CN114721258A - Lower limb exoskeleton backstepping control method based on nonlinear extended state observer - Google Patents

Lower limb exoskeleton backstepping control method based on nonlinear extended state observer Download PDF

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CN114721258A
CN114721258A CN202210155110.XA CN202210155110A CN114721258A CN 114721258 A CN114721258 A CN 114721258A CN 202210155110 A CN202210155110 A CN 202210155110A CN 114721258 A CN114721258 A CN 114721258A
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extended state
state observer
exoskeleton
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姚继杨
郭庆
陈振雷
严尧
石岩
许猛
蒋丹
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a lower limb exoskeleton backstepping control method based on a nonlinear extended state observer, which is applied to the field of exoskeleton robots and aims at the influence of external disturbance in the prior art; according to the method, a nonlinear extended state observer is adopted, and external disturbance is used as a new state variable to obtain a new state space equation; designing an estimation value of a state space equation as a nonlinear extended state observer; therefore, external disturbance is eliminated, unmeasured parameters are estimated, the backstepping controller is used for carrying out motor driving on the exoskeleton device based on the nonlinear extended state observer, and the response capability and the tracking precision of the exoskeleton device can be effectively improved.

Description

Lower limb exoskeleton backstepping control method based on nonlinear extended state observer
Technical Field
The invention belongs to the field of exoskeleton robots, and particularly relates to a technology for controlling backstepping of a lower limb exoskeleton.
Background
The exoskeleton is a man-machine integrated device which combines human intelligence and mechanical strength, and can enable strong power provided by machinery to be applied by a human body through simple control of an operator, so that the operator can complete tasks which cannot be completed by the operator. The lower limb exoskeleton is used as an auxiliary walking device, couples the mechanical structure of the exoskeleton and the two legs of a person together, and enables an operator who is inconvenient to move or cannot walk to walk independently in a human body control and external energy supply mode. And different gaits and pace speeds can be designed to adapt to patients with different disability conditions, so that the treatment effect is improved. The exoskeleton is mainly composed of the following parts: (1) a mechanical structure part. The load-bearing exoskeleton is mainly of a hip + knee + ankle structure due to the requirement of load-bearing function, and the rehabilitation exoskeleton is mainly used for patients and needs to reduce the movement of joints, so that the hip + knee structure is mainly adopted. The mechanical structure is mainly made of materials with light weight, high strength and fatigue resistance, such as aluminum alloy, titanium alloy, nano materials and the like; (2) a power system. The power system of the exoskeleton mainly provides a power source for the assistance of the exoskeleton, and the power can be provided by hydraulic pressure, a motor, pneumatic power and the like; (3) a sensor system. The sensor system of the exoskeleton is mainly used for acquiring various signals in the human-computer interaction process so as to judge human gait or exercise intention; (4) and (5) controlling the system. The proposed control algorithm and related methods are usually implemented by software such as Matlab/Simulink, and then downloaded to a corresponding hardware controller. However, in the prior art, the external disturbance effect exists, so that the response capability and the tracking precision of the controller are not high, and the rehabilitation training is not facilitated.
Disclosure of Invention
In order to solve the technical problems, the invention firstly provides a lower limb exoskeleton backstepping control method based on a nonlinear extended state observer, the nonlinear extended state observer is adopted to eliminate external disturbance and estimate unmeasured parameters, the total disturbance of the system is effectively estimated, and the influence caused by the total disturbance is reduced; secondly, an exoskeleton device is provided, and a backstepping controller based on a nonlinear extended state observer is adopted for motor driving.
One of the technical schemes adopted by the invention is as follows: a lower limb exoskeleton backstepping control method based on a nonlinear extended state observer is characterized in that the nonlinear extended state observer is adopted to eliminate external disturbance and estimate unmeasured parameters, and a backstepping controller based on the nonlinear extended state observer is adopted to control a motor of a lower limb exoskeleton device;
the nonlinear extended state observer inputs the large leg moment tau and the actual joint position q and outputs the estimation of external disturbance
Figure BDA0003512036540000011
Estimating a location
Figure BDA0003512036540000012
And estimating the velocity
Figure BDA0003512036540000013
The joint position information q with ideal input based on the input of the backstepping controller of the nonlinear extended state observerdMicro-division of
Figure BDA0003512036540000021
Estimation of joint actual position q and external disturbances output by nonlinear extended state observer
Figure BDA0003512036540000022
Estimating a location
Figure BDA0003512036540000023
Estimating speed
Figure BDA0003512036540000024
The output is the leg moment τ.
The nonlinear extended state observer is designed as follows:
Figure BDA0003512036540000025
wherein,
Figure BDA0003512036540000026
is an estimate of the state x of the device,
Figure BDA0003512036540000027
to represent
Figure BDA0003512036540000028
The derivative of (a) of (b),
Figure BDA0003512036540000029
u is τ, τ denotes the thigh and calf moment,
Figure BDA00035120365400000210
represents an estimate of phi (x),
Figure BDA00035120365400000211
x1representing the joint angle, x2Representing the angular acceleration of the joint, H is the observer gain,
Figure BDA00035120365400000212
a non-linear feedback matrix is used,
Figure BDA00035120365400000213
τextrepresenting human-computer interaction moments.
The backstepping controller is designed as follows:
Figure BDA00035120365400000214
wherein M is0Is M0Abbreviation of (q), M0(q) represents an inertia matrix; c0Is composed of
Figure BDA00035120365400000215
For the short term of (A) or (B),
Figure BDA00035120365400000216
expressing the Coriolis forceA matrix; g0Is G0Abbreviation of (q), G0(q) represents gravity;
Figure BDA00035120365400000217
is tauf,0Estimate of τf,0Is composed of
Figure BDA00035120365400000218
For the short term of (A) or (B),
Figure BDA00035120365400000219
representing a friction force;
Figure BDA00035120365400000220
is z2Estimate of z1Is corresponding to x1Of the defined system error, z2Is corresponding to x2Defined systematic error of, K2A positive definite matrix is represented, and,
Figure BDA00035120365400000221
is that
Figure BDA00035120365400000222
The derivative of (a) is determined,
Figure BDA00035120365400000223
represents an estimated value of β, β represents a virtual control amount,
Figure BDA00035120365400000224
is x3Estimate of (a), x3To extend state variables.
Figure BDA00035120365400000225
Wherein,
Figure BDA00035120365400000226
representing the set uncertainty.
Figure BDA00035120365400000227
Wherein d (t) represents external disturbances, M△(q)、
Figure BDA00035120365400000228
G△(q)、
Figure BDA00035120365400000229
Respectively, the identification errors of the inertia matrix, the Coriolis force matrix, the gravity and the friction.
The invention has the beneficial effects that: the invention designs a lower limb exoskeleton backstepping control method based on a nonlinear extended state observer; according to the invention, the nonlinear extended state observer is used for observing unknown external disturbance and joint speed which is not directly measured, so that the total disturbance of the system is effectively estimated, and the influence caused by the total disturbance is reduced; the invention realizes the stable control of the lower limb exoskeleton system by using the backstepping controller based on the non-linear extended state observer.
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FIG. 1 is a block diagram of an implementation of the method of the present invention;
FIG. 2 is a block diagram of a back-step controller implementation of the present invention.
Detailed Description
In order to facilitate understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
1. In this embodiment, a block diagram of a lower extremity exoskeleton system as shown in fig. 1 is taken as an example for explanation:
fig. 1 is a System block diagram, which mainly includes a backstepping controller, a lower extremity exoskeleton System module (i.e., System in fig. 1), and an extended state observer. As shown in fig. 1; wherein the backstepping controller can be used for inputting the joint position information q according to the idealdDifferential, differential
Figure BDA0003512036540000031
Actual joint position q obtained by exoskeleton system and estimated position estimated by extended state observerDevice for placing
Figure BDA0003512036540000032
Estimating speed
Figure BDA0003512036540000033
Estimation of external disturbances
Figure BDA0003512036540000034
Obtaining the moment tau of the upper and lower legs; the lower limb exoskeleton system module can obtain the actual position q of the joint according to the input large and small leg moment tau; wherein the extended state observer can estimate to obtain the estimation of the external disturbance according to the input large and small leg moment tau and the actual position q of the joint
Figure BDA0003512036540000035
Estimating a location
Figure BDA0003512036540000036
And estimating the velocity
Figure BDA0003512036540000037
Those skilled in the art will appreciate that the ideal inputs mentioned in the present invention are specifically: the exoskeleton aims at rehabilitation training, the ideal input function is to input a track to help a patient to perform rehabilitation training, the track is specified according to the condition of the patient, and the track can be specified as input after digital conversion.
2. Design of lower limb exoskeleton backstepping controller based on nonlinear extended state observer
21. Lagrange dynamics modeling
The dynamics model of the two-degree-of-freedom lower extremity exoskeleton is described as follows
Figure BDA0003512036540000038
Wherein
Figure BDA0003512036540000039
The positions of two exoskeleton joints, specifically the knee joints of the left leg and the right leg,
Figure BDA00035120365400000310
and
Figure BDA00035120365400000311
respectively an inertia matrix, a Coriolis force matrix, gravity, friction and external disturbance,
Figure BDA00035120365400000312
the first derivative of q is represented by,
Figure BDA00035120365400000313
representing a matrix of real numbers.
Figure BDA00035120365400000314
Is the driving torque of the two joint motors,
Figure BDA0003512036540000041
moment of human-computer interaction, τext＝JTfextThe superscript T denotes transposition, fextAnd J is a Jacobian matrix.
Wherein M (q) is selected from,
Figure BDA0003512036540000042
g (q) and
Figure BDA0003512036540000043
can be expressed as
Figure BDA0003512036540000044
Wherein M is0(q)，
Figure BDA0003512036540000045
G0(q)，
Figure BDA0003512036540000046
Is a common term identified by the parameters,
Figure BDA0003512036540000047
the complex number matrix is expressed in matrix theory, hereinafter abbreviated uniformly to M0、C0、G0、τf,0；M△(q)、
Figure BDA0003512036540000048
G△(q)、
Figure BDA0003512036540000049
Is a parameter identification error.
Therefore, (1) can be rewritten into the following form
Figure BDA00035120365400000410
Wherein,
Figure BDA00035120365400000411
representing the second derivative of q, aggregate uncertainty
Figure BDA00035120365400000412
Can be expressed as
Figure BDA00035120365400000413
22. Design of nonlinear extended state observer
To solve the problem of unmeasured joint velocity
Figure BDA00035120365400000414
And external disturbances d (t), designing a NESO (non-linear extended state observer) based backstepping controller to improve the responsiveness and tracking accuracy of the exoskeleton device.
Exoskeleton state variables can be definedIs x1＝[q1,q2]T，
Figure BDA00035120365400000415
x1Indicates the angle of the joint, x2Representing angular acceleration of joints, and expanding state variables
Figure BDA00035120365400000416
The state space equation of (3) can be expressed as
Figure BDA00035120365400000417
Wherein δ (t) is x3The time derivative of (a).
If the total state vector can be defined as x ═ x1,x2,x3]TThen (5) can be expressed as
Figure BDA00035120365400000418
Wherein
Figure BDA0003512036540000051
Wherein, 02×2Is a 2 × 2 matrix of 0, I2×2Is a 2 x 2 unit matrix and is,
Figure BDA0003512036540000052
are temporary variables used to simplify matrix representation.
Exoskeleton joint position q and man-machine interaction force tauextCan be measured by absolute encoders and 3-D force sensors, but joint velocity
Figure BDA00035120365400000510
Cannot be obtained directly by an absolute encoder. Therefore, the design of NESO requires not only estimation of the unmeasured system states x2And the total uncertainty x needs to be estimated3。
The exoskeleton joint position q measured by the absolute encoder is the actual joint position q obtained by the exoskeleton system; it should be understood by those skilled in the art that the motor of the lower extremity exoskeleton includes an absolute encoder, and the specific lower extremity exoskeleton system can refer to patent application No. 202111332323.7, which is a prior art and will not be described in detail in the present invention; as described in patent application No. 202111332323.7, the 3-D force sensors in the lower extremity exoskeleton system include a 3-D force sensor for the waist and a 3-D force sensor for the legs, and a multi-dimensional human-computer interaction force τ is measured by the two 3-D force sensorsext。
According to (7), NESO can be designed in the following form
Figure BDA0003512036540000053
Wherein,
Figure BDA0003512036540000054
is an estimate of the state x of the device,
Figure BDA0003512036540000055
to represent
Figure BDA0003512036540000056
The derivative of (a) is determined,
Figure BDA0003512036540000057
Figure BDA0003512036540000058
is observer gain, ω0Is an adjustable bandwidth of the observer,
Figure BDA0003512036540000059
a non-linear feedback matrix, wherein
Figure BDA0003512036540000061
Wherein, delta and alpha are constants, sign (x) is a sign function, when x is>0, sign (x) 1; when x is 0, sign (x) is 0; when x is<0, sign (x) ═ 1. Those skilled in the art will appreciate that x11For representing x1First dimension of (i.e. q)1Same principle as x12For representing x1A second dimension of (i.e. q)2。
23. Design of backstepping controller
According to the exoskeleton dynamics model (3), taking x1＝[q1,q2]T，
Figure BDA0003512036540000062
The state space expression is
Figure BDA0003512036540000063
Defining systematic errors
Figure BDA0003512036540000064
Figure BDA0003512036540000065
Wherein z is1Is corresponding to x1Of the defined system error, z2Is corresponding to x2Of the defined system error, xd＝[q1d,q2d]TIn order to be able to input the desired input,
Figure BDA0003512036540000066
in order to virtually control the amount of control,
Figure BDA0003512036540000067
is a positive definite matrix. The desired input here corresponds to q in FIG. 1d，qdIs two-dimensional.
The NESO-based back-stepping controller can be designed as
Figure BDA0003512036540000068
Wherein, K2In order to be a positive definite matrix,
Figure BDA0003512036540000069
Figure BDA00035120365400000610
the exoskeleton device controls the motor to operate according to the tau, and then the actual joint position q is measured according to the absolute value encoder of the motor.
The observer and the controller also only adopt the appropriate Lyapunov function to verify the stability, the specific verification process is the prior known technology, and the invention is not elaborated.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (6)

1. The method is characterized in that a nonlinear extended state observer is adopted to eliminate external disturbance and estimate unmeasured parameters, and a backstepping controller based on the nonlinear extended state observer is adopted to control a motor of a lower limb exoskeleton device;
the nonlinear extended state observer inputs the large leg moment tau and the actual joint position q and outputs the estimation of external disturbance
Figure FDA0003512036530000011
Estimating a location
Figure FDA0003512036530000012
And estimating the velocity
Figure FDA0003512036530000013
The joint position information q with ideal input based on the input of the backstepping controller of the nonlinear extended state observerdAnd a differential value
Figure FDA0003512036530000014
Estimation of joint actual position q and external disturbances output by nonlinear extended state observer
Figure FDA0003512036530000015
Estimating a position
Figure FDA0003512036530000016
Estimating velocity
Figure FDA0003512036530000017
The output is the leg moment τ.
2. The method for the control of the exoskeleton of lower limbs back-stepping based on a nonlinear extended state observer of claim 1, wherein the nonlinear extended state observer is designed to:
Figure FDA0003512036530000018
wherein,
Figure FDA0003512036530000019
is an estimate of the state x of the device,
Figure FDA00035120365300000110
to represent
Figure FDA00035120365300000111
The derivative of (a) of (b),
Figure FDA00035120365300000112
u is τ, τ denotes the thigh and calf moment,
Figure FDA00035120365300000113
represents an estimate of phi (x),
Figure FDA00035120365300000114
x2the angular acceleration of the joint is represented,
Figure FDA00035120365300000115
denotes x1Estimation error of x1Which represents the joint angle, H is the observer gain,
Figure FDA00035120365300000116
a non-linear feedback matrix is used,
Figure FDA00035120365300000117
τextrepresenting human-computer interaction moments.
3. The method for controlling the backstepping of the exoskeleton of lower limbs based on a nonlinear extended state observer according to claim 2,
Figure FDA00035120365300000118
the expression of (a) is:
Figure FDA00035120365300000119
wherein,
Figure FDA00035120365300000120
represents x11Estimation error of x11For representing x1Is measured in a first dimension of (a) a,
Figure FDA00035120365300000121
denotes x12Estimation error of x12For representing x1In the second dimension of (a) is,
Figure FDA00035120365300000122
delta, alpha are constants, sign (x) is a sign function when x is>0, sign (x) 1; when x is 0, sign (x) is 0; when x is<0，sign(x)＝-1。
4. The method of claim 3, wherein the controller is configured to:
Figure FDA0003512036530000021
Figure FDA0003512036530000022
wherein, M0Is M0Abbreviation of (q), M0(q) represents an inertia matrix; c0Is composed of
Figure FDA0003512036530000023
For the short term of (A) or (B),
Figure FDA0003512036530000024
representing a Coriolis force matrix; g0Is G0Abbreviation of (q), G0(q) represents gravity;
Figure FDA0003512036530000025
is tauf,0Estimate of τf,0Is composed of
Figure FDA0003512036530000026
For the short term of (A) or (B),
Figure FDA0003512036530000027
representing a friction force;
Figure FDA0003512036530000028
is z2Estimate of z1Is corresponding to x1Of the defined system error, z2Is corresponding to x2Defined systematic error of, K2A positive definite matrix is represented, and,
Figure FDA0003512036530000029
is that
Figure FDA00035120365300000210
The derivative of (a) of (b),
Figure FDA00035120365300000211
denotes an estimated value of β, β denotes a virtual control amount,
Figure FDA00035120365300000212
is x3Estimate of (a), x3To extend state variables.
5. The method for controlling the backstepping of the exoskeleton of lower limbs based on a nonlinear extended state observer according to claim 4,
Figure FDA00035120365300000213
wherein,
Figure FDA00035120365300000214
representing the set uncertainty.
6. The method for controlling the backstepping of the exoskeleton of lower limbs based on the nonlinear extended state observer according to claim 5The method is characterized in that the raw materials are mixed,
Figure FDA00035120365300000215
the expression of (a) is:
Figure FDA00035120365300000216
wherein d (t) represents an external disturbance, M△(q)、
Figure FDA00035120365300000217
G△(q)、
Figure FDA00035120365300000218
Respectively, the identification errors of an inertia matrix, a Coriolis force matrix, gravity and friction.
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陈振雷 等: "下肢外骨骼伺服电机驱动控制方案设计" *
韩宜峰: "下肢外骨骼关节伺服控制研究" *

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