CN111796525A - Model prediction control method based on exoskeleton robot mechanical arm - Google Patents

Model prediction control method based on exoskeleton robot mechanical arm Download PDF

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CN111796525A
CN111796525A CN202010889859.8A CN202010889859A CN111796525A CN 111796525 A CN111796525 A CN 111796525A CN 202010889859 A CN202010889859 A CN 202010889859A CN 111796525 A CN111796525 A CN 111796525A
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tracking error
exoskeleton robot
mechanical arm
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CN111796525B (en
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孙振兴
朱静豪
张兴华
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Nanjing Tech University
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Abstract

The invention discloses a model prediction control method based on an exoskeleton robot mechanical arm, and belongs to the field of exoskeleton robots. Aiming at the problem of overlarge steady-state error under the condition of time-varying disturbance and parameter uncertainty in the prior art, the invention provides a model prediction control method based on an exoskeleton robot mechanical arm, which comprises the following steps: firstly, a high-gain observer based on continuous time is provided for estimating the state and disturbance of a tracking error; then, an improved performance index is provided, which comprises a tracking error part and a control input part; and finally, obtaining a model predictive control law after the performance indexes are subjected to rolling time domain optimization. The method can meet the requirement of optimal non-offset tracking, has better steady-state performance under the condition of time-varying disturbance, and is easy to realize.

Description

Model prediction control method based on exoskeleton robot mechanical arm
Technical Field
The invention relates to the field of exoskeleton robots, in particular to a model prediction control method of a mechanical arm of an exoskeleton robot.
Background
The exoskeleton robot technology is a comprehensive technology which integrates sensing, control, information, fusion and mobile computing and provides a wearable mechanical mechanism for a person as an operator. Exoskeleton robots can find full application in civilian, military and commercial areas, for example: the walking aid can assist people with physical disabilities to walk in the civil aspect, and can assist soldiers to fight in the military aspect, and the like. Due to the complexity of the mechanical structure of the exoskeleton robot and the influence of various parameters such as friction force, accurate values of the parameters of the exoskeleton robot are difficult to obtain.
Chinese patent application, publication No. CN105955015A, published 2016, 9, 21, discloses a fuzzy control method for exoskeleton systems. The method is designed aiming at the conditions that the traditional exoskeleton is easily influenced by the external environment when the PID control is mostly adopted, and the control effect of the system is poor. After the control model is changed, the controller can better track an expected curve compared with PID (proportion integration differentiation) in fuzzy self-adaptive control, and has obvious advantages in the aspects of instantaneity, robustness and the like. But the fuzzy control rule of the method is complex and is not easy to realize.
The Chinese patent application, application No. CN105796286B, published 2016, 7, 27, discloses a control method based on a lower limb exoskeleton robot, which adds an air bag pressure sensor on the basis of a traditional lower limb exoskeleton human intention detection sensor, and reflects the acting force of a human body and an exoskeleton by measuring a signal generated by pressing an air bag by a thigh of the human body, thereby feeding back the human body movement intention and correcting the deviation of an exoskeleton control algorithm; the air bag sensor is used, and meanwhile, a flexible human-computer interface can be provided for a human body, so that the acting force of the human body and the exoskeleton robot is buffered; meanwhile, the assistance effect of the lower limb exoskeleton robot can be better evaluated by collecting the motion curve of the human body wearing the exoskeleton and the force curve of the airbag sensor. The method corrects the offset by a fuzzy controller. However, the fuzzy rule of the method is complex to make and is not easy to realize depending on expert experience.
Disclosure of Invention
1. Technical problem to be solved
Aiming at the problem of overlarge steady-state error under the conditions of time-varying disturbance and parameter uncertainty in the prior art, the invention provides a model prediction control method based on an exoskeleton robot mechanical arm, which can meet the requirement of optimal non-offset tracking, ensures better dynamic stability and is easy to realize.
2. Technical scheme
The purpose of the invention is realized by the following technical scheme.
A model prediction control method based on an exoskeleton robot mechanical arm comprises the following steps:
step 1: providing an improved performance index which comprises a tracking error part and a control input part;
step 2: providing a high-gain observer based on continuous time, and estimating the state and disturbance of a tracking error;
and step 3: and (3) combining the errors and the disturbances in the step (2), and obtaining a model predictive control law after the performance indexes in the step (1) are subjected to rolling time domain optimization.
Further, in the step 1, the method comprises the following steps:
step 101, providing a mechanical arm motion control system equation of the exoskeleton robot:
Figure BDA0002656580570000021
wherein u is the moment generated on the actuator shaft, d is the disturbance moment on the link shaft, and q is1To perform angular positions on the shaft, q2Angular position of the connecting rod, J1Is the moment of inertia of the actuator, J2Is the moment of inertia of the connecting rod, F1Is the coefficient of friction of the actuator, F2Is the friction coefficient of the connecting rod, K is the spring elastic coefficient, N is the transmission ratio of the transmission gear, m is the connecting rod mass, l is the connecting rod length, and g is the gravitational acceleration;
step 102, a dynamic tracking error equation of a mechanical arm motion system of the exoskeleton robot is given:
Figure BDA0002656580570000022
wherein q is2r(t) is a reference output signal,
Figure BDA0002656580570000026
is a set of positive integers, b0Is the nominal value of b (t), b (t) is controlAnd (5) making a gain. e (t) is the error of the actual output from the reference output, w (t) is the sum of various unknown disturbances and uncertainties, w4(t) contains a known reference output;
Figure BDA0002656580570000023
step 103, providing performance indexes of a mechanical arm motion control system equation based on the exoskeleton robot:
Figure BDA0002656580570000024
wherein: t: (>0) Is the prediction period; u. ofr(t) is the desired steady state control input,
Figure BDA0002656580570000025
is the weight of the tracking error; r (R)>0) Is the weight of the controller input.
Further, in the step 2, the continuous-time based high-gain observer is:
Figure BDA0002656580570000031
wherein the content of the first and second substances,
Figure BDA0002656580570000032
and
Figure BDA0002656580570000033
are all generated by an observer,/iiAnd τ is the adjustable observer gain.
Further, the method of estimating the tracking error system is as follows:
in step 201, a tracking error e (T + τ) at a future time is given in a prediction period T, and after taylor series expansion, the tracking error e (T + τ) can be expressed as follows:
Figure BDA0002656580570000034
where 0. ltoreq. tau. ltoreq.T, simply by symbolizing the estimated values of the variables
Figure BDA00026565805700000315
Indicating that the predicted value of the variable is signed
Figure BDA00026565805700000316
Represents;
in step 202, the estimated value generated by the disturbance observer is represented as
Figure BDA0002656580570000035
The predicted tracking error can be expressed in the form:
Figure BDA0002656580570000036
the control input is represented in the form:
Figure BDA0002656580570000037
the predicted tracking error can be expressed in the form:
Figure BDA0002656580570000038
wherein:
Figure BDA0002656580570000039
Figure BDA00026565805700000310
Figure BDA00026565805700000311
Figure BDA00026565805700000312
Figure BDA00026565805700000313
Figure BDA00026565805700000314
step 203, the controller input and the expected controller input at the future time are given as follows:
Figure BDA0002656580570000041
wherein the vector
Figure BDA0002656580570000042
The method is used for correcting the interference and uncertainty existing in the traditional Taylor series expansion prediction method.
Further, combining the formulas (6), (7) and (8), the performance index in the formula (3) is rewritten as follows:
Figure BDA0002656580570000043
wherein:
Figure BDA0002656580570000044
further, the process of obtaining the model predictive control law after the performance index is optimized in a rolling time domain is as follows:
will be in the formula (9)
Figure BDA0002656580570000045
To pair
Figure BDA0002656580570000046
Calculating the partial derivative to obtain:
Figure BDA0002656580570000047
knowing matrix
Figure BDA0002656580570000048
Is a positive definite matrix. Order to
Figure BDA0002656580570000049
The optimized control output is obtained as follows:
Figure BDA00026565805700000410
the model predictive control law is given in conjunction with equation (10) as follows:
Figure BDA00026565805700000411
wherein the gain is controlled
Figure BDA00026565805700000412
To meet the practical application, the estimated value
Figure BDA00026565805700000413
And
Figure BDA00026565805700000414
are generated by an observer. And the following assumptions must be satisfied: there is a known constant L ≧ 0, m ∈ N+I.e. | w(m)(t)|≤L。
3. Advantageous effects
Compared with the prior art, the invention has the advantages that: the invention designs a continuous time model prediction control system method based on an exoskeleton robot, and by designing a model prediction control method with a nonlinear disturbance observer, optimal offset-free tracking can be realized under various disturbances. Compared with the traditional model prediction control law, the method has better steady-state performance under the condition of time-varying disturbance; meanwhile, the method provides a new performance index, and definitely analyzes the influence of the control input weight on the stability of the closed loop.
Drawings
FIG. 1 is a block diagram of a model predictive control method implementation proposed by the present invention;
FIG. 2 is a schematic view of an exoskeleton-based robotic arm;
FIG. 3 is a graph of q in the case of system uncertainty and external interference2The output curve of (a);
FIG. 4 is q of FIG. 3 after enlargement in 0-15 seconds2The output curve of (1).
Detailed Description
The invention is described in detail below with reference to the drawings and specific examples.
Examples
As shown in fig. 1, the invention discloses a model prediction control method for an exoskeleton robot mechanical arm, comprising the following steps:
step 1: the improved performance index comprises a tracking error part and a control input part, and comprises the following specific steps:
step 101, a motion control system equation of a mechanical arm of the exoskeleton robot is given:
Figure BDA0002656580570000051
as shown in fig. 2, in the schematic diagram of the exoskeleton robot mechanical arm, u is the moment generated on the actuator shaft, d is the disturbance moment on the link shaft, and q is1To perform angular positions on the shaft, q2Angular position of the connecting rod, J1Is the moment of inertia of the actuator, J2Is the moment of inertia of the connecting rod, F1Is the coefficient of friction of the actuator, F2Is the friction coefficient of the connecting rod, K is the spring elastic coefficient, N is the transmission ratio of the transmission gear, m is the connecting rod mass, l is the connecting rod length, and g is the gravitational acceleration;
step 102, a dynamic tracking error equation of a mechanical arm motion system of the exoskeleton robot is given:
Figure BDA0002656580570000052
wherein q is2r(t) is a reference output signal,
Figure BDA0002656580570000053
is a set of positive integers, b0Is the nominal value of b (t), b (t) is the control gain, e (t) is the error of the actual output from the reference output, w (t) is the sum of various unknown disturbances and uncertainties, w (t) is the sum of the various unknown disturbances and uncertainties4(t) contains a known reference output;
Figure BDA0002656580570000054
step 103, providing performance indexes of a motion control system equation based on the mechanical arm of the exoskeleton robot:
Figure BDA0002656580570000055
wherein T: (>0) Is the prediction period; u. ofr(t) is the desired steady state control input,
Figure BDA0002656580570000056
Q(>0) is a weight of the tracking error, R: (>0) Is the weight of the controller input.
Step 2: designing a high-gain observer based on continuous time to estimate the state and disturbance of a tracking error, and specifically comprising the following steps of:
first, a continuous-time based high-gain observer is given:
Figure BDA0002656580570000061
wherein the content of the first and second substances,
Figure BDA0002656580570000062
and
Figure BDA0002656580570000063
are all generated by an observer,/iiAnd τ is the adjustable observer gain.
Next, the method of estimating the tracking error system is as follows:
step 201, a tracking error e (T + τ) at a future time is given in a prediction period T, and after Taylor series expansion, the tracking error e (T + τ) can be expressed in the following form
Figure BDA0002656580570000064
Where 0. ltoreq. tau. ltoreq.T, simply by symbolizing the estimated values of the variables
Figure BDA00026565805700000614
Indicating that the predicted value of the variable is signed
Figure BDA00026565805700000615
Represents;
in step 202, the estimated value generated by the disturbance observer is represented as
Figure BDA0002656580570000065
The predicted tracking error can be expressed in the form:
Figure BDA0002656580570000066
the control input is represented in the form:
Figure BDA0002656580570000067
the predicted tracking error can be expressed in the form:
Figure BDA0002656580570000068
wherein:
Figure BDA0002656580570000069
Figure BDA00026565805700000610
Figure BDA00026565805700000611
Figure BDA00026565805700000612
Figure BDA00026565805700000613
Figure BDA0002656580570000071
step 203, the controller input and the expected controller input at the future time are given as follows:
Figure BDA0002656580570000072
wherein the vector
Figure BDA0002656580570000073
The method is used for correcting the interference and uncertainty existing in the traditional Taylor series expansion prediction method.
And 3, combining the errors and the disturbances in the step 2, and obtaining a model predictive control law after the performance indexes are subjected to rolling time domain optimization, wherein the method specifically comprises the following steps:
first, the performance index in the formula (3) is rewritten in the following form in combination with the formulas (6), (7), and (8):
Figure BDA0002656580570000074
wherein:
Figure BDA0002656580570000075
finally, the method for obtaining the model predictive control law after the performance indexes are optimized by the rolling time domain is as follows:
will be in the formula (9)
Figure BDA0002656580570000076
To pair
Figure BDA0002656580570000077
Calculating the partial derivative to obtain:
Figure BDA0002656580570000078
knowing matrix
Figure BDA0002656580570000079
Is a positive definite matrix. Order to
Figure BDA00026565805700000710
The optimized control output is obtained as follows:
Figure BDA00026565805700000711
the model predictive control law is given in conjunction with equation (10) as follows:
Figure BDA00026565805700000712
wherein the gain is controlled
Figure BDA00026565805700000713
To meet the practical application, the estimated value
Figure BDA00026565805700000714
And
Figure BDA00026565805700000715
are generated by an observer. And the following assumptions must be satisfied: there is a known constant L ≧ 0, m ∈ N+I.e. | w(m)(t)|≤L。
As shown in fig. 3 and 4, q in case of system uncertainty and external interference2The dotted line, the broken line and the dotted line represent that the system parameters have values of 10%, 20% and 30%, respectivelyUncertainty, black line is a parameter of the actual system. It can be seen from the figure that the output can be quickly restored to the set value even under the conditions of uncertainty and interference, and the excellent effect of the method is reflected.
The invention and its embodiments have been described above schematically, without limitation, and the invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The representation in the drawings is only one of the embodiments of the invention, the actual construction is not limited thereto, and any reference signs in the claims shall not limit the claims concerned. Therefore, if a person skilled in the art receives the teachings of the present invention, without inventive design, a similar structure and an embodiment to the above technical solution should be covered by the protection scope of the present patent. Furthermore, the word "comprising" does not exclude other elements or steps, and the word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. Several of the elements recited in the product claims may also be implemented by one element in software or hardware. The terms first, second, etc. are used to denote names, but not any particular order.

Claims (6)

1. A model prediction control method based on an exoskeleton robot mechanical arm is characterized by comprising the following steps:
step 1: providing an improved performance index which comprises a tracking error part and a control input part;
step 2: a high-gain observer based on continuous time is provided, and the state and disturbance of a tracking error system are estimated;
and step 3: and (3) combining the errors and the disturbances in the step (2), and obtaining a model predictive control law after the performance indexes in the step (1) are subjected to rolling time domain optimization.
2. The method for model predictive control based on exoskeleton robot mechanical arms as claimed in claim 1, wherein the step 1 comprises the following steps:
step 101, providing a mechanical arm motion control system equation of the exoskeleton robot:
Figure FDA0002656580560000011
Figure FDA0002656580560000012
wherein u is the moment generated on the actuator shaft, d is the disturbance moment on the link shaft, and q is1To perform angular positions on the shaft, q2Angular position of the connecting rod, J1Is the moment of inertia of the actuator, J2Is the moment of inertia of the connecting rod, F1Is the coefficient of friction of the actuator, F2The friction coefficient of the connecting rod, K is the elastic coefficient of the spring, N is the transmission ratio of the transmission gear, m is the mass of the connecting rod, 1 is the length of the connecting rod, and g is the gravity acceleration;
step 102, providing a dynamic tracking error equation of the exoskeleton robot mechanical arm motion system:
Figure FDA0002656580560000013
Figure FDA0002656580560000014
Figure FDA0002656580560000015
wherein q is2r(t) is a reference output signal,
Figure FDA0002656580560000019
is a set of positive integers, b0Is the nominal value of b (t), b (t) is the control gain, e (t) is the error of the actual output from the reference output, w (t) is the sum of various unknown disturbances and uncertainties, w (t) is the sum of the various unknown disturbances and uncertainties4(t) contains a known reference output;
Figure FDA0002656580560000016
step 103, providing performance indexes of the motion control system equation of the exoskeleton robot mechanical arm:
Figure FDA0002656580560000017
where T (> 0) is the prediction period, ur(t) is the desired steady state control input,
Figure FDA0002656580560000018
q (> 0) is the weight of the tracking error and R (> 0) is the weight of the controller input.
3. The method of claim 1, wherein in step 2, the continuous-time based high-gain observer is:
Figure FDA0002656580560000021
Figure FDA0002656580560000022
Figure FDA0002656580560000023
Figure FDA0002656580560000024
Figure FDA0002656580560000025
Figure FDA0002656580560000026
wherein the content of the first and second substances,
Figure FDA0002656580560000027
Figure FDA0002656580560000028
Figure FDA0002656580560000029
in the formula, v1(t) and vk(t) is the adjustable observer gain,
Figure FDA00026565805600000210
and
Figure FDA00026565805600000211
are generated by the observer.
4. The method for model predictive control based on exoskeleton robot mechanical arms as claimed in claim 1 wherein in step 2, the method for estimating the tracking error system is as follows:
in step 201, a tracking error e (T + τ) at a future time is given in a prediction period T, and after taylor series expansion, the tracking error e (T + τ) can be expressed as follows:
Figure FDA00026565805600000212
where 0 is more than or equal to tau is less than or equal to T, and the estimated value of the variable is signed
Figure FDA00026565805600000213
Indicating that the predicted value of the variable is signed
Figure FDA00026565805600000214
Represents;
in step 202, the estimated value generated by the disturbance observer is represented as
Figure FDA00026565805600000215
The predicted tracking error can be expressed in the form:
Figure FDA00026565805600000216
the control input is represented in the form:
Figure FDA00026565805600000217
the predicted tracking error can be expressed in the form:
Figure FDA00026565805600000218
wherein:
Figure FDA00026565805600000219
Figure FDA0002656580560000031
Figure FDA0002656580560000032
Figure FDA0002656580560000033
Figure FDA0002656580560000034
Figure FDA0002656580560000035
step 203, the controller input and the expected controller input at the future time are given as follows:
Figure FDA0002656580560000036
Figure FDA0002656580560000037
wherein the vector
Figure FDA0002656580560000038
The method is used for correcting the interference and uncertainty existing in the traditional Taylor series expansion prediction method.
5. The method of claim 1, wherein in step 3, the performance index is optimized as follows:
combining the formulas (6), (7) and (8), the performance index in the formula (3) is rewritten as follows:
Figure FDA0002656580560000039
wherein the content of the first and second substances,
Figure FDA00026565805600000310
6. the method for model predictive control based on an exoskeleton robot mechanical arm as claimed in claim 1, wherein in step 3, the method for obtaining the model predictive control law after optimization is as follows:
will be in the formula (9)
Figure FDA00026565805600000311
To pair
Figure FDA00026565805600000312
Calculating the partial derivative to obtain:
Figure FDA00026565805600000313
matrix array
Figure FDA00026565805600000314
Is a positive definite matrix, such that
Figure FDA00026565805600000315
The optimized control output is obtained as follows:
Figure FDA00026565805600000316
the model predictive control law is given in conjunction with equation (10) as follows:
Figure FDA00026565805600000317
wherein the gain [ k ] is controlled1k2k3k4]=(ζ3+hζ4)-1ζ2 T
Figure FDA00026565805600000318
To meet the practical application, the estimated value
Figure FDA0002656580560000041
And
Figure FDA0002656580560000042
both are generated by the observer and the following assumptions must be satisfied: there is a known constant L ≧ 0, m ∈ N+I.e. | w(m)(t)|≤L。
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Publication number Priority date Publication date Assignee Title
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CN109648564A (en) * 2019-01-15 2019-04-19 西安科技大学 A kind of control method of the multiple degrees of freedom flexible articulated mechanical arm system based on hierarchical structure MPC
CN111152225A (en) * 2020-01-15 2020-05-15 北京科技大学 Uncertain mechanical arm fixed time trajectory tracking control method with input saturation
CN111290273A (en) * 2020-02-18 2020-06-16 湖州和力机器人智能科技有限公司 Position tracking optimization control method based on exoskeleton robot flexible actuator

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Publication number Priority date Publication date Assignee Title
CN109648564A (en) * 2019-01-15 2019-04-19 西安科技大学 A kind of control method of the multiple degrees of freedom flexible articulated mechanical arm system based on hierarchical structure MPC
CN111152225A (en) * 2020-01-15 2020-05-15 北京科技大学 Uncertain mechanical arm fixed time trajectory tracking control method with input saturation
CN111290273A (en) * 2020-02-18 2020-06-16 湖州和力机器人智能科技有限公司 Position tracking optimization control method based on exoskeleton robot flexible actuator

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114721258A (en) * 2022-02-21 2022-07-08 电子科技大学 Lower limb exoskeleton backstepping control method based on nonlinear extended state observer
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