CN107671861B - Improved SCARA robot dynamics parameter identification method - Google Patents

Improved SCARA robot dynamics parameter identification method Download PDF

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CN107671861B
CN107671861B CN201711112065.5A CN201711112065A CN107671861B CN 107671861 B CN107671861 B CN 107671861B CN 201711112065 A CN201711112065 A CN 201711112065A CN 107671861 B CN107671861 B CN 107671861B
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CN107671861A (en
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李新
白瑞林
严浩
吉峰
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Wuxi Xinje Electric Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control

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Abstract

The invention relates to the field of dynamic parameter identification of SCARA robots and discloses an improved method for identifying dynamic parameters of SCARA robots. And (3) establishing a complete dynamic model of the SCARA robot containing the friction term by adopting a Lagrange method, and linearizing the complete dynamic model. Adopting a 5-order Fourier series as a basic form of an excitation track, and replacing a constant term in the traditional Fourier series by a 5-order polynomial to ensure that the joint angular velocity and the joint angular acceleration are zero at the starting time and the stopping time of the track; aiming at minimizing the condition number of the observation matrix, and aiming at enhancing the global optimization capability, the niche genetic algorithm based on the displacement mechanism is adopted to optimize each coefficient of the excitation track. In order to avoid transmission errors caused by direct twice differentiation of joint angles, sampled joint angular velocity data are fitted into a Fourier series form, and then differentiation is carried out to obtain joint angular acceleration signals. In consideration of the influence of measurement noise, a weighted least squares method (WLS) is employed as a parameter estimation method.

Description

Improved SCARA robot dynamics parameter identification method
Technical Field
The invention belongs to the field of SCARA robot dynamics parameter identification, and particularly relates to an improved SCARA robot dynamics parameter identification method.
Background
With the application of industrial robots in high precision fields such as life medical treatment, laser welding, automotive electronics and the like, the robot technology is developing towards high speed and high precision. The control strategies of industrial robots can be divided into two categories: (1) and performing negative feedback control according to the deviation between the actual track and the expected track of the robot. The control method is simple in control law and easy to realize, and is called as motion control, such as PID control, fuzzy control, robust control and the like. (2) The dynamics of the robot are fully considered, a more refined nonlinear control law, namely a model-based control strategy, is designed, and the control method is called dynamic control, such as gravity compensation control, a moment calculation method, internal model control and the like.
Due to the time-varying, strong coupling and nonlinear dynamics characteristics of the robot, the high-speed and high-precision control requirement of the industrial robot is difficult to meet only by a feedback-based motion control strategy. At present, most domestic industrial robots still adopt the traditional PID control strategy. Therefore, designing a control strategy based on a robot dynamics model is an effective method for realizing high-speed and high-precision motion control, and the control strategy is based on the precise dynamics parameters of the robot. The method for acquiring the kinetic parameters of the robot can be divided into the following steps: disintegration measurement, CAD, and global identification. The robot has a complex structure, many parameters are difficult to directly measure, the assembly error and the material distribution characteristic of the robot are ignored by adopting a computer-aided design (CAD) method of computer modeling, and the influence of various factors in the actual work of the robot can be considered by the integral identification method, so that the robot is widely concerned.
In the identification process of the kinetic parameters of the robot, the excitation track generally adopts a Fourier series form, so that the continuous periodicity of the excitation track can be ensured, repeated sampling can be facilitated for many times, and the kinetic characteristics of the robot can be fully excited. However, the traditional Fourier series cannot ensure that the angular velocity and the angular acceleration of the robot joint are zero at the starting time and the ending time of the track; moreover, the condition number of the observation matrix is too large due to the non-optimized Fourier series, and the identification error of the dynamic parameters is too amplified due to the sampling error of the moment, the joint position and the like. Since the condition number of the observation matrix is a multi-peak function, when a basic genetic algorithm (SGA) is adopted to optimize Fourier series, a local optimal solution is easily caused, and the optimization result is easily premature.
In addition, when sampling data is processed, besides the averaging is performed by multiple times of sampling to improve the signal-to-noise ratio, how to acquire the effective angular acceleration signal is a relatively difficult problem. Because the speed signal obtained by sampling has noise, the speed signal is directly differentiated, and the obtained acceleration signal has a large error. Therefore, the angular acceleration is generally obtained by performing inverse fitting on the sampled joint angle and performing differentiation twice, but the transfer error is easily caused by differentiation twice.
Disclosure of Invention
For a specific SCARA robot, a 5-order Fourier series is adopted as a basic form of an excitation track, and a 5-order polynomial is used for replacing a constant term in a traditional Fourier series, so that the angular velocity and the angular acceleration of each joint of the robot are zero at the starting time and the ending time of the excitation track. In order to enhance the global optimization capability, the niche genetic algorithm based on the displacement mechanism is adopted to optimize the Fourier series coefficient, and the condition number of the observation matrix is reduced as much as possible. In order to avoid transmission errors caused by direct twice differentiation of joint angles, sampled joint angular velocity data are fitted into a Fourier series form, and then differentiation is carried out to obtain joint angular acceleration signals.
In order to achieve the above technical object, the present invention provides an improved method for identifying dynamic parameters of a SCARA robot, comprising the following steps:
(1) according to the actual situation, a complete dynamic model of the SCARA robot containing a friction term is established by adopting a Lagrange method;
(2) linearizing the complete kinetic model in the step (1), and expressing the complete kinetic model in a form of a product of a regression matrix and a kinetic parameter vector of the robot;
(3) the method comprises the following steps of adopting a 5-order Fourier series as a basic form of an excitation track, and replacing constant terms in the traditional Fourier series with 5-order polynomials to enable angular velocities and angular accelerations of joints of the robot to be zero at the starting time and the ending time of the excitation track;
(4) in order to enhance the global optimization capability, optimizing the Fourier series coefficient obtained in the step (3) by adopting a niche genetic algorithm based on a displacement mechanism, and reducing the condition number of an observation matrix as much as possible;
(5) the joint angle and the joint angular velocity are collected through a high-precision encoder, in order to avoid the influence of noise of velocity measurement on joint angular acceleration calculation, sampled joint angular velocity data are fitted into a Fourier series form, the Fourier series of the joint angular velocity is differentiated to obtain a joint angular acceleration signal, and the transmission error caused by direct twice differentiation on the joint angle is avoided;
(6) and constructing an observation matrix according to the input torque of each joint of the robot obtained by sampling and the output angle, angular velocity and angular acceleration of each joint, and identifying the kinetic parameters by adopting a weighted least square method.
Further, the excitation locus of the improved fourier series obtained in the step (3) is as follows:
Figure GDA0002688735680000031
the coefficients of the 5 th order polynomial are solved as:
Figure GDA0002688735680000032
Figure GDA0002688735680000033
Figure GDA0002688735680000034
Figure GDA0002688735680000035
Figure GDA0002688735680000036
Figure GDA0002688735680000037
in the formula: i denotes the ith joint, ωfFundamental frequency of Fourier series, the fundamental frequency of each joint being the same, ai，k、bi，kIs a coefficient of Fourier series, theta0iFor the offset, M is the order of the Fourier series, determining the bandwidth of the trace, ai，k、bi，k、θ0iIs a free coefficient; thetai_initThe initial angle of the ith joint is determined by the mechanical structure of the robot, the angle of the robot joint is changed from the initial angle in increment and finally returns to the initial angle, t0＝0，ttf＝2π/(2πωf) Respectively, representing the start and of a periodic movementAnd (4) ending the moment.
Further, the niche genetic algorithm based on the extrusion mechanism in the step (4) has the following differences compared with the traditional genetic algorithm:
let the ith individual be piThe jth individual is pjThen the individual piAnd pjThe Euclidean distance between them is shown as the following formula;
||pi-pj||
taking a smaller integer xi, f (·) to represent the fitness of the individual, comparing the similarity of any two individuals in the population before selecting, crossing and mutating each generation, if | | | pi-pjIf | is less than xi, then p is indicatediAnd pjThe degree of similarity is large; by applying a stronger penalty function to the smaller-fitness-degree person, the fitness of the smaller-fitness-degree person becomes extremely small, so that the smaller-fitness-degree person is eliminated; namely if: f (p)i)＞f(pj) Let f (p) bei)＝·f(pj) (a very small positive number), p is then used in the subsequent evolutionjWill be eliminated with great probability.
Further, the Fourier series of the joint angular velocity in the step (5) is expressed as:
Figure GDA0002688735680000041
in the formula:
Figure GDA0002688735680000042
i represents the ith joint, t represents time,
Figure GDA0002688735680000043
expressing the 5 th degree polynomial coefficient, omega, of each jointfFundamental frequency of Fourier series, the fundamental frequency of each joint being the same, ai，k、bi，kThe coefficient of the Fourier series, M is the order of the Fourier series, and the bandwidth of the track is determined.
Obtaining parameter a by linear least square methodi，k、bi，kAnd differentiating the Fourier series of the joint velocity to obtain a joint acceleration signal.
As shown in the attached figure 1, the working principle of the invention is as follows: taking the optimized and improved Fourier series obtained in the step (3) and the step (4) as excitation tracks of joints of the robot, and sampling input torque, output angle and angular speed of each joint of the robot during operation; the sampled joint angular velocity signals are reversely fitted into an optimized Fourier series velocity expression form, and then accurate joint angular acceleration signals are obtained through differentiation, so that the transmission errors caused by directly reversely fitting joint position signals and differentiating the joint angular acceleration twice are avoided; and finally, considering the influence of measurement noise, and identifying the kinetic parameters by adopting a weighted least square method.
According to the scheme, the following beneficial effects can be realized:
(1) aiming at the problem that the conventional Fourier series cannot ensure that the joint angular velocity and the joint angular acceleration are zero at the starting time and the ending time of a track, so that the robot shakes during running, a constant term in the conventional Fourier series is replaced by a polynomial of degree 5, so that the joint angular velocity and the joint angular acceleration of the robot are zero at the starting time and the ending time of an excitation track.
(2) Aiming at the problem that the condition number of an observation matrix is overlarge due to the unoptimized Fourier series, the niche genetic algorithm with stronger global optimizing capability and based on a displacement mechanism is adopted to optimize the Fourier series coefficient, so that the condition number of the observation matrix is reduced as much as possible, and the identification precision of the kinetic parameters is improved.
(3) Aiming at the problem of transmission error caused by the fact that a joint angle is directly subjected to reverse fitting and then subjected to differential calculation twice in the traditional method, the method is provided for directly performing reverse fitting on the joint angular velocity and then performing differential calculation to obtain the joint angular acceleration, and the transmission error caused by the differential calculation twice is avoided.
Drawings
FIG. 1 is a flow chart of an improved method for identifying dynamic parameters of a SCARA robot according to the present invention;
FIG. 2 is a schematic diagram of the main body of the SCARA robot according to the present invention;
FIG. 3 is a coordinate system of a connecting rod of the SCARA robot according to the present invention;
FIG. 4 is a schematic diagram of Fourier series optimization based on a niche genetic algorithm of a displacement mechanism.
Detailed Description
In order to make the objects, technical solutions and advantageous effects of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with a specific SCARA robot.
Step (1): a Lagrange method is adopted to establish a complete dynamic model of the front two joints of the SCARA robot.
As shown in fig. 2 and fig. 3, the two joints 3 and 4 of the SCARA robot share one connecting rod, and the servo motors, the synchronous belts, the ball screws, the lifting tables and the like of the joints 2, 3 and 4 are all installed on the connecting rod of the joint 2, so that the joint 1 and the joint 2 determine the plane positioning precision and the track tracking precision of the SCARA robot, and the joint 3 determines the motion in the vertical direction. Since the joint 3 is perpendicular to the first two joints, the motion of the first two joints does not affect the joint 3. Therefore, only the joint 1 and the joint 2 are subjected to the kinetic modeling and the kinetic parameter identification.
Considering joint friction, the dynamic model of the SCARA robot can be expressed by a second-order nonlinear differential equation, specifically as shown in formula (1).
Figure GDA0002688735680000061
In the formula, theta ∈ RnIs a vector of the angle of the joint,
Figure GDA0002688735680000062
is the angular velocity vector of the joint,
Figure GDA0002688735680000063
for the angular acceleration vector of the joint, D (theta) belongs to Rn×nIs a matrix of the inertia of the robot,
Figure GDA0002688735680000064
g (theta) is an element of R for the centrifugal force and Goldfish force matrixnAs a vector of the gravity moment,
Figure GDA0002688735680000065
for the friction torque vector, τ ∈ RnIs a control moment vector.
Expression (1) is expressed as a scalar form of a matrix, as shown in expression (2):
Figure GDA0002688735680000066
according to the structure of the SCARA robot, the Lagrange method is utilized to carry out dynamic modeling on the SCARA robot, and various parameters in the formula (2) are obtained as follows:
Figure GDA0002688735680000067
Figure GDA0002688735680000068
D21＝D12
Figure GDA0002688735680000071
C0＝m2l1(x2sin(θ2)+l2sin(θ2)+y2cos(θ2))
Figure GDA0002688735680000072
Gl＝0，G2＝0
Figure GDA0002688735680000073
in the formula, m1、m2Mass of connecting rod 1 and connecting rod 2, respectively,/1、l2Length of connecting rod 1 and connecting rod 2, respectively, (x)1，y1，z1)、(x2，y2，z2) Position coordinates of the center of mass of the front two connecting rods in a coordinate system 1 and a coordinate system 2 respectively, IZZ1、IZZ2Moment of inertia, f, of connecting rods 1 and 2, respectively, along the Z-axisciAnd fviExpressing the coulomb friction coefficient and the viscous friction coefficient of the ith joint respectively.
Step (2): the complete kinetic model is linearized and expressed in the form of the product of a regression matrix and the robot kinetic parameter vector.
For an industrial robot, there is a parameter vector that depends on the robot parameters, so that the robot dynamics equations can be linearized, i.e.:
Figure GDA0002688735680000074
in the formula (I), the compound is shown in the specification,
Figure GDA0002688735680000075
the joint variable function is composed of the generalized coordinates of the robot and each derivative of the generalized coordinates; phi epsilon to RpThe unknown constant matrix including the friction coefficient is called a Basic Parameter Set (BPS), i.e., the kinetic parameters to be recognized by the robot, n is the number of joints, and p is the number of kinetic parameters to be recognized.
And (3) obtaining the display expression of the linearization equation as shown in the formula (4) according to the specific form of the SCARA robot dynamics equation of the formula (2).
Figure GDA0002688735680000076
The parameters in the formula are:
Figure GDA0002688735680000081
φ2＝m2(x2+l2)
φ3＝m2y2
Figure GDA0002688735680000082
φ5＝fc1，φ6＝fv1，φ7＝fc2，φ8＝fv2
Figure GDA0002688735680000083
Figure GDA0002688735680000084
Figure GDA0002688735680000085
Figure GDA0002688735680000086
Figure GDA0002688735680000087
Y21＝0
Figure GDA0002688735680000088
Figure GDA0002688735680000089
Figure GDA00026887356800000810
Figure GDA00026887356800000811
and (3): improvement of the conventional fourier series.
The conventional M-th order fourier series is defined as:
Figure GDA00026887356800000812
in the formula: i denotes the ith joint, ωfFundamental frequency of Fourier series, the fundamental frequency of each joint being the same, ai，k、bi，kIs a coefficient of Fourier series, theta0iFor the offset, M is the order of the Fourier series, determining the bandwidth of the trace, ai，k、bi，k、θ0iIs a free coefficient.
The corresponding joint operating speeds and accelerations are as follows:
Figure GDA0002688735680000091
Figure GDA0002688735680000092
in the process of identifying the dynamic parameters of the robot, in order to ensure the continuous periodicity of operation and the stability of the starting time and the ending time, the excitation track is required to meet the following conditions:
Figure GDA0002688735680000093
in the formula, t0＝0，ttf＝2π/(2πωf) Respectively representing the starting and ending moments of the periodic movement, conventional fourier transformsThe number of the inner leaf stages is difficult to ensure the above conditions.
In order to meet the conditions, the excitation locus of the traditional Fourier series is improved, and a constant term theta is used0iInstead of a polynomial of degree 5, the excitation trajectory resulting in an improved fourier series is as follows:
Figure GDA0002688735680000094
the coefficients of the 5 th order polynomial are solved as:
Figure GDA0002688735680000095
Figure GDA0002688735680000096
Figure GDA0002688735680000097
Figure GDA0002688735680000098
Figure GDA0002688735680000099
Figure GDA00026887356800000910
and (4): and optimizing Fourier series coefficients.
The robot dynamics parameter identification comprises the following steps: and tracking specific excitation tracks of all joints of the robot, obtaining input torque, joint angles, angular speeds and angular accelerations of the joints through sampling or indirect calculation, and estimating a kinetic parameter phi. When each joint of the robot tracks the excitation track, at the sampling time t1，t2，…，tNThe joint input torque and the like are indirectly sampled for N times, and then the equation set shown in the formula (10) can be obtained.
YN·φ＝τN (10)
Namely:
Figure GDA0002688735680000101
in the formula, YNIs composed of theta,
Figure GDA0002688735680000102
The right side of the formed observation matrix is the output torque vector of the two joints at different sampling moments.
Defining an observation matrix YNCondition number of (2) is Cond (Y)N)＝||YN -1||·||YNIf the condition number is the minimum, the fourier series needs to be optimized to reduce the influence of the measurement error on the identification of the dynamic parameters.
After the form of the excitation track is determined, sampling is carried out on the improved Fourier series shown in the formula (9) at a certain frequency to obtain the corresponding joint angle, angular velocity and angular acceleration, and N groups of data are collected together, so that an observation matrix Y is constructedN. By observing the matrix YNThe condition number is used as a target function, namely a fitness function, in order to enhance the global optimization capability, the niche genetic algorithm based on the displacement mechanism is adopted to optimize the Fourier series coefficient, and the corresponding coefficient a when the condition number is minimum is obtainedi，k、bi，k。
The niche genetic algorithm optimizing method based on the extrusion mechanism comprises the following steps:
1) selecting a coding strategy: taking M to be 5, wherein the improved Fourier series has 20 parameters to be optimized, and therefore, the 20 parameters are subjected to real number coding to form a feasible solution set;
2) determining a fitness function: calculating according to the formula (11) to obtain an observation matrix YNAnd the condition number is used as a target function, namely a fitness function;
3) establishing a displacement mechanism: let the ith individual be piThe jth individual is pjThen the individual piAnd pjThe Euclidean distance therebetween is shown as formula (12).
||pi-pj|| (12)
A smaller integer xi, f (-) is taken to represent the fitness value of the individual. Before each generation is selected, crossed and mutated, the similarity of any two individuals in the population is compared, if pi-pjIf | is less than xi, then p is indicatediAnd pjThe degree of similarity is greater. By applying a stronger penalty function to the less suitable one, the less suitable one is excluded from being excluded. Namely if: f (p)i)＞f(pj) Let f (p) bei)＝·f(pj) (a very small positive number), p is then used in the subsequent evolutionjWill be eliminated with great probability.
3) Determining genetic algorithm parameters: co-evolution for 400 generations, wherein the population scale is set to be 50, the cross probability is 0.4, and the variation probability is 0.1;
4) selecting operation: the selection of individuals in the population is performed by roulette, and the fitness value of the individuals in the population is inverted so that individuals with smaller fitness values have a greater probability of being selected in the roulette. Selecting operation to control the evolution direction so that the next generation population is superior to the previous generation population;
5) and (3) cross operation: carrying out chromosome crossing operation on individuals in the population according to a certain probability, wherein the crossing positions of the selected chromosomes are the same;
6) mutation operation: carrying out mutation operation on chromosomes in the population according to a certain probability to obtain new population individuals;
7) and judging whether the preset evolution algebra is completed or not, and stopping the evolution if the preset evolution algebra is reached. A schematic diagram of Fourier series optimization of the niche genetic algorithm based on the extrusion mechanism is shown in FIG. 4.
And (5): and sampling and processing joint angles, joint angular velocities and joint angular accelerations.
The optimized and improved Fourier series is used as the excitation track of the robot, namely the position of two joints of the SCARA robot is given, the robot runs under the action of a servo driver, and the joint output angle and the angular speed are acquired by a high-precision encoder.
However, the sampled data is susceptible to measurement noise. Therefore, the excitation trajectory is repeatedly executed for multiple times, and then the sampled joint angle and joint angular velocity are averaged to improve the signal-to-noise ratio, that is:
Figure GDA0002688735680000121
where L is the number of cycles of execution of the excitation trace, j is the jth run cycle, θj(g)、
Figure GDA0002688735680000122
Respectively representing the joint angle and the joint angular speed at the g sampling point in the j running period.
In order to avoid the influence of noise of velocity measurement on acceleration calculation, the conventional method is to perform inverse fitting to a Fourier series form according to angle data of each joint obtained by sampling, and then obtain the angular velocity and the angular acceleration of each joint according to differentiation. However, the servo motor generally adopts a high-precision encoder at present, the joint angular velocity is obtained according to the joint angle, and the joint angular velocity signal is obtained through filtering, so that the invention only performs fitting on the joint angular velocity data obtained by sampling into a Fourier series form, and the Fourier series expression of the joint angular velocity is as follows:
Figure GDA0002688735680000123
obtaining parameter a by linear least square methodi，k、bi，kAnd differentiating the Fourier series of the joint angular velocity to obtain a joint angular acceleration signal, thereby avoiding the transfer error caused by two differentiations.
And (6): and identifying the inertia parameters by adopting a weighted least square method.
According to the joint angle, the joint angular velocity and the joint angular acceleration obtained by sampling, an observation matrix Y is obtainedNAnd sampling the joint input torque to obtain a torque vector tauN。
The solution of equation (11) may be solved using a weighted least squares method. In the data sampling, the joint angle and the joint angular speed are measured after filtering processing is carried out on the joint angle and the joint angular speed through a high-resolution photoelectric encoder, and compared with the measurement noise of joint torque, the measurement noise can be ignored. At this time, the weighted least squares estimate of the inertia φ parameter is:
Figure GDA0002688735680000131
in the formula (I), the compound is shown in the specification,
Figure GDA0002688735680000132
is the estimation value of the dynamic parameter vector, and is a diagonal matrix of the moment measurement noise variance. The moment measurement noise variance is estimated by:
Figure GDA0002688735680000133
Figure GDA0002688735680000134
where L is the number of cycles of execution of the excitation trace, N is the number of points sampled in one cycle, and τij(g) The torque output of the ith joint obtained by sampling at the g time in the j period is shown,
Figure GDA0002688735680000135
and the average value of the torque output of the ith joint obtained in the g-th sampling is shown.
As shown in the attached figure 1, the working principle of the invention is as follows: taking the optimized and improved Fourier series obtained in the step (3) and the step (4) as excitation tracks of joints of the robot, and sampling input torque, output angle and angular speed of each joint of the robot during operation; the sampled joint angular velocity signals are reversely fitted into an optimized Fourier series velocity expression form, and then accurate joint angular acceleration signals are obtained through differentiation, so that the transmission errors caused by directly reversely fitting joint position signals and differentiating the joint angular acceleration twice are avoided; and finally, considering the influence of measurement noise, and identifying the kinetic parameters by adopting a weighted least square method.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can conceive of changes or substitutions within the technical scope of the present invention. Therefore, the protection scope of the invention should be subject to the protection scope of the claims.

Claims (3)

1. An improved method for identifying dynamic parameters of a SCARA robot is characterized by comprising the following steps:
(1) establishing a complete dynamic model of the SCARA robot containing a friction term by adopting a Lagrange method;
(2) linearizing the complete kinetic model in the step (1), and expressing the complete kinetic model in a form of a product of a regression matrix and a kinetic parameter vector of the robot;
(3) the method comprises the following steps of adopting a 5-order Fourier series as a basic form of an excitation track, and replacing constant terms in the traditional Fourier series with 5-order polynomials to enable angular velocities and angular accelerations of joints of the robot to be zero at the starting time and the ending time of the excitation track;
(4) optimizing the Fourier series coefficient obtained in the step (3) by adopting a niche genetic algorithm based on a displacement mechanism, and reducing the condition number of an observation matrix;
(5) collecting joint angles and joint angular velocities through a high-precision encoder, fitting the sampled joint angular velocity data into a Fourier series form, and differentiating the Fourier series of the joint angular velocities to obtain joint angular acceleration signals;
(6) and constructing an observation matrix according to the input torque of each joint of the robot obtained by sampling and the output angle, angular velocity and angular acceleration of each joint, and identifying the kinetic parameters by adopting a weighted least square method.
2. The improved method for identifying dynamic parameters of a SCARA robot as claimed in claim 1, wherein the excitation trajectory of the improved fourier series obtained in step (3) is as follows:
Figure FDA0002688735670000011
the coefficients of the 5 th order polynomial are solved as:
Figure FDA0002688735670000021
Figure FDA0002688735670000022
Figure FDA0002688735670000023
Figure FDA0002688735670000024
Figure FDA0002688735670000025
Figure FDA0002688735670000026
in the formula: i denotes the ith joint, ωfFundamental frequency of Fourier series, eachFundamental frequencies of joints are the same, ai，k、bi，kIs the coefficient of the Fourier series, M is the order of the Fourier series, determines the bandwidth of the track, ai，k、bi，kIs a free coefficient; thetai_initThe initial angle of the ith joint is determined by the mechanical structure of the robot, the angle of the robot joint is changed from the initial angle in increment and finally returns to the initial angle, ttf＝2π/(2πωf) Indicating the end time of the periodic movement.
3. The improved method for identification of dynamic parameters of SCARA robot as claimed in claim 1, wherein the fourier series expression of joint velocity in step (5) is:
Figure FDA0002688735670000027
in the formula:
Figure FDA0002688735670000028
i represents the ith joint, t represents time,
Figure FDA0002688735670000029
expressing the 5 th degree polynomial coefficient, omega, of each jointfFundamental frequency of Fourier series, the fundamental frequency of each joint being the same, ai，k、bi，kThe coefficient of the Fourier series, M is the order of the Fourier series, and the bandwidth of the track is determined.
Obtaining parameter a by linear least square methodi，k、bi，kAnd differentiating the Fourier series of the joint velocity to obtain a joint acceleration signal.
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