CN112847365A - Torque estimation method - Google Patents

Torque estimation method Download PDF

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CN112847365A
CN112847365A CN202110016764.XA CN202110016764A CN112847365A CN 112847365 A CN112847365 A CN 112847365A CN 202110016764 A CN202110016764 A CN 202110016764A CN 112847365 A CN112847365 A CN 112847365A
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estimation method
filtering
harmonic
torque estimation
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CN112847365B (en
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赵鹏兵
刘哲
王卓阳
杨金虎
张洁
段学超
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Xidian University
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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
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control

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  • Control Of Electric Motors In General (AREA)

Abstract

The invention discloses a moment estimation method, which comprises two steps of a and b: a. establishing a harmonic transmission model comprising a harmonic transmission kinematics model, a motion error model and a harmonic transmission compliance model; b. constructing a redundant self-adaptive robust Kalman filter; an adaptive conversion module is added while taking a function of the motor current as a redundancy factor. The moment estimation method is based on a harmonic drive model and a redundant self-adaptive robust Kalman filter, the torque estimation filtering has optimality and robustness to load change through self-adjusting filtering gain and self-adaptive switching filtering modes, meanwhile, a function of motor current is used as a redundancy factor of RARKF to tolerate modeling error and switching of the filtering modes changing along with the load, the optimality and robustness of filtering in a moment estimation algorithm are considered, and the contradiction that the traditional algorithm only has optimality or only has robustness but cannot have optimality and robustness at the same time is solved.

Description

Torque estimation method
Technical Field
The invention relates to the technical field of cooperative robot control, in particular to a moment estimation method.
Background
Joint torque feedback can improve the control performance of a robot, is generally used for motion control of a robot manipulator to suppress the influence of load torque, and can be used for dynamic control of the robot without calculating inverse dynamics of the robot, and joint torque sensing or estimation is also essential for controlling the force and compliance of the robot and collision detection.
Joint torque sensors or multi-axis force/torque (F/T) sensors are used in force control of conventional robots. When joint moments are estimated using an F/T sensor on a robot wrist, a large number of calculations are required, and the results are affected by calculation delays and model errors, while the following drawbacks exist in the prior art:
1. the measurement accuracy is inversely proportional to the rigidity of the sensor, and in order to obtain higher measurement accuracy, lower rigidity of the sensor is required, so that the joint dynamics are complex;
2. the use of a low pass filter to filter the output of the harmonic drive model, while providing a simple and convenient way to combat high frequency noise, the speed of response of the torque estimate is limited by the bandwidth of the filter;
3. the filtering gain in the standard Kalman filtering algorithm is optimal and cannot be adjusted automatically, the external environment can only be reflected by the preset measurement noise variance, and the method is difficult to adapt to the change of actual external interference and respond in time;
4. non-linear modeling errors in the state model and metrology model may cause switching failure of the AREKF decision mechanism.
To this end, the present invention develops a torque estimation method.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of complex joint dynamics, limited response speed of torque estimation, incapability of self-adjustment and failure of switching function of an AREKF judgment mechanism in the prior art, the invention provides a torque estimation method which has the advantages of good fault-tolerant capability, dynamic balance optimality and robustness according to load change and the like, and solves the problems in the background art.
(II) technical scheme
In order to achieve the purpose, the invention provides the following technical scheme: a torque estimation method comprises two steps of a and b:
a. establishing a harmonic transmission model comprising a harmonic transmission kinematics model, a motion error model and a harmonic transmission compliance model;
b. constructing a redundant self-adaptive robust Kalman filter;
an adaptive conversion module is added while taking a function of the motor current as a redundancy factor.
Preferably, harmonic drive compliance is modeled from link side absolute encoder readings, motor side encoder readings, and motor current.
Preferably, the total torsional deflection of the harmonic drive is measured by both the link-side and motor-side encoders.
Preferably, the fault tolerance of the filter is adjusted on-line, and the filtering mode is switched between the robust mode and the optimal mode according to load changes.
Preferably, optimality and robustness are dynamically balanced in accordance with changes in load.
Preferably, the total harmonic drive torsional deformation comprises deformation of a flexspline and a wave generator.
(III) advantageous effects
Compared with the prior art, the invention provides a moment estimation method, which has the following beneficial effects:
according to the moment estimation method, the redundancy factor of the RARFF is designed as a function of the motor current to process modeling errors and disturbance, the optimal filtering mode and the robust filtering mode can be switched in a self-adaptive mode according to joint loads, the estimation precision and the response speed are effectively balanced, the optimality and the robustness of filtering in a moment estimation algorithm are considered, the moment estimation precision is further improved, the problem that the traditional algorithm only has optimality or only has robustness but cannot have the optimality and the robustness at the same time is solved, and the good fault-tolerant capability is provided for the modeling errors.
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FIG. 1 is a schematic diagram of the general structure of the process of the present invention;
FIG. 2 is a schematic diagram of the flexible drive of the flexspline and wave generator of the present invention;
FIG. 3 is a graphical representation of typical stiffness and hysteresis curves for a harmonic drive of the present invention;
FIG. 4 is a schematic diagram of the basic principle of the redundant adaptive robust Kalman filter switching module in the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-4, a torque estimation method includes two steps a and b:
a. establishing a harmonic transmission model comprising a harmonic transmission kinematics model, a motion error model and a harmonic transmission compliance model;
the harmonic transmission kinematic model is used for describing the input/output kinematic relationship of the harmonic reducer;
the motion error model is used for describing the motion error when the encoder on the link side measures;
and the harmonic drive compliant model is used for describing the deformation of a flexible gear and a wave generator in the harmonic reducer and estimating the output torque.
b. Constructing a redundant self-adaptive robust Kalman filter;
an adaptive conversion module is added, and meanwhile, a function of the motor current is used as a redundancy factor to tolerate modeling errors and filtering mode switching along with load change.
Preferably, harmonic drive compliance is modeled from link side absolute encoder readings, motor side encoder readings, and motor current.
Preferably, the total torsional deflection of the harmonic drive is measured by both the link-side and motor-side encoders.
Preferably, the fault tolerance of the filter is adjusted on-line, and the filtering mode is switched between the robust mode and the optimal mode according to load changes.
Preferably, optimality and robustness are dynamically balanced in accordance with changes in load.
Preferably, the total harmonic drive torsional deformation comprises deformation of a flexspline and a wave generator.
The embodiment of the moment estimation method is as follows:
a harmonic transmission model is established, and the model can be divided into three parts during model establishment, namely a harmonic transmission kinematic model, a motion error model and a harmonic transmission compliant model.
The harmonic drive kinematics model is first built, assuming that the ideal input/output kinematics relationship is equal to the angular position at the harmonic drive component:
θw＝Nθf (1)
θwis the position of the wave generator, thetafIs the flexspline output position and N is the gear ratio.
Static balance can be described as:
Figure BDA0002887173080000041
τwis the torque of the wave generator, τfIs the flexspline output torque;
equations (1) and (2) represent the ideal linear input/output relationship for harmonic drives, which are considered to be fully rigid gear reduction mechanisms; however, empirical measurements of the input/output relationship provided in the cited documents indicate that the output is not linearly related to the input.
The reason for this non-linearity is the torsional compliance of the harmonic drive components, non-linear friction, and motion errors caused by gear mesh and machining errors. Given the ideal kinematic relationships that describe the motion and force constraints present in harmonic drives, other effects can be incorporated by modeling compliance, friction, and kinematic errors.
The torsional compliance of the harmonic drive is due to the compliance of the flexspline and the wave generator. By considering the torsional flexibility of the wave generator, the hysteresis behavior of harmonic drive can be captured without a separate hysteresis model, taking into account the flexibility of the flexspline and the wave generator.
The torsion angle of the flexspline can be defined as:
Δθf＝θfo-θfi (3)
θfiangular position, theta, representing the circumference of the flexsplinefoIndicating the angular position of the flexspline on the load side measured using a link-side encoder.
The twist angle of the wave generator is defined as:
Δθw＝θwo-θwi (4)
θwoand thetawiRespectively indicating the position of the outer and central parts of the wave generator;
only thetafoAnd thetawiMeasured by a link-side encoder and a motor-side encoder, respectively, [ theta ]fiAnd thetawoIs not available.
The motion error is defined as the measured flexible spline output minus the expected flexible spline output.
Thus, kinematic errors
Figure BDA0002887173080000051
Can be expressed as:
Figure BDA0002887173080000052
the total twist angle of the harmonic drive is written as:
Figure BDA0002887173080000053
substituting equations (3) to (5) into equation (6) yields:
Figure BDA0002887173080000054
in view of harmonic drive friction, equation (2) is expressed as:
Figure BDA0002887173080000055
Figure BDA0002887173080000056
is the harmonic drive friction torque seen with respect to the transmission output side.
For practical and simplicity, the Stribeck friction model has proven useful and validated when used on a robotic arm for joint friction compensation, the model being used for harmonic drive torque estimation and written as:
Figure BDA0002887173080000057
v is the relative velocity, FsIs static friction, FcThe minimum value of the coulomb friction force is shown,
Figure BDA0002887173080000058
and FvIs the lubricant and load parameter and δ is an additional empirical parameter.
The second part of the harmonic drive model, the motion error model, is established below.
Effective torque estimation can be achieved only when the effect of motion error is compensated for, and motion error of a complete round of output can be measured using a high resolution link-side absolute encoder. To determine kinematic errors
Figure BDA0002887173080000061
The test sub is rotated clockwise and counterclockwise one full revolution output without payload. The total torsional deformation Δ θ was measured during this processcwAnd Δ θccw。
Figure BDA0002887173080000062
Figure BDA0002887173080000063
Figure BDA0002887173080000064
And
Figure BDA0002887173080000065
the torsional deformations of the wave generator in the clockwise and counterclockwise direction, respectively, are measured by means of the link-side and motor-side encoders rotating in both directions in the absence of load.
Since the output torque is equal to zero, the torsional deformation of the flexible spline curve is also equal to zero, Δ θ f0. Assuming that the torsional deformation of the wave generator is symmetrical
Figure BDA0002887173080000066
The motion error can be determined by the following equation:
Figure BDA0002887173080000067
the third part of the harmonic drive model, the harmonic drive compliant model, is established below. A typical harmonic drive stiffness curve is characterized by increasing stiffness with displacement and hysteresis behavior. Total harmonic drive torsional deformations include deformations of the flexspline and wave generator. Harmonic drive torsional distortion is largely caused by the torsional compliance of the flexspline. Delta thetafApproximated by a piecewise linear function of the output torque.
Figure BDA0002887173080000068
K1,K2,K3,τ1And τ2Given by the manufacturer, the curve is given by a stiffness K1,K2,K3Are approximated by three straight line segments. Rigidity K1Adapted for flexspline torques 0 to tau1(ii) a Rigidity K2Adapted for flexspline torque τ1To tau2(ii) a Rigidity K3Adapted for flexible gear torque greater than tau2The case (1).
At zero torque output, the torsional deformation of the harmonic reducer can be controlled
Figure BDA0002887173080000071
To
Figure BDA0002887173080000072
To replicate the hysteresis shape of this stiffness curve, the local elastic modulus of the wave generator is approximated by
Figure BDA0002887173080000073
KwAnd CwIs a constant that needs to be determined. The twist angle of the waveform generator can be calculated using the following formula:
Figure BDA0002887173080000074
by substituting the formula (15) into the formula (16), the expression
Figure BDA0002887173080000075
The total torsional deflection of the harmonic drive is measured by both the link-side and motor-side encoders. Wave generator torque tauwApproximated by the motor torque command.
ΔθfAnd τfThe relationship therebetween is expressed in equation (14), where Δ θfIs calculated by combining equation (17) with equation (7), and is shown as:
Figure BDA0002887173080000076
using the inverse solution of equation (14), the flexible spline output torque τ can be estimatedfCan be expressed as:
Figure BDA0002887173080000077
wherein
Figure BDA0002887173080000078
The variable symbols used in the above model are shown in the following table.
Figure BDA0002887173080000079
Figure BDA0002887173080000081
Figure BDA0002887173080000091
After the model part is completed, a second part in the overall structure is established, namely a redundant self-adaptive robust Kalman filtering algorithm part, due to inevitable noise, an estimation result calculated according to a torque formula cannot be directly used for a control law of a joint, so that a filtering algorithm is required, and a strong filtering function is required to realize quick response due to the fact that the torque of the joint may change rapidly.
Considering that the estimation accuracy is more or less sacrificed in robust filtering, the adaptive robust filtering is employed to suppress excessive sacrifice by introducing a self-switching of the filtering mode between optimal and robust. For joint torque estimation as referred to herein, it is desirable that the filtering mode switch from optimal to robust as the load increases and from robust to optimal as the load decreases, but there are unmodeled non-linear errors that can vary with load and can lead to filtering mode switching errors.
If the load size is much larger than the uncertainty, the filter will remain in robust mode without fail-over; if the load magnitude is less than the uncertainty magnitude, the filter preferably remains in the best mode, thereby providing a more accurate torque estimate.
In order to restrain the influence of errors, a redundant self-adaptive robust Kalman filtering algorithm is introduced and used for joint torque estimation. The method has a redundancy factor and can help reduce the negative influence of modeling errors. Since the modeling error depends on the joint load, and the joint load is reflected by the motor current, the redundancy coefficient is designed as a function of the motor current. And adjusting the fault tolerance of the filter on line, and switching the filtering mode between the robust mode and the optimal mode according to load change. The input to the filtering section comprises τ in equation (19)fAnd the measured current IM。
Design the filtering model as
X(k)＝f(k,X(k-1))+w(k) (20)
Y(k)＝X(k)+v(k) (21)
X (k) is the state of the system over time step k, Y (k) is the measured value over time step k, k ∈ N.
The system function f (k, X (k-1)) shows the dynamics of the system in the X (k) state, W and V are process and measurement noise, assuming uncorrelated zero mean Gaussian white noise and covariance matrices W and V, respectively.
For joint torque estimation, f (k, X (k-1)) ═ X (k-1), and the state variable X is τ in equation (19)fIs the calculation result from equation (19), and n and m are the spatial dimensions equal to 1. Corresponding to the torque model, w represents the unknown change in torque from time step k to k-1, and v describes the randomness contained in the torque calculationNoise. At a step of time step k, the time of the step k,
Y(k)＝τf(k) (22)
the redundant adaptive robust Kalman filtering algorithm is in the form as follows:
1. and (3) state prediction: the current state prediction and its covariance matrix are
Figure BDA0002887173080000101
P(k|k-1)＝P(k-1|k-1)+W(k-1) (24)
2. Gain adjustment: the covariance matrix of the prediction error is adjusted by
∑(k|k-1)＝S(P(k|k-1)) (25)
S is the gain scheduling operator.
3. And (3) updating the measured value: updating of measured values and their covariance matrix
Figure BDA0002887173080000102
PY(k)＝∑(k|k-1)+V(k) (27)
4. And (3) estimation updating: the filter gain and state estimates and their covariance matrices are
Figure BDA0002887173080000103
Figure BDA0002887173080000104
P(k|k)＝(∑(k|k-1)-1+V-1(k))-1 (30)
When S is a unit operator, the algorithm is equivalent to a standard kalman filter algorithm.
Typical linear H∞The design goal of the robust filtering algorithm is to ensure the stability of the filter in the presence of modeling errors. The modeling error is denoted as E if the following condition is satisfied:
Figure BDA0002887173080000111
for a minimum value γ, named decay factor, the gain scheduling operator may be determined as:
∑(k|k-1)＝(P-1(k|k-1)-γ-2LTL(k))-1 (32)
L(k)∈R1is a user-defined matrix used to adjust the prediction covariance matrix.
Equation (31) indicates that γ is defined as the minimum transfer function between the estimated error and the sum of all other errors. In this context, modeling errors refer to joint moments and other unmodeled uncertainties.
Obviously, a small γ means that the transfer efficiency from noise and modeling error to estimation error is low, i.e. the system gains robustness. The balance of robustness and optimality can be adjusted by adjusting the attenuation factor. The filter robustness decreases as the attenuation factor increases. When γ ∞, the filter is the same as the kalman filter.
The attenuation factor is user defined and has a disadvantage. Because the algorithm will operate in a robust filtering mode once gamma is given, filtering optimality may not be achieved. Therefore, the adaptive robust Kalman filtering algorithm provides an adaptive switching mechanism, so that the filter has adaptivity. In the adaptive robust Kalman filtering algorithm, the gain scheduling operator in equation (25) is determined by P (k | k-1)
Figure BDA0002887173080000112
Alpha is a factor to be defined in equation (37) later,
Figure BDA0002887173080000113
the definition is as follows:
Figure BDA0002887173080000114
ρ is a forgetting factor. If the measurement error variance PY(k) Is less than
Figure BDA0002887173080000115
The algorithm will be in the robust filtering mode. To satisfy the filter stability condition, as in equation (17)
Figure BDA0002887173080000116
The compensation factor in L (k) satisfies
Figure BDA0002887173080000117
The adaptive robust kalman filter algorithm is defined by equations (23) - (30) and (33) - (36).
The goal of the adaptive robust kalman filtering algorithm is to balance filtering optimality and robustness by using adaptive real-time switching of the filtering mode based on the update frequency. However, if there is an inequality
Figure BDA0002887173080000121
With modeling error always true, equation (33) will be equivalent to equation (32).
When the modeling error exceeds the load magnitude, the robust filtering state need not be triggered. Therefore, an adjustable switching threshold is required to recover the transfer function of equation (33), i.e., α > 1.
Therefore, considering that the torque model given by the formula (19) has modeling errors, a redundancy factor and a compensation function in the adaptive robust kalman filter are designed, a redundant adaptive robust kalman filter algorithm is formed, and the redundant adaptive robust kalman filter algorithm is applied to the torque filter estimation. The modeling error increases with increasing joint load, so the redundancy factor a needs to be increased to avoid excessive loss of filter optimality.
Taking into account the time step of joint loadMeasured motor current I on kM(k) To express, design the redundancy factor as
Figure BDA0002887173080000122
The compensation function term is:
Figure BDA0002887173080000123
wherein the compensation factor is:
Figure BDA0002887173080000124
in case of a redundancy factor α ≠ 1, the stability of the filter can be guaranteed.
The redundant adaptive robust kalman filter algorithm for torque estimation can be fully represented by equations (23) - (30).
The threshold is set as the upper limit of the modeling error and the filter switches to the robust filtering mode if the difference between the measured and predicted joint loads exceeds a preset threshold. This helps to reduce unnecessary optimization losses. Thus, the switching of the torque estimation between optimality and robustness becomes more efficient, resulting in a reasonable balance between estimation accuracy and fast tracking capability.
The invention constructs a harmonic transmission model of the joint of the cooperative robot, designs a redundant self-adaptive robust Kalman filtering algorithm for filtering, and enables the moment estimation filtering to have optimality and robustness to load change through self-adjusting filtering gain and self-adaptively switching a filtering mode, thereby improving the precision of moment estimation.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the use of the verb "comprise a" to define an element does not exclude the presence of another, same element in a process, method, article, or apparatus that comprises the element.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. A torque estimation method is characterized by comprising two steps of a and b:
a. establishing a harmonic transmission model comprising a harmonic transmission kinematics model, a motion error model and a harmonic transmission compliance model;
b. constructing a redundant self-adaptive robust Kalman filter;
an adaptive conversion module is added while taking a function of the motor current as a redundancy factor.
2. A torque estimation method according to claim 1, characterized in that: and modeling the harmonic transmission compliance according to the link side absolute encoder reading, the motor side encoder reading and the motor current.
3. A torque estimation method according to claim 1, characterized in that: the total torsional deflection of the harmonic drive is measured by both the link-side and motor-side encoders.
4. A torque estimation method according to claim 1, characterized in that: and adjusting the fault tolerance of the filter on line, and switching the filtering mode between a robust mode and an optimal mode according to load change.
5. A torque estimation method according to claim 1, characterized in that: and dynamically balancing optimality and robustness according to the change of the load.
6. A torque estimation method according to claim 1, characterized in that: total harmonic drive torsional deformations include deformations of the flexspline and wave generator.
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CN110018073A (en) * 2019-04-02 2019-07-16 无锡智动力机器人有限公司 A kind of On-line Estimation method for elastic actuator elastomer rigidity of connecting
CN110220625A (en) * 2019-05-30 2019-09-10 南开大学 A kind of measurement method of harmonic reducer flexible wheel output torque
CN110303521A (en) * 2018-03-27 2019-10-08 清华大学 Joint of robot torque signals acquisition system and method
DE102018125079A1 (en) * 2018-10-10 2020-04-16 Schaeffler Technologies AG & Co. KG Tension shaft transmission and transmission element therefor as well as robot arm and method for measuring a torque

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106709102A (en) * 2015-11-17 2017-05-24 黑龙江恒能自控科技有限公司 Hysteresis modeling method for harmonic reducer in magnetically suspended control moment gyroscope system
CN106426174A (en) * 2016-11-05 2017-02-22 上海大学 Robot contact force detecting method based on torque observation and friction identification
CN107590317A (en) * 2017-08-17 2018-01-16 河海大学 A kind of generator method for dynamic estimation of meter and model parameter uncertainty
CN110303521A (en) * 2018-03-27 2019-10-08 清华大学 Joint of robot torque signals acquisition system and method
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