CN112947071B - Backstepping-based lower limb exoskeleton control method - Google Patents

Backstepping-based lower limb exoskeleton control method Download PDF

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CN112947071B
CN112947071B CN202110117310.1A CN202110117310A CN112947071B CN 112947071 B CN112947071 B CN 112947071B CN 202110117310 A CN202110117310 A CN 202110117310A CN 112947071 B CN112947071 B CN 112947071B
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CN112947071A (en
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张燕
张现磊
樊琪
李思宁
孙善乐
杨安杰
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Hebei University of Technology
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention relates to a Backstepping-based lower limb exoskeleton control method, which comprises the following steps of establishing a lower limb exoskeleton dynamics model and converting the model into a control system state equation; secondly, designing a Backstepping controller; thirdly, improving the RBF disturbance observer, wherein the RBF disturbance observer and the RBF neural network adaptive law are designed; and fourthly, controlling to implement, so that the lower limb exoskeleton can move according to the expected track. Aiming at external random disturbance, the method designs a disturbance observer by utilizing the approximation characteristic of an RBF neural network to approximate the external random disturbance; aiming at network approximation errors existing in the RBF neural network, the disturbance observer is further improved, an auxiliary variable is introduced to compensate the network approximation errors, and then external random disturbance is compensated, so that approximation of the external random disturbance is closer to a true value, and the approximation errors of the RBF neural network are reduced.

Description

Backstepping-based lower limb exoskeleton control method
Technical Field
The invention belongs to the technical field of exoskeleton control, and particularly relates to a Backstepping-based lower limb exoskeleton control method.
Background
The exoskeleton can complete the work tasks which cannot be completed by the human body independently according to the subjective intention of the human body while providing support and protection for the human body. The lower limb exoskeleton is researched for enhancing the physical strength of a human body and expanding the lower limb walking capability of the human body, and has very wide application prospect in both military fields and civil fields.
Because the lower limb exoskeleton system is a typical nonlinear control system and Backstepping control algorithm has superiority in controlling the nonlinear system, the Backstepping control algorithm is applied to control the lower limb exoskeleton system, and control precision can be ensured. And when external random disturbance exists in the lower limb exoskeleton, the RBF neural network is applied to approach the disturbance. However, due to the approximation error of the RBF neural network, the accuracy of disturbance approximation is affected, and the tracking effect of the joint angle is further affected.
In conclusion, the invention further improves the disturbance observer aiming at the approximation error existing in the RBF neural network to compensate the disturbance, thereby reducing the approximation error of the RBF neural network and achieving better joint angle tracking effect.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a Backstepping-based lower limb exoskeleton control method.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a Backstepping-based lower limb exoskeleton control method is characterized by comprising the following steps:
firstly, establishing a lower limb exoskeleton dynamic model, and converting the lower limb exoskeleton dynamic model into a control system state equation;
secondly, designing a Backstepping controller of a formula (9):
Figure BDA0002920843990000011
in the formula (9), τ is a joint moment,
Figure BDA0002920843990000012
is an estimate of an external random disturbance, z1For joint angle error, K2Is a constant matrix, z2Error of angular velocity of the joint, G (x)1) To control the gravity matrix of the system equation of state, C (x)1,x2) The matrix of coriolis forces and centrifugal forces, M (x), for the control system equation of state1) To control the moment of inertia matrix, alpha, of the system equation of state1In order to virtually control the amount of control,
Figure BDA0002920843990000013
is alpha1First order differential of (x)1For controlling the joint output angle, x, of the lower extremity exoskeleton in the system equation of state2Controlling the joint angular velocity of the lower extremity exoskeleton in the system state equation;
thirdly, improving an RBF disturbance observer;
designing an RBF disturbance observer according to the formula (12):
Figure BDA0002920843990000014
in the formula (12), the reaction mixture is,
Figure BDA0002920843990000015
representing ideal weight of RBF neural networkEstimated value of, H (X)d) Expressing a Gaussian basis function of an RBF neural network hidden layer, and expressing matrix transposition by T;
Figure BDA0002920843990000021
represents an estimate of the network approximation error and satisfies equation (14):
Figure BDA0002920843990000022
Figure BDA0002920843990000023
is an estimate of an auxiliary variable, and the auxiliary variable estimate
Figure BDA0002920843990000024
First order differential of
Figure BDA0002920843990000025
Satisfies formula (20):
Figure BDA0002920843990000026
in the formula (20), R (z)2) Is a constant coefficient, M-1(x1) Is M (x)1) The inverse matrix of (d);
designing an adaptive law of the RBF neural network of the formula (23):
Figure BDA0002920843990000027
in the formula (23), the compound represented by the formula,
Figure BDA0002920843990000028
represents the estimated value of the ith node weight of the hidden layer of the RBF neural network,
Figure BDA0002920843990000029
is composed of
Figure BDA00029208439900000210
First order differential of (a)iDenotes the normal number, ΓiRepresenting a positive definite matrix; z is a radical of2iRepresenting the joint angular velocity error of the ith node of the hidden layer of the RBF neural network;
fourthly, controlling to implement;
step 1, setting the initial values of joint output angles and joint moments to be 0, and applying external random disturbance to the lower limb exoskeleton; setting a joint desired angle, and using the joint desired angle as a given signal of a Backstepping controller in the second step;
step 2, inputting the initial values of the joint output angle and the joint moment into the RBF disturbance observer improved in the third step, and calculating according to the formulas (14) and (20) to obtain an estimated value of a network approximation error; obtaining an estimated value of the ideal weight of the RBF neural network through a formula (23); then, substituting the estimated value of the network approximation error and the estimated value of the ideal weight of the RBF neural network into a formula (12) to obtain the estimated value of the external random disturbance, namely, the estimated value of the external random disturbance is output by the RBF disturbance observer and then input into a Backstepping controller formula (9) in the second step for disturbance compensation to obtain the joint moment of the current control period; substituting the joint torque of the current control period into the state equation of the control system in the first step to obtain the joint output angle of the current control period, so as to complete the control task of the current control period;
and 3, based on the joint output angle and the joint torque of the current control cycle obtained in the step 2, repeatedly executing the step 2 to complete the control task of the next control cycle, so that the lower limb exoskeleton moves according to the expected track.
In the third step the auxiliary variable z3Satisfies formula (13);
z3＝ε+Ψ(z2)＝ε+R(z2)z2 (13)
in formula (13), Ψ (z)2)＝R(z2)z2Denotes with respect to z2Represents the network approximation error.
The second step further comprises constructing the Lyapuno of the first subsystem of the control systemV function V1And verifying the stability of the first subsystem of the control system; the specific process is as follows:
error z of joint angle1Satisfies formula (3):
z1＝y-yd (3)
definition of alpha1Satisfies the formula (4),
Figure BDA00029208439900000211
a matrix of constants is represented by a matrix of constants,
Figure BDA00029208439900000212
denotes ydFirst order differential of (y)dA desired angle for the joint;
Figure BDA0002920843990000031
definition of z2Satisfies formula (5);
z2＝x2-α1 (5)
the first order differential is obtained for the formula (3), and then the y of the state equation of the control system is changed to x1、
Figure BDA0002920843990000032
And formula (5) substituting formula (3) to obtain formula (6) after first order differentiation;
Figure BDA0002920843990000033
in the formula (6), the reaction mixture is,
Figure BDA0002920843990000034
denotes z1The first order differential of the first order of the,
Figure BDA0002920843990000035
the first order differential of y is represented by,
Figure BDA0002920843990000036
denotes x1First order differentiation of;
lyapunov function V of first subsystem of control system of structural formula (7)1；
Figure BDA0002920843990000037
Obtaining a first order differential of the formula (7), and obtaining a formula (8) by substituting the formula (4) and the formula (6) for the formula (7) and obtaining a formula after the first order differential;
Figure BDA0002920843990000038
when z is represented by formula (8)2When the content is equal to 0, the content,
Figure BDA0002920843990000039
it indicates that the first subsystem of the control system is stable.
The third step also comprises constructing a Lyapunov function V of the second subsystem of the control system2And verifying the stability of the second subsystem of the control system.
Compared with the prior art, the invention has the beneficial effects that:
(1) aiming at external random disturbance, a disturbance observer is designed by utilizing the approximation characteristic of a RBF neural network to approximate the external random disturbance; aiming at network approximation errors existing in the RBF neural network, the disturbance observer is further improved, an auxiliary variable is introduced to compensate the network approximation errors, and then external random disturbance is compensated, so that approximation of the external random disturbance is closer to a true value, the approximation errors of the RBF neural network are reduced, and finally a better joint angle tracking effect is achieved.
(2) Aiming at the lower limb exoskeleton system, due to the fact that the Backstepping control method has typical nonlinear characteristics, the control method is applied to control the lower limb exoskeleton system, a good control effect can be achieved, the approaching effect on external random disturbance is good, robustness is strong, control accuracy is high, and track tracking of the lower limb exoskeleton joint angle is achieved.
Drawings
FIG. 1 is a control flow diagram of the control system of the present invention;
FIG. 2 is a simplified model of a unilateral leg of the lower extremity exoskeleton of the present invention;
FIG. 3 is a waveform of the external stochastic perturbations applied to the lower extremity exoskeleton hip joint of the present invention;
FIG. 4 is a waveform of the external random perturbation applied to the lower extremity exoskeleton knee joint in accordance with the present invention;
FIG. 5 is a graph of the angle error of the hip joint of the exoskeleton of the lower limbs of the patient based on the conventional RBF disturbance observer;
FIG. 6 is an enlarged fragmentary view of the boxed portion of FIG. 5 in accordance with the present invention;
FIG. 7 is a graph of the error results of the lower extremity exoskeleton knee joint angle based on the conventional RBF disturbance observer of the present invention;
FIG. 8 is an enlarged fragmentary view of the boxed portion of FIG. 7 in accordance with the present invention;
FIG. 9 is a graph of the results of the angle errors of the lower extremity exoskeleton hip joints based on the improved RBF disturbance observer according to the present invention;
FIG. 10 is an enlarged fragmentary view of the boxed portion of FIG. 9 in accordance with the present invention;
FIG. 11 is a graph of the error in the knee joint angle of the exoskeleton of the lower limbs based on the improved RBF disturbance observer according to the present invention;
FIG. 12 is an enlarged fragmentary view of the boxed portion of FIG. 11 in accordance with the present invention;
in the figure, 1-Backstepping controller; 2-RBF disturbance observer; 3-lower extremity exoskeleton.
Detailed Description
The following detailed description of the embodiments of the present invention is provided with reference to the accompanying drawings and examples, which are not intended to limit the scope of the present invention.
Fig. 1 is a structural block diagram of a lower extremity exoskeleton control system based on an RBF disturbance observer according to the present invention, the control system includes a Backstepping controller 1, an RBF disturbance observer 2 and a lower extremity exoskeleton 3; external random disturbance d acts on the lower limb exoskeleton 3, and the joint desired angle ydInput into Backstepping controller 1 and then outputJoint moment tau for driving the lower extremity exoskeleton 3 to move, and the desired angle y of the jointdInputting an RBF disturbance observer 2 for observing the tracking effect of the joint angle; meanwhile, joint torque tau is input into the RBF disturbance observer 2, and the RBF disturbance observer 2 outputs an estimated value of external random disturbance
Figure BDA0002920843990000041
Estimation of external random disturbances
Figure BDA0002920843990000042
The disturbance is input into a Backstepping controller 1 to compensate for external random disturbance.
The invention relates to a Backstepping-based lower limb exoskeleton control method (a method for short, see figures 1-12), which comprises the following steps:
firstly, establishing a lower limb exoskeleton dynamic model, and converting the lower limb exoskeleton dynamic model into a control system state equation;
the formula (1) is an expression of a lower limb exoskeleton dynamics model, and the control system known by the formula (1) is a second-order system and comprises two subsystems;
Figure BDA0002920843990000043
in the formula (1), q ═ q1,q2]TJoint angle, q, for a lower extremity exoskeleton dynamics model1、q2Respectively the angles of the hip joint and the knee joint;
Figure BDA0002920843990000044
angular velocity and angular acceleration of the lower extremity exoskeleton joints, respectively; m (q) is a rotational inertia matrix of the lower limb exoskeleton dynamics model, and is a symmetric positive definite matrix;
Figure BDA0002920843990000045
a coriolis force and centrifugal force matrix for a lower extremity exoskeleton dynamics model; g (q) a gravity matrix that is a lower extremity exoskeleton dynamics model; d ═ d1,d2]TFor external random perturbations, d1、d2Respectively acting on external random disturbance of hip joint and knee joint; τ ═ τ [ τ ]1,τ2]TFor joint moment, τ1、τ2Respectively a hip joint moment and a knee joint moment; y ═ y1,y2]TFor the joint to output angle, y1、y2Respectively the hip joint and the knee joint output angles;
in the formula (1), the reaction mixture is,
Figure BDA0002920843990000051
m11, M12, M21, M22 are components of M (q), where
Figure BDA0002920843990000052
Figure BDA0002920843990000053
C11, C12, C21 and C22 are
Figure BDA0002920843990000054
Wherein
Figure BDA0002920843990000055
C22＝0；
Figure BDA0002920843990000056
G1, G2 are components of G (q), G1 ═ m2 gl2g sin(q1+q2)+(m1l1g+m2l1)g sin q1，G2＝m2 gl2g sin(q1+q2)；
As shown in FIG. 2, m1Denotes thigh bar mass, m2Indicating shank mass,/1Indicates the thigh bar length,/2Indicates the shank length,/1gIndicating the length of the thigh bar centroid position from the hip joint,/2gRepresenting the length of the position of the centre of mass of the shank from the knee joint, J1Representing the moment of inertia of the thigh lever, J2Representing the moment of inertia of the shank, g representing the acceleration of gravity;
order to
Figure BDA0002920843990000057
Converting the lower limb exoskeleton dynamics model into a control system state equation of formula (2);
Figure BDA0002920843990000058
Figure BDA0002920843990000059
y＝x1
in the formula (2), x1＝[x11,x12]TFor controlling the joint output angle, x, of the lower extremity exoskeleton in the system equation of state11For the angle of the hip joint, x12Outputting the angle for the knee joint; x is the number of2＝[x21,x22]TFor controlling the angular velocity, x, of the joints of the lower extremity exoskeleton in the system equation of state21Is the angular velocity of the hip joint, x22Knee joint angular velocity;
Figure BDA00029208439900000510
the angular acceleration of the lower extremity exoskeleton joints in the control system state equation; m-1(x1) Is M (x)1) Inverse matrix of, M (x)1) The rotational inertia matrix representing the state equation of the control system is a symmetrical positive definite matrix; c (x)1,x2) A coriolis force and centrifugal force matrix representing a control system equation of state; g (x)1) A gravity matrix representing a control system state equation;
secondly, designing a Backstepping controller;
step 1, constructing a Lyapunov function V of a first subsystem of a control system1And verifying the stability of the first subsystem of the control system;
the inventionThe control target of (1) tracks the joint desired angle y for the joint output angle ydDesired angle y of jointdAs a given signal of the Backstepping controller; suppose yd＝[yd1,yd2]THaving a second derivative, yd1Indicating the desired angle of the hip joint, yd2Representing the desired angle of the knee joint, the error z of the joint angle1＝[z11,z12]TSatisfies formula (3); z is a radical of11Indicating hip joint angle error, z12Representing the knee joint angle error; t represents matrix transposition;
z1＝y-yd (3)
definition of alpha1＝[α11,α12]TIs a virtual control quantity and satisfies the formula (4), alpha11Representing the virtual control quantity of the hip joint, alpha12Representing a knee joint virtual control quantity;
Figure BDA0002920843990000061
in the formula (4), the reaction mixture is,
Figure BDA0002920843990000062
a matrix of constants is represented by a matrix of constants,
Figure BDA0002920843990000063
denotes ydFirst order differentiation of;
definition of z2＝[z21,z22]TIs a joint angular velocity error and satisfies the formula (5), z21Representing the angular velocity error of the hip joint, z22Representing knee joint angular velocity error;
z2＝x2-α1 (5)
the first order differential of formula (3) is obtained, and y of formula (2) is defined as x1、
Figure BDA0002920843990000064
And formula (5) substituting formula (3) to obtain formula (6) after first order differentiation;
Figure BDA0002920843990000065
in the formula (6), the reaction mixture is,
Figure BDA0002920843990000066
denotes z1The first order differential of the first order of the,
Figure BDA0002920843990000067
the first order differential of y is represented by,
Figure BDA0002920843990000068
denotes x1First order differentiation of;
lyapunov function V of first subsystem of control system of structural formula (7)1；
Figure BDA0002920843990000069
And (3) verifying the stability of the first subsystem of the control system:
obtaining a first order differential of the formula (7), and obtaining a formula (8) by substituting the formula (4) and the formula (6) for the formula (7) and obtaining a formula after the first order differential;
Figure BDA00029208439900000610
when z is represented by formula (8)2When the content is equal to 0, the content,
Figure BDA00029208439900000611
it indicates that the first subsystem of the control system is stable.
Step 2, designing a Backstepping controller of a formula (9):
Figure BDA00029208439900000612
in the formula (9), the reaction mixture is,
Figure BDA00029208439900000613
the estimation value of the external random disturbance d is used for eliminating the influence of the external random disturbance on the control system;
Figure BDA00029208439900000614
representing an estimate of the external random perturbation acting on the hip joint,
Figure BDA00029208439900000615
an estimated value representing an external random perturbation acting on the knee joint;
Figure BDA0002920843990000071
a matrix of constants is represented.
Thirdly, improving the RBF disturbance observer
Because the RBF neural network has the universal approximation characteristic, the RBF neural network of the formula (10) is used for approximating the external random disturbance d;
d＝W*TH(Xd)+ε (10)
in the formula (10), H (X)d)＝[H1(Xd),...,Hi(Xd),...,Hl(Xd)]TL is the number of hidden layer nodes of the RBF neural network;
Figure BDA0002920843990000072
the input vector of the RBF neural network is represented, the number of input layer nodes of the RBF neural network is 8, and each node of a hidden layer of the RBF neural network comprises 8 inputs;
Figure BDA0002920843990000073
represents the ideal weight, W, of the RBF neural networki *The ideal weight of the ith node of the hidden layer of the RBF neural network is obtained; epsilon ═ epsilon1,ε2]TRepresenting the network approximation error, ε1Representing the net approximation error of the hip joint, epsilon2Representing a network approximation error of the knee joint;
h of formula (11)i(Xd) The Gaussian base function of the ith node of the hidden layer of the RBF neural network is represented, namely the activation function of the ith node of the hidden layer of the RBF neural network;
Figure BDA0002920843990000074
in the formula (11), ciGaussian base function center vector representing ith node of hidden layer of RBF neural network, biA gaussian base function width vector representing the ith node of the hidden layer of the RBF neural network, i is 1, 2.
Designing a RBF neural network-based disturbance observer according to the formula (12), namely an RBF disturbance observer, wherein the disturbance observer considers the factor of network approximation error, and the output layer of the RBF neural network is an estimated value of external random disturbance, so that two output layer nodes of the RBF neural network are provided;
Figure BDA0002920843990000075
in the formula (12), the reaction mixture is,
Figure BDA0002920843990000076
representing ideal weight W of RBF neural network*An estimated value of (d);
Figure BDA0002920843990000077
an estimate representing the error of the approximation of the network,
Figure BDA0002920843990000078
an estimate representing the net approximation error of the hip joint,
Figure BDA0002920843990000079
represents an estimate of the net approximation error of the knee joint.
Because the traditional RBF neural network only has ideal weight W for the RBF neural network*The estimation is carried out without considering the influence of network approximation errors on the control performance of the system, so that the traditional RBF neural network has no influence on the outsideThe approximation capability of random disturbance is poor, so that the tracking error of the lower limb exoskeleton joint angle is large, therefore, the invention introduces auxiliary variables, designs a disturbance observer considering the network approximation error, improves the approximation capability of the RBF neural network to external random disturbance, and further reduces the tracking error of the lower limb exoskeleton joint angle.
Defining an auxiliary variable z3＝[z31,z32]TSatisfies the formula (13), z31Representing a hip joint auxiliary variable, z32Representing a knee joint auxiliary variable;
z3＝ε+Ψ(z2)＝ε+R(z2)z2 (13)
in formula (13), Ψ (z)2)＝R(z2)z2Denotes with respect to z2Linear function vector of R (z)2) Is a constant coefficient;
estimation of network approximation error
Figure BDA0002920843990000081
Satisfies formula (14):
Figure BDA0002920843990000082
in the formula (14), the compound represented by the formula (I),
Figure BDA0002920843990000083
in order to be an estimate of the auxiliary variable,
Figure BDA0002920843990000084
an estimate of a hip joint auxiliary variable is represented,
Figure BDA0002920843990000085
an estimated value representing a knee joint assist variable;
first order differentiation is performed on the formula (5), and the formula (2)
Figure BDA0002920843990000086
Solving a formula after first order differentiation by substituting formula (5) to obtain formula (15);
Figure BDA0002920843990000087
in the formula (15), the reaction mixture is,
Figure BDA0002920843990000088
denotes z2First order differentiation of;
Figure BDA0002920843990000089
denotes alpha1The first order differential of the first order of the,
Figure BDA00029208439900000810
represents the first differential of the hip joint virtual control quantity of the lower extremity exoskeleton,
Figure BDA00029208439900000811
representing a first order differential of a knee joint virtual control quantity of the lower extremity exoskeleton;
substituting formula (10) for formula (15) to give formula (16):
Figure BDA00029208439900000812
first order differentiation of equation (13) yields equation (17):
Figure BDA00029208439900000813
substituting formula (16) for formula (17) to give formula (18):
Figure BDA00029208439900000814
the error matrix of the auxiliary variables of the formula (19) is obtained by subtracting the formulas (13) and (14)
Figure BDA00029208439900000815
Deviation matrix from network approximation error matrix epsilon
Figure BDA00029208439900000816
The relationship between;
Figure BDA00029208439900000817
representing the deviation of the hip joint auxiliary variable error from the network approximation error,
Figure BDA00029208439900000818
representing the deviation of the knee joint auxiliary variable error and the network approximation error;
Figure BDA00029208439900000819
defining an auxiliary variable estimate
Figure BDA00029208439900000820
First order differential of
Figure BDA00029208439900000821
Satisfies formula (20):
Figure BDA00029208439900000822
first order differentiation of equation (19) yields equation (21):
Figure BDA00029208439900000823
substituting formulae (18) and (20) for formula (21) to give formula (22):
Figure BDA0002920843990000091
designing an RBF neural network adaptive law to satisfy the formula (23):
Figure BDA0002920843990000092
in the formula (23), the compound represented by the formula,
Figure BDA0002920843990000093
represents the estimated value of the ith node weight of the hidden layer of the RBF neural network,
Figure BDA0002920843990000094
to represent
Figure BDA0002920843990000095
First order differential of (a)iDenotes the normal number, ΓiRepresenting a positive definite matrix; z is a radical of2iRepresenting the joint angular velocity error of the ith node of the hidden layer of the RBF neural network;
constructing Lyapunov function V of second subsystem of control system2And verifying the stability of the second subsystem of the control system;
weight deviation matrix of ith node of RBF neural network hidden layer
Figure BDA0002920843990000096
Constructing the Lyapunov function V of the second subsystem of the control system of the formula (24)2；
Figure BDA0002920843990000097
Obtaining a first order differential of the formula (24) to obtain a formula (25);
Figure BDA0002920843990000098
derived from the equation of state of the control system
Figure BDA0002920843990000099
Is a skew symmetric matrix and satisfies
Figure BDA00029208439900000910
Will be provided with
Figure BDA00029208439900000911
Substituting to obtain formula (25) to obtain formula (26);
Figure BDA00029208439900000912
substituting formula (16), formula (22) and formula (23) for formula (26) to obtain formula (27):
Figure BDA00029208439900000913
substituting formula (12) for formula (9) to give formula (28):
Figure BDA00029208439900000914
substituting formula (28) for formula (27) to give formula (29):
Figure BDA0002920843990000101
substituting equations (30) to (33) for formula (29) using the inequality properties of equations (30) to (33) to obtain equation (34):
Figure BDA0002920843990000102
Figure BDA0002920843990000103
Figure BDA0002920843990000104
Figure BDA0002920843990000105
Figure BDA0002920843990000106
in the formula (34), ρ1、C1Satisfy formulas (35), (36), respectively:
Figure BDA0002920843990000107
Figure BDA0002920843990000108
wherein, | | H (X)d) | | < mu > mu, mu is Gaussian function H (X)d) Maximum value of (d); | | represents a norm; mu and r are normal numbers; lambda [ alpha ]min、λmaxRespectively representing the minimum and maximum eigenvalues, p, of the corresponding matrix1、C1Is a normal number; and I is an identity matrix.
There is a lemma for the Lyapunov function: "if there is a continuous positive definite differentiable function V (x) satisfies κ1(||x||)＜V(x)＜κ2(||x||)(κ1、κ2Belonging to a function of class K) and has a bounded initial condition if
Figure BDA0002920843990000109
ρ, C are normal numbers, then the solution V (t) is consistently bounded ".
Obtaining the Lyapunov function V of the second subsystem of the control system according to the lemma2The consistency is bounded, so that the stability of the RBF disturbance observer is ensured; meanwhile, it can be known from the theory that under the Backstepping controller of the formula (9), the joint angle error matrix z of the formula (3)1And the consistency is bounded, so that the stability of the whole control system is ensured.
Fourthly, controlling to implement;
step 1, setting the initial values of a joint output angle y and a joint moment tau to be 0, and applying external random disturbance d to the lower limb exoskeleton; is provided withDesired angle y of jointdAnd the desired angle y of the jointdAs given signal of Backstepping controller in the second step;
step 2, inputting the initial values of the joint output angle and the joint moment into the RBF disturbance observer improved in the third step, and calculating according to the formulas (14) and (20) to obtain an estimated value of the network approximation error
Figure BDA0002920843990000111
Obtaining RBF neural network ideal weight W through formula (23)*Is estimated value of
Figure BDA0002920843990000112
Estimating the network approximation error
Figure BDA0002920843990000113
And RBF neural network ideal weight W*Is estimated value of
Figure BDA0002920843990000114
Substituting into equation (12) to obtain the estimated value of the external random disturbance
Figure BDA0002920843990000115
Namely, the RBF disturbance observer outputs the estimated value of the external random disturbance
Figure BDA0002920843990000116
Then inputting the data into Backstepping controller formula (9) in the second step for disturbance compensation to obtain the joint moment tau of the current control period; substituting the joint torque tau of the current control period into a state equation of the control system to obtain a joint output angle of the current control period, and finishing the control task of the current control period;
and 3, based on the joint output angle and the joint torque of the current control cycle obtained in the step 2, repeatedly executing the step 2 to complete the control task of the next control cycle, so that the lower limb exoskeleton moves according to the expected track.
Simulation test:
setting parameters of the lower extremity exoskeleton: thighMass m of rod12.776kg, shank mass m20.726kg, thigh bar length l10.4m, shank length l20.4m, the length l of the center of mass of the thigh bar from the hip joint1g0.334m, the length l of the position of the barycenter of the shank from the knee joint2g0.2m, thigh bar moment of inertia J1＝0.00124kg·m2Moment of inertia of shank J2＝0.00022kg·m2Acceleration of gravity g ═ 9.8m/s2。
In order to simulate the actual working condition, random disturbance torques shown in fig. 3 and 4 are respectively applied to hip joints and knee joints of the lower-limb exoskeleton, and joint output angles of the lower-limb exoskeleton are tracked by using a traditional RBF disturbance observer (without considering network approximation errors) and an improved RBF disturbance observer of the invention.
Fig. 5 to 8 are graphs showing the tracking results obtained by using a conventional RBF disturbance observer, fig. 5 showing the hip joint angle error, fig. 6 showing a partially enlarged view of a block portion in fig. 5, fig. 7 showing the knee joint angle error, and fig. 8 showing a partially enlarged view of a block portion in fig. 7; the hip joint angle error is 0.2 degrees, and the knee joint angle error is 0.3 degrees;
FIGS. 9-12 are graphs showing the results of tracking using the improved RBF perturbation observer of the present invention, FIG. 9 is a view showing the angle error of the hip joint, FIG. 10 is a partial enlarged view of the box portion of FIG. 9, FIG. 11 is a view showing the angle error of the knee joint, and FIG. 12 is a partial enlarged view of the box portion of FIG. 11; the hip joint angle error is 0.1 degree, which is reduced by 0.1 degree compared with the traditional RBF disturbance observer; the knee joint angle error is 0.05 degrees, and is reduced by 0.25 degrees compared with the traditional RBF disturbance observer, so that the lower extremity exoskeleton joint angle tracking error is smaller, a better joint angle tracking effect is obtained, and the effectiveness of the invention is proved.
The external random disturbance of the test is applied for simulation, and under the condition of actual working conditions, the invention can obtain good tracking effect under the condition that the external random disturbance changes greatly.
Nothing in this specification is said to apply to the prior art.

Claims (4)

1. A Backstepping-based lower limb exoskeleton control method is characterized by comprising the following steps:
firstly, establishing a lower limb exoskeleton dynamic model, and converting the lower limb exoskeleton dynamic model into a control system state equation;
secondly, designing a Backstepping controller of a formula (9):
Figure FDA0002920843980000011
in the formula (9), τ is a joint moment,
Figure FDA0002920843980000012
is an estimate of an external random disturbance, z1For joint angle error, K2Is a constant matrix, z2Error of angular velocity of the joint, G (x)1) To control the gravity matrix of the system equation of state, C (x)1,x2) The matrix of coriolis forces and centrifugal forces, M (x), for the control system equation of state1) To control the moment of inertia matrix, alpha, of the system equation of state1In order to virtually control the amount of control,
Figure FDA0002920843980000013
is alpha1First order differential of (x)1For controlling the joint output angle, x, of the lower extremity exoskeleton in the system equation of state2Controlling the joint angular velocity of the lower extremity exoskeleton in the system state equation;
thirdly, improving an RBF disturbance observer;
designing an RBF disturbance observer according to the formula (12):
Figure FDA0002920843980000014
in the formula (12), the reaction mixture is,
Figure FDA0002920843980000015
an estimate, H (X), representing the ideal weight of the RBF neural networkd) Expressing a Gaussian basis function of an RBF neural network hidden layer, and expressing matrix transposition by T;
Figure FDA0002920843980000016
represents an estimate of the network approximation error and satisfies equation (14):
Figure FDA0002920843980000017
Figure FDA0002920843980000018
is an estimate of an auxiliary variable, and the auxiliary variable estimate
Figure FDA0002920843980000019
First order differential of
Figure FDA00029208439800000110
Satisfies formula (20):
Figure FDA00029208439800000111
in the formula (20), R (z)2) Is a constant coefficient, M-1(x1) Is M (x)1) The inverse matrix of (d);
designing an adaptive law of the RBF neural network of the formula (23):
Figure FDA00029208439800000112
in the formula (23), the compound represented by the formula,
Figure FDA00029208439800000113
represents the estimated value of the ith node weight of the hidden layer of the RBF neural network,
Figure FDA00029208439800000114
is composed of
Figure FDA00029208439800000115
First order differential of (a)iDenotes the normal number, ΓiRepresenting a positive definite matrix; z is a radical of2iRepresenting the joint angular velocity error of the ith node of the hidden layer of the RBF neural network;
fourthly, controlling to implement;
step 1, setting the initial values of joint output angles and joint moments to be 0, and applying external random disturbance to the lower limb exoskeleton; setting a joint desired angle, and using the joint desired angle as a given signal of a Backstepping controller in the second step;
step 2, inputting the initial values of the joint output angle and the joint moment into the RBF disturbance observer improved in the third step, and calculating according to the formulas (14) and (20) to obtain an estimated value of a network approximation error; obtaining an estimated value of the ideal weight of the RBF neural network through a formula (23); then, substituting the estimated value of the network approximation error and the estimated value of the ideal weight of the RBF neural network into a formula (12) to obtain the estimated value of the external random disturbance, namely, the estimated value of the external random disturbance is output by the RBF disturbance observer and then input into a Backstepping controller formula (9) in the second step for disturbance compensation to obtain the joint moment of the current control period; substituting the joint torque of the current control period into the state equation of the control system in the first step to obtain the joint output angle of the current control period, so as to complete the control task of the current control period;
and 3, based on the joint output angle and the joint torque of the current control cycle obtained in the step 2, repeatedly executing the step 2 to complete the control task of the next control cycle, so that the lower limb exoskeleton moves according to the expected track.
2. The Backstepping-based lower extremity exoskeleton control method of claim 1, wherein in the third step, the auxiliary variable z is3Satisfies formula (13);
z3＝ε+Ψ(z2)＝ε+R(z2)z2 (13)
in formula (13), Ψ (z)2)＝R(z2)z2Denotes with respect to z2Represents the network approximation error.
3. The Backstepping-based lower extremity exoskeleton control method as claimed in claim 1 or 2, wherein the second step further comprises constructing the Lyapunov function V of the first subsystem of the control system1And verifying the stability of the first subsystem of the control system; the specific process is as follows:
error z of joint angle1Satisfies formula (3):
z1＝y-yd (3)
definition of alpha1Satisfies the formula (4),
Figure FDA0002920843980000021
a matrix of constants is represented by a matrix of constants,
Figure FDA0002920843980000022
denotes ydFirst order differential of (y)dA desired angle for the joint;
Figure FDA0002920843980000023
definition of z2Satisfies formula (5);
z2＝x2-α1 (5)
the first order differential is obtained for the formula (3), and then the y of the state equation of the control system is changed to x1、
Figure FDA0002920843980000024
And formula (5) substituting formula (3) to obtain formula (6) after first order differentiation;
Figure FDA0002920843980000025
in the formula (6), the reaction mixture is,
Figure FDA0002920843980000026
denotes z1The first order differential of the first order of the,
Figure FDA0002920843980000027
the first order differential of y is represented by,
Figure FDA0002920843980000028
denotes x1First order differentiation of;
lyapunov function V of first subsystem of control system of structural formula (7)1；
Figure FDA0002920843980000029
Obtaining a first order differential of the formula (7), and obtaining a formula (8) by substituting the formula (4) and the formula (6) for the formula (7) and obtaining a formula after the first order differential;
Figure FDA00029208439800000210
when z is represented by formula (8)2When the content is equal to 0, the content,
Figure FDA00029208439800000211
it indicates that the first subsystem of the control system is stable.
4. The Backstepping-based lower extremity exoskeleton control method of claim 3, wherein the third step further comprises constructing the Lyapunov function V of the second subsystem of the control system2And verifying the stability of the second subsystem of the control system.
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Publication number Priority date Publication date Assignee Title
CN114721258B (en) * 2022-02-21 2023-03-10 电子科技大学 Lower limb exoskeleton backstepping control method based on nonlinear extended state observer
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Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102914972A (en) * 2012-11-01 2013-02-06 河海大学常州校区 Micro-gyroscope RBF (Radial Basis Function) network self-adapting control method based on model global approximation
CN105159084A (en) * 2015-09-06 2015-12-16 台州学院 Manipulator nerve network control system with interference observer and control method
CN109465825A (en) * 2018-11-09 2019-03-15 广东工业大学 The adaptive dynamic surface control method of the RBF neural of mechanical arm flexible joint
CN110193830A (en) * 2019-05-24 2019-09-03 上海大学 Ankle-joint gait prediction technique based on RBF neural
CN110221170A (en) * 2019-06-05 2019-09-10 贵州电网有限责任公司 A kind of small current earthing wire-selecting method based on TABU search optimization RBF network
CN111390877A (en) * 2020-04-23 2020-07-10 电子科技大学 Exoskeleton device and exoskeleton admittance variation control method
CN111459051A (en) * 2020-04-23 2020-07-28 河北工业大学 Discrete terminal sliding mode model-free control method with disturbance observer
CN111941432A (en) * 2020-09-28 2020-11-17 南京工业大学 Artificial intelligence output feedback control method for high-performance mechanical arm
CN112180729A (en) * 2020-10-09 2021-01-05 电子科技大学中山学院 Self-adaptive trajectory tracking control method for mechanical arm

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8260732B2 (en) * 2009-11-24 2012-09-04 King Fahd University Of Petroleum And Minerals Method for identifying Hammerstein models

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102914972A (en) * 2012-11-01 2013-02-06 河海大学常州校区 Micro-gyroscope RBF (Radial Basis Function) network self-adapting control method based on model global approximation
CN105159084A (en) * 2015-09-06 2015-12-16 台州学院 Manipulator nerve network control system with interference observer and control method
CN109465825A (en) * 2018-11-09 2019-03-15 广东工业大学 The adaptive dynamic surface control method of the RBF neural of mechanical arm flexible joint
CN110193830A (en) * 2019-05-24 2019-09-03 上海大学 Ankle-joint gait prediction technique based on RBF neural
CN110221170A (en) * 2019-06-05 2019-09-10 贵州电网有限责任公司 A kind of small current earthing wire-selecting method based on TABU search optimization RBF network
CN111390877A (en) * 2020-04-23 2020-07-10 电子科技大学 Exoskeleton device and exoskeleton admittance variation control method
CN111459051A (en) * 2020-04-23 2020-07-28 河北工业大学 Discrete terminal sliding mode model-free control method with disturbance observer
CN111941432A (en) * 2020-09-28 2020-11-17 南京工业大学 Artificial intelligence output feedback control method for high-performance mechanical arm
CN112180729A (en) * 2020-10-09 2021-01-05 电子科技大学中山学院 Self-adaptive trajectory tracking control method for mechanical arm

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
Memetic algorithm with normalized RBF ANN for approximation of objective function and secondary RBF ANN for error mapping;Peter Pecháč等;《procedia engineering》;20170228;全文 *
Model Reference Adaptive Control for MIMO Nonlinear Systems Using RBF Neural Networks;Sabrine Slama等;《2018 International Conference on Advanced Systems and Electric Technologies (IC_ASET)》;20180614;全文 *
Model-Free Based Back-Stepping Sliding Mode Control for Wearable Exoskeletons;zhang yan等;《2019 25th International Conference on Automation and Computing (ICAC)》;20191111;全文 *
Novel RBF Approximation Method Based on Geometrical Properties for Signal Processing with a New RBF Function: Experimental Comparison;Vaclav Skala，Martin Cervenka;《2019 IEEE 15th International Scientific Conference on Informatics》;20200607;全文 *
基于人机耦合的下肢外骨骼动力学分析及仿真;张燕等;《应用数学和力学》;20190701;全文 *
基于扰动观测器的机器人自适应神经网络跟踪控制研究;于欣波等;《自动化学报》;20190731;全文 *
快速二阶终端滑模控制及其在下肢外骨骼的应用;宋胜利等;《控制与决策》;20190131;全文 *

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