CN111965979B - Limited time control method based on exoskeleton robot actuator - Google Patents

Limited time control method based on exoskeleton robot actuator Download PDF

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CN111965979B
CN111965979B CN202010888568.7A CN202010888568A CN111965979B CN 111965979 B CN111965979 B CN 111965979B CN 202010888568 A CN202010888568 A CN 202010888568A CN 111965979 B CN111965979 B CN 111965979B
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孙振兴
王辽堉
张兴华
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Nanjing Tech University
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Abstract

The invention discloses a finite time control method based on an exoskeleton robot actuator, and belongs to the field of exoskeleton robot systems. Aiming at the problems of complex control method, low precision, poor robustness and anti-interference capability in the prior art, the invention provides a finite time control method based on an exoskeleton robot actuator, which comprises the steps of firstly, constructing a lower triangular nonlinear system finite time controller by partial state vectors, full state vectors and output of a system; then, a nominal mathematical model is established by analogy of a damped double-mass system and neglecting interference, and the nominal mathematical model is converted into a state space model of the exoskeleton robot actuator; and finally, designing a robust finite time control law by utilizing a finite time controller and combining a state space model. The scheme adopts semi-global control instead of global control, can realize control gain according to a pole configuration mode, improves control speed and enhances robustness.

Description

Limited time control method based on exoskeleton robot actuator
Technical Field
The present invention relates to the field of exoskeleton robots, and more particularly to a limited time control method based on exoskeleton robot actuators.
Background
The exoskeleton robot technology is a comprehensive technology integrating sensing, control, information, fusion and mobile computing, provides a wearable mechanical mechanism for a person as an operator, and is a robot sleeved outside a human body, which is also called a wearable robot. The safety and flexibility of the existing control method need to be improved, and the parameters of the exoskeleton robot are difficult to accurately obtain due to the complexity of mechanical structures, such as nonlinear friction force, clearance and the complexity of a robot actuator. In addition, the dynamic characteristics of subjects vary according to their physiological conditions. The current control methods are not adaptive in the presence of dynamic and motion uncertainties and unknown disturbances of the system.
The Chinese patent application, application No. CN202010132049.8, published as 2020, 6.16.A self-adaptive compliance control method for exoskeleton robots for upper limb rehabilitation belongs to the field of robot control; the control algorithm consists of two parts: the first part is an admittance control module which is arranged as a control outer ring and can establish a dynamic relation between interaction force between a patient and the exoskeleton and a rehabilitation training track regulating variable, so that the patient can remold a rehabilitation training track according to own active intention; the second part is an adaptive sliding mode control module which is arranged as a control inner ring and used for realizing accurate tracking control of the expected training track and the position adjustment quantity, and the control precision and the system stability are partially dependent on inner ring position control. The method has high control precision, stronger robustness and anti-interference capability to uncertain factors of the system and good real-time performance. The method has the disadvantages that the model predictive control of the invention is difficult to process model uncertainty and interference problems in a physical control system, and a large amount of calculation is required, so that the method is not easy to realize.
The Chinese patent application, application number CN202010093076.9, published 2020, 6.12.C., discloses a multi-joint combined control system and method for an exoskeleton robot, wherein the control system inputs real-time feedback signals of a whole sole pressure sensing system and a limb posture sensing system into a multi-signal fusion and decoupling model, the model completes fusion and decoupling of various signals, and outputs various joint motor control quantities to control the operation of a motor; building a multi-signal fusion and decoupling model by using a neural network, and generating a mature application model with multi-signal fusion and decoupling through a large amount of training; the control quantity of various joint motors output by the model is corrected in real time according to a human-computer interaction sensing system in the control system, so that the auxiliary optimization effect is achieved, and the optimal wearing effect of the exoskeleton robot is achieved; in the aspect of joint motor control, the motor is controlled quickly and accurately by real-time current closed-loop control and position (joint angle) closed-loop control of the motor. The method has the disadvantages of more parameters, large calculation amount and complex algorithm realization.
Disclosure of Invention
1. Technical problem to be solved
Aiming at the problems of complex control scheme, low precision and poor robustness and anti-interference capability of the exoskeleton robot in the prior art, the invention provides a finite time control method based on an exoskeleton robot actuator, which adopts semi-global rather than global control to improve the engineering applicability, can realize control gain according to a pole configuration mode, improves the control speed and enhances the robustness.
2. Technical scheme
A method for limited time control of exoskeleton-based robotic actuators comprising the steps of:
step 1: constructing a lower triangular nonlinear system finite time controller by using a part of state vectors, a full state vector and output of the system;
step 2: establishing a nominal mathematical model by analogy of a damped double-mass system and neglecting interference, and converting the nominal mathematical model into a state space model of the exoskeleton robot actuator;
and step 3: and (3) designing a robust finite time control law by utilizing the finite time controller constructed in the step (1) and combining the state space model in the step (2).
Further, the lower triangular nonlinear system finite time controller may take the form of:
Figure GDA0003221148910000021
wherein the content of the first and second substances,
Figure GDA0003221148910000022
Figure GDA0003221148910000023
Figure GDA0003221148910000024
Figure GDA0003221148910000025
are the partial state vector and the full state vector of the system; y is the system output; phi is ai(·)，i∈N1:4Is a known smooth non-linear function, and outputs a reference signal, using yrY (t) and its nth derivative, u (t) is a feedback law.
Further, a finite time controller for implementing exoskeleton robot actuators specifically comprises the following steps:
step 101, first defining an auxiliary variable vector
Figure GDA0003221148910000026
Figure GDA0003221148910000027
Figure GDA0003221148910000028
Figure GDA0003221148910000029
Figure GDA00032211489100000210
In
Figure GDA00032211489100000211
Determined by the steady state generator given below:
Figure GDA0003221148910000031
step 102, let z ═ col (z)1,z2,z3,z4) Wherein
Figure GDA0003221148910000032
Figure GDA0003221148910000033
Figure GDA0003221148910000034
Figure GDA0003221148910000035
Wherein
Figure GDA00032211489100000310
Is a bandwidth factor that is determined later in the stability analysis.
Without recursive stability analysis, a simple generalized finite time controller can be explicitly pre-configured in the form:
Figure GDA0003221148910000036
where v is the finite time controller and u is the feedback law, the definition
Figure GDA0003221148910000039
K＝[k1,k2,k3,k4]Is the coefficient vector p(s) s of the Hall-polynomial4+k4s3+k3s2+k2s+k1，r＝(1,1+τ,1+2τ,1+3τ)，
Figure GDA0003221148910000037
Further, in step 2, the method for establishing the state space model of the exoskeleton robot actuator comprises the following steps:
step 201, a motor is coupled with a ball screw at a joint through a high-rigidity torsion spring. The angular displacement of the motor shaft and the lead screw is measured by two incremental encoders. Using an analogy of two mass-spring-damper systems, ignoring the inevitable unmodeled disturbances, a nominal mathematical model of the form:
Figure GDA0003221148910000038
wherein m ismIs the moment of inertia of the motor, mlIs the moment of inertia of the connecting rod, bmIs the viscous friction coefficient of the motor, blIs the viscous friction coefficient of the connecting rod, qmIs the angle of rotation of the motor, qlIs the rotation angle of the connecting rod, k is the stiffness coefficient of the cascade elastic driver, FmIs the motor torque.
Step 202, the nominal mathematical model established in step 201 is converted into a state space form.
Is provided with
Figure GDA0003221148910000041
Substituting into equation (4), the nominal model can then be transformed into the following state space form:
Figure GDA0003221148910000042
further, in step 3, the method for designing the robust finite time control law of the exoskeleton robot by using the generalized finite time control method provided above is as follows:
by giving
Figure GDA0003221148910000043
The state space form substituted into equation (5) for the tracking reference is calculated as:
Figure GDA0003221148910000044
substituting the above calculated quantities into equation (3) can construct the following finite time control law applicable to exoskeleton robot actuators:
Figure GDA0003221148910000045
where v is the finite time controller and u is the feedback law, the definition
Figure GDA00032211489100000410
K＝[k1,k2,k3,k4]Is the coefficient vector of the Hall-Viz polynomial, FmIs the torque of the motor or motors,
Figure GDA0003221148910000046
Figure GDA0003221148910000047
Figure GDA0003221148910000048
Figure GDA0003221148910000049
wherein
Figure GDA00032211489100000411
Is a bandwidth factor.
3. Advantageous effects
Compared with the exoskeleton robot actuator design based on other control methods in the prior art, the exoskeleton robot actuator has the main improvements as follows: the control scheme is simpler, and the control gain can be easily selected according to the pole arrangement mode; the method has high control precision, stronger robustness and anti-interference capability to the uncertain factors of the system and good real-time performance; by introducing negative justification a lower steady state error can be obtained and hence a much more robust than optimal controllers.
Drawings
FIG. 1 is a schematic block diagram of a limited time control method of the present invention;
FIG. 2 is a schematic view of an exoskeleton robot actuator according to the present invention;
fig. 3 is a schematic diagram of the tracking performance of the actuator based on the present invention when τ is 0;
FIG. 4 is a schematic diagram of the tracking performance of an actuator based on the present invention when τ is-0.05;
FIG. 5 is a schematic diagram of the tracking performance of an actuator based on the present invention when τ is-0.1;
fig. 6 is a schematic diagram showing the tracking performance of the actuator based on the present invention when τ is-0.15.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Examples
The invention discloses a finite time control method based on an exoskeleton robot actuator, which specifically comprises the following steps:
step 1: and constructing a lower triangular nonlinear system finite time controller by using the partial state vector, the full state vector and the output of the system, wherein the lower triangular nonlinear system finite time controller can be expressed in the following form:
Figure GDA0003221148910000051
wherein
Figure GDA0003221148910000052
Figure GDA0003221148910000053
Figure GDA0003221148910000054
Figure GDA0003221148910000055
Are the partial state vector and the full state vector of the system; y is the system output; phi is ai(·)，i∈N1:4Is a known smooth non-linear functionAnd (4) counting. Output reference signal, with yrY (t) and its nth derivative, u (t) being the feedback law;
the scheme for realizing the control of the exoskeleton robot actuator comprises the following steps:
step 101, first defining an auxiliary variable vector
Figure GDA0003221148910000056
Figure GDA0003221148910000057
Figure GDA0003221148910000058
Figure GDA0003221148910000059
Figure GDA00032211489100000510
In
Figure GDA00032211489100000511
Determined by the steady state generator given below:
Figure GDA0003221148910000061
step 102, let z ═ col (z)1,z2,z3,z4) Wherein
Figure GDA0003221148910000062
Figure GDA0003221148910000063
Figure GDA0003221148910000064
Figure GDA0003221148910000065
Wherein
Figure GDA0003221148910000069
Is a bandwidth factor that is determined later in the stability analysis. Without recursive stability analysis, a simple generalized finite time controller can be explicitly pre-configured in the form:
Figure GDA0003221148910000066
wherein is defined
Figure GDA00032211489100000610
K＝[k1,k2,k3,k4]Is the coefficient vector p(s) s of the Hall-polynomial4+k4s3+k3s2+k2s+k1，r＝(1,1+τ,1+2τ,1+3τ)，
Figure GDA0003221148910000067
Step 2: through analogy of a damped double-mass system, interference is ignored, a nominal mathematical model is established and converted into a state space model of the exoskeleton robot actuator, and the specific method is as follows:
step 201, as shown in fig. 2, the motor is coupled with the ball screw at the joint through the high-stiffness torsion spring. The two incremental encoders have resolutions of 2048 and 1024 pulses per revolution respectively and are used for measuring the angular displacement of the motor shaft and the lead screw. Using an analogy of two mass-spring-damper systems, ignoring the inevitable unmodeled disturbances, a nominal mathematical model of the form:
Figure GDA0003221148910000068
wherein m ismIs the moment of inertia of the motor, mlIs the moment of inertia of the connecting rod, bmIs the viscous friction coefficient of the motor, blIs the viscous friction coefficient of the connecting rod, qmIs the angle of rotation of the motor, qlIs the rotation angle of the connecting rod, k is the stiffness coefficient of the cascade elastic driver, FmIs the motor torque.
Step 202, the nominal mathematical model established in step 201 is converted into a state space form. Is provided with
Figure GDA0003221148910000071
Substituting into equation (4), the nominal model can then be transformed into the following state space form:
Figure GDA0003221148910000072
and step 3: a robust finite time control law is designed by utilizing a finite time controller and combining a state space model, so that accurate position control is realized, and the specific method comprises the following steps:
by giving
Figure GDA0003221148910000073
The state space form substituted into equation (5) for the tracking reference is calculated as:
Figure GDA0003221148910000074
substituting the above calculated quantities into equation (3) can construct the following finite time control law applicable to exoskeleton robot actuators:
Figure GDA0003221148910000075
where v is the finite time controller and u is the feedback law, the definition
Figure GDA00032211489100000710
K＝[k1,k2,k3,k4]Is the coefficient vector of the Hall-Viz polynomial, FmIs the torque of the motor or motors,
Figure GDA0003221148910000076
Figure GDA0003221148910000077
Figure GDA0003221148910000078
Figure GDA0003221148910000079
wherein
Figure GDA00032211489100000711
Is a bandwidth factor.
The results of the simulation of the present invention using simulation software are shown in fig. 3 to 6, where K is [0.5,0.01,0.1,0.01 ]]，
Figure GDA00032211489100000712
Time of day, trajectory tracking performance under finite time controllers of different uniformity τ. The progressive tracking performance of the state feedback controller is clearly seen in comparison to the black dotted line in the figure. When tau is a negative value, the control performance is obviously improved, and the smaller tau is, the faster the convergence speed is, and the smaller the steady-state error is.
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 (5)

1. A method for finite time control of an exoskeleton-based robotic actuator, comprising the steps of:
step 1: constructing a lower triangular nonlinear system finite time controller by using a part of state vectors, a full state vector and an output of the system;
step 2: establishing a nominal mathematical model after neglecting interference through analogy of a damped double-mass system, and converting the mathematical model into a state space model of the exoskeleton robot actuator;
and step 3: designing a robust finite time control law by using the finite time controller constructed in the step 1 and combining the state space model in the step 2, wherein in the step 1, the lower triangular nonlinear system finite time controller can be expressed in the following form:
Figure FDA0003221148900000011
wherein the content of the first and second substances,
Figure FDA0003221148900000012
is the partial state vector and the full state vector of the system, y is the system output, phii(·)，i∈N1:4Is a known smooth non-linear function, and the output reference signal is yrY (t) and its nth derivative, u (t) is a feedback law.
2. A method for finite time control based on exoskeleton robot actuators as claimed in claim 1 wherein in step 1, the method for implementing the finite time controller is as follows:
step 101, first defining an auxiliary variable vector
Figure FDA0003221148900000013
Figure FDA0003221148900000014
Wherein
Figure FDA0003221148900000015
Determined by the steady state generator given below:
Figure FDA0003221148900000016
step 102, let z ═ col (z)1,z2,z3,z4) Wherein
Figure FDA0003221148900000017
Figure FDA0003221148900000021
Wherein l>1 is a bandwidth factor;
without recursive stability analysis, a simple generalized finite time controller can be explicitly pre-configured in the form:
Figure FDA0003221148900000022
Figure FDA0003221148900000023
where v is the finite time controller and u is the feedback law, the definition
Figure FDA0003221148900000024
K＝[k1,k2,k3,k4]Is the coefficient vector of the Hall-Retz polynomial, p(s) ═ s4+k4s3+k3s2+k2s+k1，r＝(1,1+τ,1+2τ,1+3τ)，
Figure FDA0003221148900000025
3. A method for finite time control of exoskeleton robot actuators as claimed in claim 1 where in step 2 the angular displacement of the motor shaft and lead screw is measured by two incremental encoders, neglecting inevitable unmodeled disturbances by analogy with damped dual mass system, and the nominal mathematical model is established as follows:
Figure FDA0003221148900000026
wherein m ismIs the moment of inertia of the motor, mlIs the moment of inertia of the connecting rod, bmIs the viscous friction coefficient of the motor, blIs the viscous friction coefficient of the connecting rod, qmIs the angle of rotation of the motor, qlIs the rotation angle of the connecting rod, k is the stiffness coefficient of the cascade elastic driver, FmIs the motor torque.
4. A method for finite time control of exoskeleton robot actuators as claimed in claim 3 wherein in step 2 the method of transforming the established nominal mathematical model into a state space form is as follows:
is provided with
Figure FDA0003221148900000027
Substituting into equation (4), the nominal model can then be transformed into the following state space form:
Figure FDA0003221148900000031
5. a method for finite time control based on exoskeleton robot actuators as claimed in claim 4 wherein in step 3, the method for designing robust finite time control laws is as follows:
by giving
Figure FDA0003221148900000032
Calculated for tracking the reference quantity and substituting into the state space form in equation (5):
Figure FDA0003221148900000033
Figure FDA0003221148900000034
Figure FDA0003221148900000035
substituting the above calculated quantities into equation (3) can construct the following finite time control law applicable to exoskeleton robot actuators:
Figure FDA0003221148900000036
where v is the finite time controller and u is the feedback law, the definition
Figure FDA0003221148900000037
K＝[k1,k2,k3,k4]Is the coefficient vector of the Hall-Viz polynomial, FmIs the torque of the motor or motors,
Figure FDA0003221148900000038
Figure FDA0003221148900000039
wherein l>1 is a bandwidth factor.
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