coefficient f s The corresponding q s The Stribeck speed ζ2 is introduced to describe the partial friction characteristics of the robot joint friction in the boundary lubrication, partial lubrication and full lubrication stages, as shown in formula (7):

4. A parameter identification method for improving the GMS friction model of an industrial robot as claimed in claim 3, characterized in that: The process of step 3 is as follows: 3.1 Excitation trajectory design for Stribeck effect identification According to the Newton-Euler theorem, the robot dynamics model is constructed and the expression is sorted as follows: Where τ is the robot joint torque, M(q) is the moment of inertia, are the centrifugal force and G(q) force matrices, G(q) is the gravity; The designed excitation trajectory is shown below: Among them, k 11 ,k 12 ,k 21 ,k 22 ,k 31 and k 32 It is the velocity trajectory coefficient in the three switching stages. Multiple sets of experiments are conducted on each joint to set the velocity of each joint. 3.2 Identification of Stribeck effect parameters based on SOS algorithm Assume the Coulomb friction coefficient f c , static friction coefficient f s , viscous friction coefficient f v , Stribeck speed ζ2,ζ2, and Stribeck factor δ are the parameters to be identified. The upper and lower bounds of the parameter search are roughly set based on experience, and the fitness function is designed as: in, At speeds of The friction torque after collection and processing and the friction torque estimated based on the improved Stribeck friction model are collected and processed, σ is the data point, σ=1……μ, and the search goal is to obtain the minimum value of the fitness value.

5. A parameter identification method for improving the GMS friction model of an industrial robot as claimed in claim 4, characterized in that: In step 4, a set of piecewise functions is therefore designed, which is assumed to be divided into four segments and expressed as: Wherein, τ(q(γ)) is the friction torque of the γth point, γ = 1…κ, a1, a2, a3, a4, k1, k2, k3, k4 are the initial values ​​and slopes of the torque of each segment respectively, q(1), q(κ), q1, q2, q3 are the designed pre-slip initial point, end point and initial point of each segment; In order to use the SOS algorithm to determine the segmentation points and slopes, it is necessary to design a fitness function. Since the first and last values ​​of each segmentation function are the same, the relationship based on this is: From this we can deduce: According to the principle of SOS algorithm, let a1, a2, a3, a4, k1, k2, k3, k4 be the search parameters, roughly set the upper and lower bounds of the parameter search based on experience, and design the fitness function based on the designed segmentation points: in, It is the data after τ(q(γ)) filtering, and the search goal is to obtain the minimum value of the fitness value; Design the trajectory of dynamic parameter identification, and design the robot to move back and forth at a constant speed while avoiding the influence of joint gravity. The trajectory relationship is: Among them, q init is the initial position of the joint, The speed is extremely low.

Images