Parameter identification method for improving gms friction model of industrial robot

Abstract

The application discloses a parameter identification method for improving an industrial robot GMS friction model, and comprises the following steps: step 1, introducing a Sigmoid function to design a GMS friction model satisfying a switch point differential; step 2, constructing an improved Stribeck effect model of the GMS friction model; step 3, designing an excitation trajectory for Stribeck effect identification and identifying parameters based on a SOS algorithm; and step 4, designing a GMS dynamic parameter identification method based on SOS state point determination. The application satisfies the switch point differential, avoids model oscillation, reduces resonance of a servo system for robot joint control, more accurately describes the Stribeck effect, improves the precision of a classical GMS model, avoids empirical determination of state points, improves model fitting precision, and improves the identification precision of the GMS friction model as a whole.

Description

TECHNICAL FIELD

[0001] The application 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

[0002] Industrial robots are known as the brightest jewel on the crown of manufacturing industry. Robots can work continuously without rest, and can improve production efficiency and working speed. Due to the danger of personnel operation in some special scenarios and the continuous rise of labor cost, robots can be applied to replace people, and robots have been widely applied and have produced huge economic and social benefits. With the development of robot technology, the requirements for robot control accuracy are higher and higher, and the application scenarios of robots need to be expanded to better promote the development of the robot industry. The current research direction of the hot spot includes human-robot collaborative operation. For the human-robot collaborative operation scenario, the safety of the operating personnel needs to be ensured, the collision needs to be detected to avoid injury to people, and the force applied by people to the robot needs to be perceived to better perform human-robot collaboration. To achieve these requirements, a high-precision robot dynamics model needs to be identified.

[0003] The joint torque of a robot is composed of inertia torque, Coriolis force, centrifugal force, gravity and friction. The 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 current widely used static friction model has a simple structure, but the modeling accuracy is low at low speed. Although the dynamic friction model has relatively high accuracy, the identification process is relatively complicated, and the accuracy still needs to be improved. The GMS friction model is a typical friction model. The GMS friction model can better describe the Stribeck effect of the constant speed state of friction, the hysteresis effect without local memory in the pre-sliding stage and the friction memory in the sliding stage compared with the static friction model. However, the current GMS friction model has the problems of low Stribeck effect accuracy, insufficient differentiability of switching points and low identification accuracy. SUMMARY

[0004] In order to overcome the problem of low precision of Stribeck effect in GMS friction model, the application provides a parameter identification method for improving GMS friction model of industrial robot, the Stribeck speed corresponding to Coulomb friction and static friction of the classical Stribeck model is designed as two parameters, so as to better describe the friction dynamic characteristics corresponding to Coulomb friction and static friction; regarding the problem that the switching point of GMS friction model is not differentiable, Sigmoid is introduced as a switching function to meet the differentiability requirement of the switching point; regarding the problem of low identification precision, when identifying the parameters of Stribeck friction model, the nonlinear least square method is introduced to identify the parameter value, the upper and lower bounds of symbiotic organism search (SOS) algorithm are determined based on the identification result, and the SOS algorithm is used for identification, regarding the dynamic parameter identification part, the optimal pre-sliding critical point is calculated through the SOS algorithm through a periodic trajectory of minimum displacement, so as to avoid artificial designation of critical point and improve the dynamic friction parameter identification precision.

[0005] The technical scheme for solving the above technical problems is as follows:

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

[0007] Step 1, introducing Sigmoid function to design GMS friction model meeting the differentiability of switching point;

[0008] Step 2, constructing improved Stribeck effect model of GMS friction model;

[0009] Step 3, designing excitation trajectory for Stribeck effect identification and identifying parameters based on SOS algorithm;

[0010] Step 4, designing GMS dynamic parameter identification method based on SOS state point determination.

[0011] Further, in the step 1, the GMS friction model is constructed, the GMS model is regarded as being composed of a plurality of single-state friction sub-models in parallel, the total friction force is the sum of each sub-friction, and the model is expressed as:

[0012]

[0013] Wherein, l is the number of friction sub-models, τ i represents the friction force of a single friction sub-model, f v is a viscous friction coefficient, is a robot joint speed, when τ i is different in different states, when the friction sub-model is in a viscous state:

[0014]

[0015] When the friction sub-model is in the sliding state:

[0016]

[0017] where C is the convergence coefficient, which determines the convergence speed of the friction force to the Stribeck curve in the sliding state; in formula (3) The Stribeck curve represented by formula (3) is defined as:

[0018]

[0019] where f c and f s are the Coulomb friction coefficient and the static friction coefficient, respectively; q s are the Stribeck speeds, respectively; and δ is the Stribeck factor.

[0020] A Sigmoid function is designed as a switching function to combine the functions of the two stages, i.e.:

[0021]

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

[0023]

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

[0025] Further, in step 2, for the Coulomb friction coefficient f c and the static friction coefficient f s , the corresponding Stribeck speeds q s cannot accurately describe the physical properties of the Stribeck effect model. For the Coulomb friction coefficient f c , the Stribeck speed ζ1 is introduced to describe the rising rate of the joint from the start to the maximum Coulomb friction; 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 boundary lubrication, partial lubrication and full lubrication stages of the robot joint friction, as shown in formula (7):

[0026]

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

[0028] 3.1 Excitation Trajectory Design for Stribeck Effect Identification

[0029] Based on Newton's and Euler's laws, a robot dynamics model is constructed, and the expression is simplified as follows:

[0030]

[0031] Where τ is the robot joint torque, and M(q) is the moment of inertia. Here, G(q) is the centrifugal force and Coriolis force matrix, and G(q) is gravity. From the above equation, it can be seen that the inertial torque is related to acceleration, the centrifugal force and Coriolis force are only related to velocity, and gravity is only related to the joint angle, and not to velocity or acceleration. Based on this, the excitation trajectory is designed to overcome the effects of inertial torque, centrifugal force, Coriolis force, and gravity, retaining only friction. The designed excitation trajectory is shown in the following equation:

[0032]

[0033] Where, k 11 ,k 12 ,k 21 ,k 22 ,k 31 and k 32 These are the velocity trajectory coefficients during the three reversal phases. Multiple sets of experiments were conducted for each joint, setting the velocity of each joint.

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

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

[0036]

[0037] in, They are at speeds of The friction torque after data collection and processing and the friction torque estimated based on the improved Stribeck friction model are used. σ represents the data point, σ = 1...μ. The search objective is to obtain the minimum value of the fitness value.

[0038] Furthermore, in step 4, a set of piecewise functions is designed, assuming it is divided into four segments, expressed as follows:

[0039]

[0040] Where τ(q(γ)) is the frictional torque at the γ-th point, γ=1……κ, a1,a2,a3,a4,k1,k2,k3,k4 are the initial torque values ​​and slopes of each segment respectively, and q(1),q(κ),q1,q2,q3 are the designed pre-sliding initial point, end point and initial point of each segment.

[0041] To determine the segmentation points and slope using the SOS algorithm, a fitness function needs to be designed. Since the first and last values ​​of each segmentation function are the same, the relationship is as follows:

[0042]

[0043] Therefore, we can deduce that:

[0044]

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

[0046]

[0047] in, The data is filtered by τ(q(γ)), ​​and the search objective is to find the minimum fitness value.

[0048] Design a trajectory for dynamic parameter identification, and design the robot to perform reciprocating motion at a constant speed while avoiding the influence of joint gravity. The trajectory relationship is as follows:

[0049]

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

[0051] The technical concept of this invention is as follows: For the joint friction model of industrial robots, a switching function is designed in conjunction with the Sigmoid function to combine the functions of the pre-sliding and sliding stages of the GMS friction model, thus reflecting the changes between the two states, ensuring model differentiability, and avoiding oscillations. 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 in the GMS dynamic friction model, a fitness function is designed to achieve automatic selection of state points, improving the model fitting accuracy.

[0052] The beneficial effects of this invention are as follows: Compared with the classic GMS friction model, it satisfies the requirement of differentiable switching points, avoids model oscillations, and reduces servo system resonance for robot joint control. The improved Stribeck effect model can more accurately describe the Stribeck effect, improving the accuracy of the classic GMS model. Introducing SOS for determining state points and the slopes of each sub-model avoids relying on experience to determine state points, improving model fitting accuracy and overall enhancing the identification accuracy of the GMS friction model. Attached Figure Description

[0053] Figure 1 A schematic diagram illustrating the effect of the designed Sigmoid function;

[0054] Figure 2 A schematic diagram for identifying the excitation trajectory for the Stribeck effect model;

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

[0056] Figure 4 A schematic diagram for identifying the excitation trajectory for GMS dynamic parameters;

[0057] Figure 5 A schematic diagram illustrating torque filtering for GMS dynamic parameter identification, excitation trajectory acquisition, and torque filtering of robot joints;

[0058] Figure 6 A schematic diagram illustrating the fitting effect of GMS dynamic parameter identification based on SOS state points;

[0059] Figure 7 This is a schematic diagram of the identification process of the present invention. Detailed Implementation

[0060] The invention will now be further described with reference to the accompanying drawings.

[0061] Reference Figures 1-7 An improved parameter identification method for the GMS friction model of industrial robots includes 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] Construct a GMS friction model, which is considered to be composed of multiple single-state friction sub-models connected in parallel. The total friction force is the sum of the individual sub-friction forces. The model is expressed as follows:

[0064]

[0065] Where l is the number of tribological models, τ if represents the frictional force of a single tribometer model. v The coefficient of viscous friction, Let τ be the robot joint velocity, when τ i The expression differs depending on the state. When the tribometer model is in a viscous state:

[0066]

[0067] When the friction sub-model is in a sliding state:

[0068]

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

[0070]

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

[0072] The derivative of the GMS friction model in the sliding state near the switching point is less than zero. Each time the switching point is crossed, the frictional force τ in the friction submodel increases. i The system will revert to the pre-sliding state because the derivative is less than zero, causing the friction force to repeatedly change at the switching point, resulting in oscillations. Therefore, it is necessary to satisfy differentiability at the switching point and design a Sigmoid function as the switching function to combine the functions of the two stages, i.e.:

[0073]

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

[0075]

[0076] Where ρ is the proportionality coefficient, which determines the speed of function switching; the initial and final values ​​of the designed switching function are -1 and 1, respectively, which can reflect the changes between the two states and satisfy the differentiability requirement;

[0077] Step 2: Construct an improved Stribeck effect model based on the GMS friction model.

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

[0079]

[0080] Step 3, design the excitation trajectory for Stribeck effect identification and the identification parameters based on the SOS algorithm, the process is as follows:

[0081] 3.1 Excitation Trajectory Design for Stribeck Effect Identification

[0082] Based on Newton's and Euler's laws, a robot dynamics model is constructed, and the expression is simplified as follows:

[0083]

[0084] Where τ is the robot joint torque, and M(q) is the moment of inertia. Here, G(q) is the centrifugal force and Coriolis force matrix, and G(q) is gravity. From the above equation, it can be seen that the inertial torque is related to acceleration, the centrifugal force and Coriolis force are only related to velocity, and gravity is only related to the joint angle, and not to velocity or acceleration. Based on this, the excitation trajectory is designed to overcome the effects of inertial torque, centrifugal force, Coriolis force, and gravity, retaining only friction. The designed excitation trajectory is shown in the following equation:

[0085]

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

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

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

[0089]

[0090] in, These are the frictional torque collected and processed at a speed of q(σ) and the frictional torque estimated based on the improved Stribeck friction model, respectively. σ represents the data point, σ = 1...μ, and the search objective 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] Traditional GMS models determine the characteristic states of the pre-slip state by selecting the first rising stage to define the state point and dividing it into different curves. Traditional methods rely on experience to determine the state point and the slope based on the horizontal and vertical intercepts, which is empirical, lacks precise quantitative calculation, and results in significant calculation errors. Therefore, a set of piecewise functions is designed, assuming it consists of four segments, expressed as follows:

[0093]

[0094] Where τ(q(γ)) is the frictional torque at the γ-th point, γ=1……κ, a1,a2,a3,a4,k1,k2,k3,k4 are the initial torque values ​​and slopes of each segment respectively, and q(1),q(κ),q1,q2,q3 are the designed pre-sliding initial point, end point and initial point of each segment.

[0095] To determine the segmentation points and slope using the SOS algorithm, a suitable fitness function needs to be designed. Since the first and last values ​​of each segmentation function are the same, the relationship is as follows:

[0096]

[0097] This leads to the conclusion that...

[0098]

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

[0100]

[0101] in, The data is filtered by τ(q(γ)), ​​and the search objective is to find the minimum fitness value.

[0102] Design a trajectory for dynamic parameter identification, and design the robot to perform reciprocating motion at a constant speed while avoiding the influence of joint gravity. The trajectory relationship is as follows:

[0103]

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

[0105] To verify the effectiveness of the proposed method, regarding the differentiability of the GMS friction model, this invention proposes a strategy using the Sigmoid function to switch between two states of the GMS friction model based on joint velocity. The state switching involves a switching process, and the function also satisfies the differentiability requirement. Figure 1 As can be seen, the function switches between 0 and 1, and is continuous and differentiable. Regarding the problem of improving the Stribeck friction effect, this invention designs an excitation trajectory, as follows: Figure 2 As shown, the influence of non-frictional forces was overcome, and the frictional torque was calculated. A comparison between the traditional Stribeck friction effect and the improved friction effect is given, from... Figure 3 The results show the fitting effects of the traditional Stribeck friction effect and the improved Stribeck friction effect. The calculated root mean square error (RMSE) shows that the traditional Stribeck friction effect has an error of 1.2121 Nm, while the improved model has an RMSE of 0.8241 Nm. The improved model has a smaller RMSE, indicating higher accuracy. Regarding the determination of the dynamic GMS friction state points, a uniform reciprocating motion was designed, such as... Figure 4 As shown, the collected torque data contained noise, and noise reduction processing was employed, such as... Figure 5As shown. Traditional methods rely on experience for selection, which is subjective and unpredictable due to human choice. In contrast, identifying and determining points based on the designed GMS friction effect relies on algorithms, is not influenced by subjective human judgment, and has a more scientific basis. The resulting fitting effect is shown in the specific results. Figure 6 As shown.

[0106] In summary, the parameter identification method based on the improved GMS friction model of industrial robots enables differentiable switching points, preventing oscillations in the friction model at these points. The improved Stribeck friction effect offers higher accuracy, and the determination of state switching points avoids reliance on empirical judgments, thus improving model accuracy.

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

Claims

1. A method for parameter identification of an improved GMS friction model for industrial robots, characterized in that, The method includes 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 the identification parameters based on the SOS algorithm; Step 4: Design a dynamic parameter identification method for GMS based on SOS state point determination; In step 1, a GMS friction model is constructed. The GMS model is considered to be composed of multiple single-state friction sub-models connected in parallel, and the total friction force is the sum of the individual sub-friction forces. Its model is expressed as: (1)； in, The number of tribological models. This represents the frictional force of a single tribological model. The coefficient of viscous friction, For the robot joint speed, when The expression differs depending on the state. When the tribometer model is in a viscous state: (2)； When the friction sub-model is in a sliding state: (3)； in, It is the convergence coefficient, which determines the speed at which the frictional force converges to the Stribeck curve in the sliding state; in equation (3) The Stribeck curve, as represented, is defined as follows: （4）； in, , These are the Coulomb friction coefficient and the static friction coefficient, respectively. These are the Stribeck speeds; It is the Stribeck factor; Design the Sigmoid function as the switching function to combine the functions of the two phases, that is: （5）； in The designed Sigmoid function is shown in the following equation: （6）； in, It is a proportionality coefficient that determines the speed of function switching; at this time, the initial and final values ​​of the designed switching function are -1 and 1, which can reflect the changes between the two states and satisfy the differentiability requirement.

2. The parameter identification method for an improved GMS friction model of an industrial robot as described in claim 1, characterized in that, In step 2, the Coulomb friction coefficient is calculated using formula (4). static friction coefficient Corresponding Stribeck speed The Stribeck effect model cannot accurately describe the physical properties of the Coulomb friction coefficient. Introducing Stribeck speed To describe the rate of increase of the joint's frictional force from initiation to maximum; for the static friction coefficient corresponding Introducing Stribeck speed The partial friction characteristics of the boundary lubrication, partial lubrication, and full lubrication stages of robot joint friction are described by Equation (7): （7）。 3. The parameter identification method for an improved GMS friction model of an industrial robot as described in claim 2, characterized in that, The process of step 3 is as follows: 3.1 Excitation Trajectory Design for Stribeck Effect Identification Based on Newton's and Euler's laws, a robot dynamics model is constructed, and the expression is simplified as follows: （8）； in, It refers to the joint torque of the robot. It is the moment of inertia. It is the matrix of centrifugal force and Coriolis force. It is gravity; The designed excitation trajectory is shown in the following formula: （9）； in, , , , , and These are the velocity trajectory coefficients during the three reversal phases. Multiple sets of experiments were conducted for each joint, setting the velocity of each joint. ; 3.2 Identification of Stribeck effect parameters based on SOS algorithm Let the Coulomb friction coefficient be... static friction coefficient viscous friction coefficient Stribeck speed , Stribeck factor For the parameters to be identified, based on experience, the upper and lower bounds of the parameter search are roughly set, and the fitness function is designed as follows: （10）； in, , They are at speeds of The frictional torque after data acquisition and processing, and the frictional torque estimated based on the improved Stribeck friction model, For data points, The search objective is to find the minimum fitness value.

4. The parameter identification method for an improved GMS friction model of an industrial robot as described in claim 3, characterized in that, In step 4, a set of piecewise functions are designed, assuming they are divided into four segments, as follows: （11）； in, It is the first Frictional torque at each point , , , , , , , , These are the initial torque values ​​and slopes for each segment. , , , , These are the initial and final points of the pre-sliding design, as well as the initial points of each segment. To determine the segmentation points and slope using the SOS algorithm, a fitness function needs to be designed. Since the first and last values ​​of each segmentation function are the same, the relationship is as follows: （12）； Therefore, we can deduce that: （13）； Based on the principle of the SOS algorithm, let... , , , , , , , For the search parameters, the upper and lower bounds of the parameter search are roughly set based on experience. Based on the designed segmentation points, the fitness function is designed as follows: （14）； in, yes The search objective for the filtered data is to find the minimum fitness value. Design a trajectory for dynamic parameter identification, and design the robot to perform reciprocating motion at a constant speed while avoiding the influence of joint gravity. The trajectory relationship is as follows: (15)； in, This is the initial position of the joint. The speed is extremely low.

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