CN111640495A - Variable force tracking control method and device based on impedance control - Google Patents

Variable force tracking control method and device based on impedance control Download PDF

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CN111640495A
CN111640495A CN202010477823.9A CN202010477823A CN111640495A CN 111640495 A CN111640495 A CN 111640495A CN 202010477823 A CN202010477823 A CN 202010477823A CN 111640495 A CN111640495 A CN 111640495A
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force
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李冠呈
李候
王子龙
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Beijing Machinery Equipment Research Institute
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Abstract

The application discloses a variable force tracking control method and device based on impedance control, and the method comprises the steps of obtaining the sensed contact force acting on the tail end of a robot; inputting the contact force into a trained and optimized target impedance model, wherein the impedance parameters of the target impedance model enable the force error of the contact force and the expected force to be 0; inputting the desired force output by the target impedance model into a robot kinematics model; and controlling the motion of the tail end of the robot by utilizing the motion control quantity output by the robot kinematic model. By introducing a new target impedance model, the application of the target impedance model can effectively solve the problem of complex man-machine cooperative control strategy in the rehabilitation process, ensure the flexibility of the system and avoid secondary damage to a patient; and can provide complex force training in a specific rehabilitation stage, provide high-order contact force differential-free control for a patient and ensure the stability of the system.

Description

Variable force tracking control method and device based on impedance control
Technical Field
The invention belongs to the technical field of computers, and relates to a variable force tracking control method and device based on impedance control.
Background
Hemiplegia often occurs together with acute cerebrovascular disease, and patients can have certain muscular dyskinesia after suffering from the hemiplegia, and the manifestations of upper limbs and lower limbs are particularly obvious. The most important cause of such diseases is the impairment of the motor center of cerebral hemisphere cortex. According to the degree of illness, it can be classified into paresis, incomplete paralysis and complete paralysis. Paresis is characterized by weakened muscle strength, which is in four to five grades and generally does not affect daily life; incomplete paralysis is characterized by a large range, with muscle strength of two to four grades; the muscle force of the whole paralysis is zero order, and the paralyzed limbs of the patient can not move autonomously. The clinical classification can be divided into four more specific expression forms, namely: hemiparalysis, flaccid hemiplegia, spastic hemiplegia and conscious disturbance hemiplegia
Because the patient is then recovered in-process, human and recovered equipment intercoupling, traditional rigidity is recovered easily to cause the secondary injury to the patient. Therefore, the control method applied by the rehabilitation robot controller generally adopts compliance control. The traditional compliance control usually adopts an impedance control strategy, and a rigid joint is equivalent to a flexible joint by establishing an inertia-spring-damping virtual system. However, due to system characteristics, the conventional impedance cannot realize the non-differential tracking of high-order variable force, and cannot improve the robustness of unknown complex environments such as environment positions and environment rigidity.
Disclosure of Invention
In order to solve the problems that in the related art, due to an impedance control strategy, the non-differential tracking of high-order variable force cannot be realized, and the robustness of unknown complex environments such as environment positions and environment rigidity cannot be improved, the application provides a variable force tracking control method and device based on impedance control.
In a first aspect, the present application provides a variable force tracking control method based on impedance control, the method including:
acquiring an induced contact force acting on the tail end of the robot;
inputting the contact force into a trained and optimized target impedance model, wherein the impedance parameters of the target impedance model enable the force error of the contact force and the expected force to be 0;
inputting the desired force output by the target impedance model into a robot kinematics model;
controlling the motion of the tail end of the robot by utilizing the motion control quantity output by the robot kinematic model;
the target impedance model is:
Figure BDA0002516407120000011
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure BDA0002516407120000012
indicating differentiating the difference between the actual contact force and the desired contact force.
Optionally, before inputting the contact force into the learning-optimized target impedance model, the method further comprises:
establishing a target impedance model by using the initial predetermined impedance parameters;
acquiring training contact force acting on the tail end of the robot sensed in the training process;
inputting the training contact force to the target impedance model;
determining a force error of the training contact force and a corresponding expected force using the target impedance model;
and when the force error is not 0 value, adjusting the impedance parameter of the target impedance model, and updating the target impedance model by using the adjusted impedance parameter until the determined force error is 0.
Optionally, after the determining the force error of the training contact force and the corresponding expected force using the target impedance model, the method further comprises:
when the force error is 0, taking the target impedance model when the force error is 0 as the trained and optimized target impedance model.
Alternatively to this, the first and second parts may,
Figure BDA0002516407120000021
kp,ki,kdproportional, integral, differential gain, K, respectively, of the force error integral value0Expressed as a constant;
the force error double integral is expressed as: ef＝∫∫ef；
The expected trajectory is:
Figure BDA0002516407120000022
η1、η2are all variable constants;
wherein
Figure BDA0002516407120000023
xcIs a compliant trajectory;
xdcthe first order differential and the second order differential of (a) are respectively:
Figure BDA0002516407120000024
Figure BDA0002516407120000025
optionally, the method further includes:
verifying the target impedance model for error force no-difference tracking;
the verification operation is as follows:
will be provided with
Figure BDA0002516407120000026
And
Figure BDA0002516407120000027
substituting the target impedance model to obtain:
Figure BDA0002516407120000028
actual position x and desired position xcHas deviation, satisfies the relation xc＝x+xWherein
Figure BDA0002516407120000029
xeIs the location of the external environment, keIs the stiffness of the external environment;
for xcAnd respectively obtaining a second order differential and a first order differential:
Figure BDA00025164071200000210
will be provided with
Figure BDA0002516407120000031
And
Figure BDA0002516407120000032
substituting the target impedance model to obtain:
Figure BDA0002516407120000033
merging and item shifting to obtain:
Figure BDA0002516407120000034
get
Figure BDA0002516407120000035
The following can be obtained through continuous simplification:
Figure BDA0002516407120000036
two sides of the equation multiplied by keThe following can be obtained:
Figure BDA0002516407120000037
by the relation ef＝Fref-FeWill Fe＝Fref-efThe laplace transform is performed after the carry-in:
L(Fe)＝Fref(s)-ef(s)
L(Ef)＝s2ef(s)
Figure BDA0002516407120000038
the method is simplified and can be obtained:
Figure BDA0002516407120000039
let Λ(s) be (k)eη1M+keη2M)s5+[ke(η1B+kd)+keη2B-ketd]s4+[ke(η1K0+kp)+ke(η2K0+tp)(Ms2+Bs+K0)]s3+kekiThe pull transform reduction equation is:
Figure BDA00025164071200000310
from the median theorem we can derive:
Figure BDA00025164071200000311
Fref(s) is a pull-transformed value of the desired force, and s is a pull-transformed parameter.
In a second aspect, the present application also provides a variable force tracking control apparatus based on impedance control, the apparatus comprising:
the robot comprises a first acquisition module, a second acquisition module and a control module, wherein the first acquisition module is configured to acquire the induced contact force acting on the robot tail end;
a first input module configured to input the contact force acquired by the first acquisition module into a trained and optimized target impedance model, wherein the impedance parameters of the target impedance model enable a force error of the contact force and a desired force to be 0;
a second input module configured to input the desired force output by the target impedance model into a robot kinematics model;
a control module configured to control a motion of the robot tip using a motion control amount output by the robot kinematics model;
the target impedance model is:
Figure BDA0002516407120000041
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure BDA0002516407120000042
indicating differentiating the difference between the actual contact force and the desired contact force.
Optionally, the apparatus further comprises:
a model building module configured to build a target impedance model using the initial predetermined impedance parameters;
the second acquisition module is configured to acquire a training contact force acting on the tail end of the robot, which is sensed in a training process;
the first input module further configured to input the training contact force to the target impedance model;
a determination module configured to determine a force error of the training contact force and a corresponding expected force using the target impedance model;
an adjustment update module configured to adjust an impedance parameter of the target impedance model when the force error is a non-0 value, and update the target impedance model with the adjusted impedance parameter until the determined force error is 0.
Optionally, the model establishing module is further configured to, when the force error is 0, use the target impedance model when the force error is 0 as the trained and optimized target impedance model.
Alternatively to this, the first and second parts may,
Figure BDA0002516407120000043
kp,ki,kdproportional, integral, differential gain, K, respectively, of the force error integral value0Expressed as a constant;
the force error double integral is expressed as:
Figure BDA0002516407120000044
the expected trajectory is:
Figure BDA0002516407120000045
η1、η2are all variable constants;
wherein
Figure BDA0002516407120000046
xcIs a compliant trajectory;
xdcthe first order differential and the second order differential of (a) are respectively:
Figure BDA0002516407120000047
Figure BDA0002516407120000048
optionally, the apparatus further comprises:
a verification module configured to verify a no-difference tracking of error forces by the target impedance model;
the verification module performs the following verification operations:
will be provided with
Figure BDA0002516407120000051
And
Figure BDA0002516407120000052
into the eyeA standard impedance model, yielding:
Figure BDA0002516407120000053
actual position x and desired position xcHas deviation, satisfies the relation xc＝x+xWherein
Figure BDA0002516407120000054
xe is the position of the external environment, ke is the stiffness of the external environment;
for xcAnd respectively obtaining a second order differential and a first order differential:
Figure BDA0002516407120000055
will be provided with
Figure BDA0002516407120000056
And
Figure BDA0002516407120000057
substituting the target impedance model to obtain:
Figure BDA0002516407120000058
merging and item shifting to obtain:
Figure BDA0002516407120000059
get
Figure BDA00025164071200000510
The following can be obtained through continuous simplification:
Figure BDA00025164071200000511
two sides of the equation multiplied by keThe following can be obtained:
Figure BDA00025164071200000512
by the relation ef＝Fref-FeWill Fe＝Fref-efThe laplace transform is performed after the carry-in:
L(Fe)＝Fref(s)-ef(s)
L(Ef)＝s2ef(s)
Figure BDA00025164071200000513
the method is simplified and can be obtained:
Figure BDA00025164071200000514
let Λ(s) be (k)eη1M+keη2M)s5+[ke(η1B+kd)+keη2B-ketd]s4+[ke(η1K0+kp)+ke(η2K0+tp)(Ms2+Bs+K0)]s3+kekiThe pull transform reduction equation is:
Figure BDA0002516407120000061
from the median theorem we can derive:
Figure BDA0002516407120000064
Fref(s) is a pull-transformed value of the desired force, and s is a pull-transformed parameter.
Through the technical characteristics, the technical scheme provided by the application can at least realize the following beneficial effects:
by introducing a new target impedance model, the use of the target impedance model can effectively solve the complex man-machine cooperative control strategy in the rehabilitation process, on one hand, the system can be ensured to be flexible, and secondary damage to a patient is avoided; on the other hand, the device can provide complex force training, provide high-order contact force indifferent control for a patient and ensure the stability of the system in a specific rehabilitation stage.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a flow chart of a variable force tracking control method based on impedance control provided in one embodiment of the present application;
FIG. 2 is a flow chart of a variable force tracking control method based on impedance control provided in another embodiment of the present application;
fig. 3 is a schematic structural diagram of a variable force tracking control device based on impedance control according to an embodiment of the present application.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the invention, as detailed in the appended claims.
Fig. 1 is a flowchart of a variable force tracking control method based on impedance control provided in an embodiment of the present application, where the variable force tracking control method based on impedance control provided in the present application includes the following steps:
step 101, obtaining an induced contact force acting on the tail end of a robot;
step 102, inputting the contact force into a trained and optimized target impedance model, wherein the impedance parameters of the target impedance model enable the force error of the contact force and the expected force to be 0;
the target impedance model is:
Figure BDA0002516407120000062
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure BDA0002516407120000063
indicating differentiating the difference between the actual contact force and the desired contact force.
Step 103, inputting the expected force output by the target impedance model into a robot kinematic model;
and 104, controlling the motion of the tail end of the robot by using the motion control quantity output by the robot kinematic model.
In summary, the variable force tracking control method based on impedance control provided by the application introduces a new target impedance model, and the use of the target impedance model can effectively solve a complex man-machine cooperative control strategy in the rehabilitation process, so that on one hand, the system can be ensured to be flexible, and secondary damage to a patient is avoided; on the other hand, the device can provide complex force training, provide high-order contact force indifferent control for a patient and ensure the stability of the system in a specific rehabilitation stage.
Fig. 2 is a flowchart of a variable force tracking control method based on impedance control according to another embodiment of the present application, where the variable force tracking control method based on impedance control further includes a training process of a target impedance model, and the following steps:
step 201, establishing a target impedance model by using initial preset impedance parameters;
during the training process, a target impedance model is established using initial predetermined impedance parameters.
The target impedance model is:
Figure BDA0002516407120000071
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure BDA0002516407120000072
indicating differentiating the difference between the actual contact force and the desired contact force.
Figure BDA0002516407120000073
kp,ki,kdProportional, integral, differential gain, K, respectively, of the force error integral value0Expressed as a constant;
the force error double integral is expressed as: ef＝∫∫ef；
The expected trajectory is:
Figure BDA0002516407120000074
η1、η2are all variable constants;
wherein
Figure BDA0002516407120000075
xcIs a compliant trajectory;
xdcthe first order differential and the second order differential of (a) are respectively:
Figure BDA0002516407120000076
Figure BDA0002516407120000077
step 202, acquiring training contact force acting on the tail end of the robot sensed in the training process;
step 203, inputting the training contact force into a target impedance model;
step 204, determining a force error of the training contact force and the corresponding expected force by using a target impedance model;
step 205, when the force error is not 0, adjusting the impedance parameter of the target impedance model, and updating the target impedance model by using the adjusted impedance parameter until the determined force error is 0;
and step 206, when the force error is 0, taking the target impedance model when the force error is 0 as the trained and optimized target impedance model.
When the force error is 0, the expected force and the contact force in the surface target impedance model have no error, and an ideal training state is achieved.
After the target impedance model is established, the method also verifies the error-free tracking of the target impedance model on the error force, and the verification operation flow is as follows:
will be provided with
Figure BDA0002516407120000081
And
Figure BDA0002516407120000082
substituting the target impedance model to obtain:
Figure BDA0002516407120000083
actual position x and desired position xcHas deviation, satisfies the relation xc＝x+xWherein
Figure BDA0002516407120000084
xeIs the location of the external environment, keIs the stiffness of the external environment;
for xcAnd respectively obtaining a second order differential and a first order differential:
Figure BDA0002516407120000085
will be provided with
Figure BDA0002516407120000086
And
Figure BDA0002516407120000087
substituting the target impedance model to obtain:
Figure BDA0002516407120000088
merging and item shifting to obtain:
Figure BDA0002516407120000089
get
Figure BDA00025164071200000810
The following can be obtained through continuous simplification:
Figure BDA00025164071200000811
two sides of the equation multiplied by keThe following can be obtained:
Figure BDA00025164071200000812
by the relation ef＝Fref-FeWill Fe＝Fref-efThe laplace transform is performed after the carry-in:
L(Fe)＝Fref(s)-ef(s)
L(Ef)＝s2ef(s)
Figure BDA0002516407120000091
the method is simplified and can be obtained:
Figure BDA0002516407120000092
let Λ(s) be (k)eη1M+keη2M)s5+[ke(η1B+kd)+keη2B-ketd]s4+[ke(η1K0+kp)+ke(η2K0+tp)(Ms2+Bs+K0)]s3+kekiThe pull transform reduction equation is:
Figure BDA0002516407120000093
from the median theorem we can derive:
Figure BDA0002516407120000094
Fref(s) is a pull-transformed value of the desired force, and s is a pull-transformed parameter.
It can be seen through the above formula that when the expected contact force is normal force, slope force and acceleration force, can both guarantee that the steady state is no poor and is 0, need not to consider the unknown nature of environmental rigidity, has very strong robustness to the change of environmental position, can adapt to environmental step, slope, acceleration change.
In summary, the variable force tracking control method based on impedance control provided by the application introduces a new target impedance model, and the use of the target impedance model can effectively solve a complex man-machine cooperative control strategy in the rehabilitation process, so that on one hand, the system can be ensured to be flexible, and secondary damage to a patient is avoided; on the other hand, the device can provide complex force training, provide high-order contact force indifferent control for a patient and ensure the stability of the system in a specific rehabilitation stage.
Fig. 3 is a schematic structural diagram of a variable force tracking control device based on impedance control according to an embodiment of the present application, and the variable force tracking control device based on impedance control according to the present application may be implemented by software, hardware, or a combination of software and hardware. The variable force tracking control device for impedance control may include: a first acquisition module 310, a first input module 320, a second input module 330, and a control module 340.
A first obtaining module 310 configured to obtain a sensed contact force acting on the robot tip;
a first input module 320 configured to input the contact force acquired by the first acquisition module 310 into a trained and optimized target impedance model, the target impedance model having impedance parameters such that a force error of the contact force and a desired force is 0;
a second input module 330 configured to input the desired force output by the target impedance model into a robot kinematics model;
a control module 340 configured to control the motion of the robot tip using the motion control amount output by the robot kinematics model;
the target impedance model is:
Figure BDA0002516407120000101
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure BDA0002516407120000102
indicating differentiating the difference between the actual contact force and the desired contact force.
Figure BDA0002516407120000103
kp,ki,kdProportional, integral, differential gain, K, respectively, of the force error integral value0Expressed as a constant;
the force error double integral is expressed as: ef＝∫∫ef；
The expected trajectory is:
Figure BDA0002516407120000104
η1、η2are all variable constants;
wherein
Figure BDA0002516407120000105
xcIs a compliant trajectory;
xdcthe first order differential and the second order differential of (a) are respectively:
Figure BDA0002516407120000106
Figure BDA0002516407120000107
the variable force tracking control device based on impedance control provided by the application can further comprise: the device comprises a model establishing module, a second obtaining module, a determining module and an adjusting and updating module.
A model building module configured to build a target impedance model using the initial predetermined impedance parameters;
the second acquisition module is configured to acquire a training contact force acting on the tail end of the robot, which is sensed in a training process;
the first input module 320 further configured to input the training contact force to the target impedance model;
a determination module configured to determine a force error of the training contact force and a corresponding expected force using the target impedance model;
an adjustment update module configured to adjust an impedance parameter of the target impedance model when the force error is a non-0 value, and update the target impedance model with the adjusted impedance parameter until the determined force error is 0.
In another possible implementation manner, the variable force tracking control device based on impedance control may further include a model building module 390.
The model building module is further configured to take the target impedance model with force error of 0 as the trained and optimized target impedance model when the force error is 0.
In another possible implementation, the variable force tracking control apparatus based on impedance control may further include a verification module 3100.
The verification module is configured to verify the error-free tracking of the error force with the target impedance model established by the model establishing module.
The verification process of the verification module may refer to the verification step of the variable force tracking control method based on impedance control on the target impedance model, and is not described herein again.
The variable force tracking control device based on impedance control provided by the application is a device corresponding to the variable force tracking control method based on impedance control, and specific implementation and technical features can be referred to the description of the variable force tracking control method based on impedance control, which is not repeated in this embodiment.
In summary, the variable force tracking control device based on impedance control provided by the application introduces a new target impedance model, and the use of the target impedance model can effectively solve a complex man-machine cooperative control strategy in the rehabilitation process, so that on one hand, the system can be ensured to be flexible, and secondary damage to a patient is avoided; on the other hand, the device can provide complex force training, provide high-order contact force indifferent control for a patient and ensure the stability of the system in a specific rehabilitation stage.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
It will be understood that the invention is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.

Claims (10)

1. A variable force tracking control method based on impedance control is characterized by comprising the following steps:
acquiring an induced contact force acting on the tail end of the robot;
inputting the contact force into a trained and optimized target impedance model, wherein the impedance parameters of the target impedance model enable the force error of the contact force and the expected force to be 0;
inputting the desired force output by the target impedance model into a robot kinematics model;
controlling the motion of the tail end of the robot by utilizing the motion control quantity output by the robot kinematic model;
the target impedance model is:
Figure FDA0002516407110000011
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure FDA0002516407110000012
indicating differentiating the difference between the actual contact force and the desired contact force.
2. The method of claim 1, wherein prior to inputting the contact force into the learning-optimized target impedance model, the method further comprises:
establishing a target impedance model by using the initial predetermined impedance parameters;
acquiring training contact force acting on the tail end of the robot sensed in the training process;
inputting the training contact force to the target impedance model;
determining a force error of the training contact force and a corresponding expected force using the target impedance model;
and when the force error is not 0 value, adjusting the impedance parameter of the target impedance model, and updating the target impedance model by using the adjusted impedance parameter until the determined force error is 0.
3. The method of claim 1, wherein after the determining a force error for the training contact force and a corresponding expected force using the target impedance model, the method further comprises:
when the force error is 0, taking the target impedance model when the force error is 0 as the trained and optimized target impedance model.
4. The method of claim 1,
Figure FDA0002516407110000013
kp,ki,kdproportional, integral, differential gain, K, respectively, of the force error integral value0Expressed as a constant;
the force error double integral is expressed as: ef＝∫∫ef；
The expected trajectory is:
Figure FDA0002516407110000021
η1、η2are all variable constants;
wherein
Figure FDA0002516407110000022
xcIs a compliant trajectory;
xdcthe first order differential and the second order differential of (a) are respectively:
Figure FDA0002516407110000023
Figure FDA0002516407110000024
5. the method of claim 4, further comprising:
verifying the target impedance model for error force no-difference tracking;
the verification operation is as follows:
will be provided with
Figure FDA0002516407110000025
And
Figure FDA0002516407110000026
substituting the target impedance model to obtain:
Figure FDA0002516407110000027
for xcAnd respectively obtaining a second order differential and a first order differential:
Figure FDA0002516407110000028
will be provided with
Figure FDA0002516407110000029
And
Figure FDA00025164071100000210
substituting the target impedance model to obtain:
Figure FDA00025164071100000211
merging and item shifting to obtain:
Figure FDA00025164071100000212
get
Figure FDA00025164071100000213
The following can be obtained through continuous simplification:
Figure FDA00025164071100000214
two sides of the equation multiplied by keThe following can be obtained:
Figure FDA00025164071100000215
by the relation ef＝Fref-FeWill Fe＝Fref-efThe laplace transform is performed after the carry-in:
L(Fe)＝Fref(s)-ef(s)
L(Ef)＝s2ef(s)
Figure FDA0002516407110000031
the method is simplified and can be obtained:
Figure FDA0002516407110000032
order:
Λ(s)＝(keη1M+keη2M)s5+[ke(η1B+kd)+keη2B-ketd]s4+[ke(η1K0+kp)+ke(η2K0+tp)(Ms2+Bs+K0)]s3+keki
the pull transform reduction equation is:
Figure FDA0002516407110000033
from the median theorem we can derive:
Figure FDA0002516407110000034
Fref(s) is a pull-transformed value of the desired force, and s is a pull-transformed parameter.
6. A variable force tracking control apparatus based on impedance control, the apparatus comprising:
the robot comprises a first acquisition module, a second acquisition module and a control module, wherein the first acquisition module is configured to acquire the induced contact force acting on the robot tail end;
a first input module configured to input the contact force acquired by the first acquisition module into a trained and optimized target impedance model, wherein the impedance parameters of the target impedance model enable a force error of the contact force and a desired force to be 0;
a second input module configured to input the desired force output by the target impedance model into a robot kinematics model;
a control module configured to control a motion of the robot tip using a motion control amount output by the robot kinematics model;
the target impedance model is:
Figure FDA0002516407110000035
wherein: m, B, K represent the inertia, damping and stiffness matrices, x, respectively, of the target impedance equationdcDifference of the desired trajectory and the compliant trajectory, FdTo the desired force, FeAs a contact force, tpAnd tdIn the case of a real number,
Figure FDA0002516407110000036
indicating differentiating the difference between the actual contact force and the desired contact force.
7. The apparatus of claim 6, further comprising:
a model building module configured to build a target impedance model using the initial predetermined impedance parameters;
the second acquisition module is configured to acquire a training contact force acting on the tail end of the robot, which is sensed in a training process;
the first input module further configured to input the training contact force to the target impedance model;
a determination module configured to determine a force error of the training contact force and a corresponding expected force using the target impedance model;
an adjustment update module configured to adjust an impedance parameter of the target impedance model when the force error is a non-0 value, and update the target impedance model with the adjusted impedance parameter until the determined force error is 0.
8. The apparatus of claim 6,
the model building module is further configured to take the target impedance model with force error of 0 as the trained and optimized target impedance model when the force error is 0.
9. The apparatus of claim 6,
Figure FDA0002516407110000041
kp,ki,kdproportional, integral, differential gain, K, respectively, of the force error integral value0Expressed as a constant;
the force error double integral is expressed as: ef＝∫∫ef；
The expected trajectory is:
Figure FDA00025164071100000411
η1、η2are all variable constants;
wherein
Figure FDA00025164071100000412
xcIs a compliant trajectory;
xdcthe first order differential and the second order differential of (a) are respectively:
Figure FDA0002516407110000042
Figure FDA0002516407110000043
10. the apparatus of claim 9, further comprising:
a verification module configured to verify a no-difference tracking of error forces by the target impedance model;
the verification module performs the following verification operations:
will be provided with
Figure FDA0002516407110000044
And
Figure FDA0002516407110000045
substituting the target impedance model to obtain:
Figure FDA0002516407110000046
actual position x and desired position xcHas deviation, satisfies the relation xc＝x+xWherein
Figure FDA0002516407110000047
xeIs the location of the external environment, keIs the stiffness of the external environment;
for xcAnd respectively obtaining a second order differential and a first order differential:
Figure FDA0002516407110000048
will be provided with
Figure FDA0002516407110000049
And
Figure FDA00025164071100000410
substituting the target impedance model to obtain:
Figure FDA0002516407110000051
merging and item shifting to obtain:
Figure FDA0002516407110000052
get
Figure FDA0002516407110000053
The following can be obtained through continuous simplification:
Figure FDA0002516407110000054
two sides of the equation multiplied by keThe following can be obtained:
Figure FDA0002516407110000055
by the relation ef＝Fref-FeWill Fe＝Fref-efThe laplace transform is performed after the carry-in:
L(Fe)＝Fref(s)-ef(s)
L(Ef)＝s2ef(s)
Figure FDA0002516407110000056
the method is simplified and can be obtained:
Figure FDA0002516407110000057
order:
Λ(s)＝(keη1M+keη2M)s5+[ke(η1B+kd)+keη2B-ketd]s4+[ke(η1K0+kp)+ke(η2K0+tp)(Ms2+Bs+K0)]s3+keki
the pull transform reduction equation is:
Figure FDA0002516407110000058
from the median theorem we can derive:
Figure FDA0002516407110000059
Fref(s) is a pull-transformed value of the desired force, and s is a pull-transformed parameter.
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