CN113359767B - Method for controlling safe driving of limited track tracking error of robot structure with slow change - Google Patents

Method for controlling safe driving of limited track tracking error of robot structure with slow change Download PDF

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CN113359767B
CN113359767B CN202110757256.7A CN202110757256A CN113359767B CN 113359767 B CN113359767 B CN 113359767B CN 202110757256 A CN202110757256 A CN 202110757256A CN 113359767 B CN113359767 B CN 113359767B
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robot
tracking error
follows
controller
rehabilitation training
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CN113359767A (en
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孙平
高雪峰
李树江
王硕玉
常洪彬
唐非
谢静
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Yingkou Xinyun Petrochemical Equipment Co ltd
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Shenyang University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process

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Abstract

The invention discloses a method for controlling the safe driving of a limited track tracking error of a robot structure with slow change. The method is characterized in that: utilizing a dynamic model of the rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and establishing a dynamic model of the rehabilitation training robot with structural estimation; the safety driving tracking controller which adapts to the slow change of the structure of the rehabilitation training robot is designed by taking the limitation of the track tracking error as a driving condition, so that the stability of the system is realized, the track tracking error is restrained in a designated range, and the collision danger of the robot is avoided. Based on STM32G4 series singlechip provide output PWM signal to motor drive module, make the robot adapt to the slow change of structure and help rehabilitation person to keep track of doctor appointed training orbit.

Description

Method for controlling safe driving of limited track tracking error of robot structure with slow change
Technical field:
the invention relates to the field of control of wheeled rehabilitation robots, in particular to a control method of a wheeled lower limb rehabilitation robot.
The background technology is as follows:
with the increase of the elderly population, the old people have walking dysfunction caused by diseases and natural aging, and if rehabilitation training is not performed in time, the leg muscle strength and balance ability are recovered, so that the daily life of the old people is seriously affected. Along with the application of the rehabilitation walking robot in places such as rehabilitation centers, nursing homes and the like, the walking rehabilitation problem of the old is solved in time. However, in practical application, the positions of the trainers are changed to cause the centers of the person and the robot to be misaligned, so that the eccentricity and the eccentric angle of the man-machine system are generated, and the structure of the man-machine system is changed. Because the pose of the trainer changes slowly and the robot helps the trainer to walk at a slow speed, the structure of the man-machine system changes slowly, the factor seriously influences the tracking precision of the robot on the appointed motion trail of the doctor, not only causes the rehabilitation effect of the trainer to be not ideal, but also causes the collision danger of the robot due to the overlarge trail tracking error, and influences the safety of the man-machine system. Therefore, the method for improving the tracking precision and the safety of the rehabilitation robot has important significance for solving the problem of slow structural change of the man-machine system.
In recent years, trace tracking control of rehabilitation walking robots has many research results, but these results cannot solve the problem of slow structural change of man-machine systems. If the robot cannot adapt to the slow change of the system structure in the walking training, not only the tracking precision is affected, but also the robot collides with surrounding objects due to the excessive track tracking error, so that the safety of a trainer is threatened. The invention establishes the estimation model of the structure slow change based on a new visual angle, and provides the safe driving control method which adapts to the structure slow change and constrains the track tracking error, thereby having important significance for improving the tracking precision and the safety of the man-machine system.
The invention comprises the following steps:
the invention aims to:
in order to solve the problems, the invention provides a limited track tracking error safe driving control method for a rehabilitation training robot with a slowly-changing structure, which aims to solve the problem of the slowly-changing structure of a man-machine system, improve the tracking precision of the robot and ensure the safety of a trainer.
The technical scheme is as follows:
the invention is realized by the following technical scheme:
a method for controlling the safe driving of a limited track tracking error of a rehabilitation training robot with a slowly-changing structure is characterized by comprising the following steps:
1) Utilizing a dynamic model of the rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and establishing a dynamic model of the rehabilitation training robot with structural estimation;
2) The safety driving tracking controller adapting to the slow change of the structure of the rehabilitation training robot is designed by taking the limitation of the track tracking error as a driving condition, so that the stability of the system and the limitation of the track tracking error are realized.
The method comprises the following steps:
step 1) utilizing a dynamic model of a rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and constructing the dynamic model of the rehabilitation training robot with structural estimation, and is characterized in that: the kinetic model of the system is described below
Wherein the method comprises the steps of
X (t) represents the actual motion trail of the rehabilitation training robot, u (t) represents the control input force, M represents the mass of the robot, M represents the mass of the rehabilitation person, I 0 The moment of inertia is indicated and the moment of inertia,is a coefficient matrix. θ represents the angle between the horizontal axis and the connection between the robot center and the first wheel center, i.e., θ=θ 1 As known from the structure of the rehabilitation training robot,θ 3 ＝θ+π，/>l i representing the distance of the center of gravity of the system from the center of each wheel, r 0 Represents the distance from center to center of gravity, phi i Representing the x' axis and the l corresponding to each wheel i Included angles (i=1, 2,3, 4).
Separation coefficient matrix M 0 The physical quantity p, q, r of the structural change is influenced by K (theta) 0 It is denoted as M 0 K(θ)＝M1+ΔM 1 Wherein M is 1 Consists of rehabilitation training robot mass, rehabilitation person mass and moment of inertia, and delta M 1 Representing a physical quantity of structural change, an
At the same time, coefficient matrixStructurally varied p, q, r 0 Composition; the coefficient matrix B (θ) contains the variable lambda generated by the structural change i Decompose it into B (θ) =b 1 (θ)+ΔB 1 (θ) wherein
Wherein L is a steady physical quantity and represents the distance from the center of the man-machine system to the center of each wheel; physical quantity affecting structural change in the splitting dynamics model (1) is split, and a dynamics model for describing structural change of the rehabilitation training robot is established as follows
Wherein the method comprises the steps ofPhysical quantity representing structural change of rehabilitation robot, and S (p, q, r) 0 ) The robot tracking system has the characteristics of slow structural change and nonlinearity, and influences the tracking accuracy and the safety of the robot.
Step 2) designing S (p, q, r) based on the rehabilitation training robot dynamics model (2) with structural change 0 ) And further establishes a dynamic model for estimating structural changes of the man-machine system. Let X (t) represent the actual walking track of the rehabilitation training robot, X d (t) represents a training trajectory designated by a doctor, and a trajectory tracking error e is set 1 (t) and velocity tracking error e 2 (t) are respectively
e 1 (t)＝X(t)-X d (t) (3)
Wherein α represents a parameter to be designed, e 1 (t)＝[e 11 (t) e 12 (t) e 13 (t)] T Track following errors in x-axis, y-axis and rotation angle directions, e 2 (t)＝[e 21 (t) e 22 (t) e 23 (t)] T The speed tracking errors in the x-axis, y-axis and rotational angle directions are indicated, respectively. Design S (p, q, r) 0 ) The neural network estimation model of (a) is as follows:
wherein the method comprises the steps ofRepresentation->E= [ e = [ e ] pseudo-inverse matrix of (a) 1 (t) e 2 (t)] T Input vector representing network, +_>Represents an estimated value of the network weight, and Σ (e) = [ Σ ] 1 (e) Σ 2 (e) … Σ n (e)] T And sigma f (e) (f=1, 2, …, n) represents a gaussian function as follows:
wherein beta is j Sum sigma j The center and base width parameters of the f-th node function are represented, respectively. Setting the optimal estimation weight of the network delta * For a given small positive number ε 0 The design estimation error is as follows:
definition of the definitionRepresenting the weight estimation error, there is +.>Thus S (p, q, r) 0 ) The expression form of (a) is as follows:
further, according to the formulas (2) and (8), a kinetic model of the rehabilitation robot with structural change estimation is obtained as follows:
step 3) taking the limitation of the track tracking error as a driving condition, designing a safe driving tracking controller which adapts to the slow change of the structure of the rehabilitation training robot, and realizing the stability of the system and the limitation of the track tracking error, and the method is characterized in that: according to equations (3) (4) (9), a tracking error system is obtained as follows:
the design controller u (t) and the network estimation weights adapting to the structural changes are as follows:
wherein Ω represents a positive definite symmetric matrix of appropriate dimension, λ 2 >0,ρ 1 >0 indicates that the controller adjusts the parameters,representation B 1 (θ) pseudo-inverse matrix. The drive controller is obtained from equation (11):
the safety driving bar with the limitation of the track tracking error is designed as follows:
when t 0 When the time controller drives for the first time:
t 0 ＝min{t>0；|e 1r (t)|>a 1r }，r＝1，2，3 (13)
when t i When the time controller is driven (i is more than or equal to 1):
t i ＝min{t>t i-1 ；||ξ(t)||≥ω(e 1 (t),e 2 (t))and|e 1r (t)|>a 1r } (14)
as can be seen from equations (13) (14), when the track following error exceeds the bounded range a 1r The controller is composed of u (t i ) Drive update to u (t) i+1 ) Thereby realizing a safe motion trail. Wherein a is 1r >0 denotes a trajectory tracking error bounded in x-axis, y-axis and rotation angle directions. And is also provided with
λ 1 >0,λ 2 >And 0 is a controller adjusting parameter.
When t is E [ t ] i ,t i+1 ) The tracking error system is represented as follows:
wherein the method comprises the steps ofSet variable->The form of ζ (t) is as follows:
according to an error system (16) of the time gap driven by the controller twice, a Lyapunov function is established as follows:
deriving equation (17) along error system (16), obtaining:
order theLipschitz constant of L, obtainable:
meanwhile, according to Young's inequality, for a given constant ρ 1 >0, have
The formula (19) and (20) are substituted into the formula (18)
Substituting the controller formula (11) into formula (21) yields:
wherein the method comprises the steps ofThe gap xi (t) is set at the time of driving twice to satisfy the inequality
||ξ(t)||<ω(e 1 (t),e 2 (t)) (23)
And substituting the formula (23) into the formula (22) to obtain
From (24), it can be seen thatSo that the gap tracking error system is asymptotically stable at the moment of the two driving; further, when ζ (t) does not satisfy the equation (23), the controller is configured by u (t) i ) Drive update to u (t) i+1 ) Thereby ensuring the stability of the tracking error system.
Therefore, under the action of the safety driving controllers (11) (13) (14) with slowly-changing adaptive structures, the tracking error system (10) is asymptotically stable, and a bounded track tracking error is realized, so that the safety of a trainer is ensured.
Step 4) provides output PWM signal to motor drive module based on STM32G4 series singlechip, makes rehabilitation training robot can help the patient to follow doctor appointed walking track, its characterized in that: STM32G4 series single-chip microcomputer is used as a main controller, and the input of the main controller is connected with a motor speed measuring module, and the output of the main controller is connected with a motor driving module; the motor driving module is connected with the direct current motor; the power supply system supplies power to the respective electrical devices. The control method of the main controller is to read the feedback signal of the motor encoder and the control command signal X given by the main controller d (t) andan error signal is calculated. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm and sends the control quantity to the motor driving module, and the motor rotates to drive the wheels to maintain self balance and move in a specified mode.
The advantages and effects:
the invention relates to a method for controlling the safe driving of a limited track tracking error of a rehabilitation training robot with a slowly-changing structure, which has the following advantages: according to the invention, a man-machine system dynamics model with neural network structure slow change estimation is established by splitting physical quantities influencing structure change in a rehabilitation training robot dynamics model; the safety driving tracking controller which adapts to the slow change of the structure of the rehabilitation training robot is designed by taking the limitation of the track tracking error as a driving condition, so that the stability of the system and the limitation of the track tracking error are realized, the tracking precision of the man-machine system is improved, and the safety of a trainer is ensured.
Description of the drawings:
FIG. 1 is a block diagram of the operation of a controller according to the present invention;
FIG. 2 is a graph of a system of the present invention;
FIG. 3 shows a STM32G4 single-chip microcomputer minimum system according to the present invention;
FIG. 4 is a power circuit of the present invention;
FIG. 5 is a circuit of the motor drive and speed measurement module of the present invention;
fig. 6 is a circuit of the general principles of the hardware of the present invention.
The specific embodiment is as follows:
the present invention will be further described with reference to the accompanying drawings, but the scope of the present invention is not limited by the examples.
The method comprises the steps of utilizing a dynamic model of a rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and constructing a dynamic model of the rehabilitation training robot with structural estimation; the method is characterized in that the bounded nature of the track tracking error is used as a driving condition, a safe driving tracking controller which is suitable for the slow change of the structure of the rehabilitation training robot is designed, the stability of the system is realized, the track tracking error is restrained in a designated range, and the collision danger of the robot is avoided;
a method for controlling the safe driving of a limited track tracking error of a rehabilitation training robot with a slowly-changing structure is characterized by comprising the following steps:
1) Utilizing a dynamic model of the rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and establishing a dynamic model of the rehabilitation training robot with structural estimation;
2) The safety driving tracking controller adapting to the slow change of the structure of the rehabilitation training robot is designed by taking the limitation of the track tracking error as a driving condition, so that the stability of the system and the limitation of the track tracking error are realized.
The method comprises the following steps:
step 1) utilizing a dynamic model of a rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and constructing the dynamic model of the rehabilitation training robot with structural estimation, and is characterized in that: the kinetic model of the system is described below
Wherein the method comprises the steps of
X (t) represents the actual motion trail of the rehabilitation training robot, u (t) represents the control input force, M represents the mass of the robot, M represents the mass of the rehabilitation person, I 0 The moment of inertia is indicated and the moment of inertia,is a coefficient matrix. θ represents the angle between the horizontal axis and the connection between the robot center and the first wheel center, i.e., θ=θ 1 As known from the structure of the rehabilitation training robot,θ 3 ＝θ+π，/>l i representing the distance of the center of gravity of the system from the center of each wheel, r 0 Represents the distance from center to center of gravity, phi i Representing the x' axis and the l corresponding to each wheel i Included angles (i=1, 2,3, 4).
Separation coefficient matrix M 0 The physical quantity p, q, r of the structural change is influenced by K (theta) 0 It is denoted as M 0 K(θ)＝M 1 +ΔM 1 Wherein M is 1 Consists of rehabilitation training robot mass, rehabilitation person mass and moment of inertia, and delta M 1 Representing a physical quantity of structural change, an
At the same time, coefficient matrixStructurally varied p, q, r 0 Composition; the coefficient matrix B (θ) contains the variable lambda generated by the structural change i Decompose it into B (θ) =b 1 (θ)+ΔB 1 (θ) wherein
Wherein L is a steady physical quantity and represents the distance from the center of the man-machine system to the center of each wheel; physical quantity affecting structural change in the splitting dynamics model (1) is split, and a dynamics model for describing structural change of the rehabilitation training robot is established as follows
Wherein the method comprises the steps ofPhysical quantity representing structural change of rehabilitation robot, and S (p, q, r) 0 ) The robot tracking system has the characteristics of slow structural change and nonlinearity, and influences the tracking accuracy and the safety of the robot.
Step 2) designing S (p, q, r) based on the rehabilitation training robot dynamics model (2) with structural change 0 ) And further establishes a dynamic model for estimating structural changes of the man-machine system. Let X (t) represent the actual walking track of the rehabilitation training robot, X d (t) represents a training trajectory designated by a doctor, and a trajectory tracking error e is set 1 (t) and velocity tracking error e 2 (t) are respectively
e 1 (t)＝X(t)-X d (t) (3)
Wherein α represents a parameter to be designed, e 1 (t)＝[e 11 (t) e 12 (t) e 13 (t)] T Track following errors in x-axis, y-axis and rotation angle directions, e 2 (t)＝[e 21 (t) e 22 (t) e 23 (t)] T The speed tracking errors in the x-axis, y-axis and rotational angle directions are indicated, respectively. Design S (p, q, r) 0 ) The neural network estimation model of (a) is as follows:
wherein the method comprises the steps ofRepresentation->E= [ e = [ e ] pseudo-inverse matrix of (a) 1 (t) e 2 (t)] T Input vector representing network, +_>Represents an estimated value of the network weight, and Σ (e) = [ Σ ] 1 (e) Σ 2 (e) … Σ n (e)] T And sigma f (e) (f=1, 2, …, n) represents a gaussian function as follows:
wherein beta is j Sum sigma j The center and base width parameters of the f-th node function are represented, respectively. Setting the optimal estimation weight of the network delta * For a given small positive number ε 0 The design estimation error is as follows:
definition of the definitionRepresenting the weight estimation error, there is +.>Thus S (p, q, r) 0 ) The expression form of (a) is as follows:
further, according to the formulas (2) and (8), a kinetic model of the rehabilitation robot with structural change estimation is obtained as follows:
step 3) taking the limitation of the track tracking error as a driving condition, designing a safe driving tracking controller which adapts to the slow change of the structure of the rehabilitation training robot, and realizing the stability of the system and the limitation of the track tracking error, and the method is characterized in that: according to equations (3) (4) (9), a tracking error system is obtained as follows:
the design controller u (t) and the network estimation weights adapting to the structural changes are as follows:
wherein Ω represents a positive definite symmetric matrix of appropriate dimension, λ 2 >0，ρ 1 >0 indicates that the controller adjusts the parameters,representation B 1 (θ) pseudo-inverse matrix. Is controlled by the drive of (11)The preparation device comprises:
the safety driving bar with the limitation of the track tracking error is designed as follows:
when t 0 When the time controller drives for the first time:
t 0 ＝min{t>0；|e 1r (t)|>a 1r },r＝1,2,3 (13)
when t i When the time controller is driven (i is more than or equal to 1):
t i ＝min{t>t i-1 ；||ξ(t)||≥ω(e 1 (t),e 2 (t))and|e 1r (t)|>a 1r } (14)
as can be seen from equations (13) (14), when the track following error exceeds the bounded range a 1r The controller is composed of u (t i ) Drive update to u (t) i+1 ) Thereby realizing a safe motion trail. Wherein a is 1r >0 denotes a trajectory tracking error bounded in x-axis, y-axis and rotation angle directions. And is also provided with
λ 1 >0,λ 2 >And 0 is a controller adjusting parameter.
When t is E [ t ] i ,t i+1 ) The tracking error system is represented as follows:
wherein the method comprises the steps ofSet variable->The form of ζ (t) is as follows:
according to an error system (16) of the time gap driven by the controller twice, a Lyapunov function is established as follows:
deriving equation (17) along error system (16), obtaining:
order theLipschitz constant of L, obtainable:
meanwhile, according to Young's inequality, for a given constant ρ 1 >0, have
The formula (19) and (20) are substituted into the formula (18)
Substituting the controller formula (11) into formula (21) yields:
wherein the method comprises the steps ofThe gap xi (t) is set at the time of driving twice to satisfy the inequality
||ξ(t)||<ω(e 1 (t),e 2 (t)) (23)
And substituting the formula (23) into the formula (22) to obtain
From (24), it can be seen thatSo that the gap tracking error system is asymptotically stable at the moment of the two driving; further, when ζ (t) does not satisfy the equation (23), the controller is configured by u (t) i ) Drive update to u (t) i+1 ) Thereby ensuring the stability of the tracking error system.
Therefore, under the action of the safety driving controllers (11) (13) (14) with slowly-changing adaptive structures, the tracking error system (10) is asymptotically stable, and a bounded track tracking error is realized, so that the safety of a trainer is ensured.
Step 4) provides output PWM signal to motor drive module based on STM32G4 series singlechip, makes rehabilitation training robot can help the patient to follow doctor appointed walking track, its characterized in that: STM32G4 series single-chip microcomputer is used as a main controller, and the input of the main controller is connected with a motor speed measuring module, and the output of the main controller is connected with a motor driving module; the motor driving module is connected with the direct current motor; the power supply system supplies power to the respective electrical devices. The control method of the main controller is to read the feedback signal of the motor encoder and the control command signal X given by the main controller d (t) andan error signal is calculated. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm and sends the control quantity to the motor driving module, and the motor rotates to drive the wheels to maintain self balance and move in a specified mode.
The invention solves the problems of the slow structural change estimation and the safe driving control of the adaptive structure slow change of the rehabilitation training robot. Establishing a rehabilitation walking robot dynamics model with neural network structure change estimation; the method is characterized in that a safe driving tracking controller adapting to slow structural change of the rehabilitation training robot is designed by taking the bounded nature of track tracking errors as driving conditions; the stability of the system and the limitation of track tracking errors are realized, the tracking precision of the man-machine system is effectively improved, and the safety of a trainer is ensured.
The control method solves the problem of tracking precision of the human-machine system from a new view angle adapting to structural change, and simultaneously limits tracking error of the human-machine system and ensures safety of a trainer by designing driving conditions of a controller.

Claims (1)

1. The method for controlling the safe driving of the bounded track tracking error of the slow change of the robot structure is characterized by comprising the following steps:
1) Utilizing a dynamic model of the rehabilitation training robot to split physical quantities influencing structural changes, constructing a neural network estimation model of the structural changes, and establishing a dynamic model of the rehabilitation training robot with structural estimation;
2) The method is characterized in that the limitation of the track tracking error is used as a driving condition, a safe driving tracking controller which is suitable for the slow change of the structure of the rehabilitation training robot is designed, and the stability of the system and the limitation of the track tracking error are realized;
the kinetic model is described below
Wherein the method comprises the steps of
X (t) represents the actual motion trail of the rehabilitation training robot, u (t) represents the control input force, M represents the mass of the robot, M represents the mass of the rehabilitation person, I 0 The moment of inertia is indicated and the moment of inertia,is a coefficient matrix; θ represents the angle between the horizontal axis and the connection between the robot center and the first wheel center, i.e., θ=θ 1 As known from the structure of the rehabilitation training robot,θ 3 ＝θ+π，/>l i representing the distance of the center of gravity of the system from the center of each wheel, r 0 Represents the distance from center to center of gravity, phi i Representing the x' axis and the l corresponding to each wheel i The included angle between (i=1, 2,3, 4);
separation coefficient matrix M 0 The physical quantity p, q, r of the structural change is influenced by K (theta) 0 It is denoted as M 0 K(θ)＝M 1 +ΔM 1 Wherein M is 1 Consists of rehabilitation training robot mass, rehabilitation person mass and moment of inertia, and delta M 1 Representing a physical quantity of structural change, an
At the same time, coefficient matrixStructurally varied p, q, r 0 Composition; the coefficient matrix B (theta) contains the structural variation productsThe raw variable lambda i Decompose it into B (θ) =b 1 (θ)+ΔB 1 (θ) wherein
Wherein L is a steady physical quantity and represents the distance from the center of the man-machine system to the center of each wheel; physical quantity affecting structural change in the splitting dynamics model (1) is split, and a dynamics model for describing structural change of the rehabilitation training robot is established as follows
Wherein the method comprises the steps ofPhysical quantity representing structural change of rehabilitation robot, and S (p, q, r) 0 ) The structure is slowly changed and nonlinear, and the tracking precision and the safety of the robot are affected;
on the basis of obtaining a rehabilitation training robot dynamics model (2) with structural changes, designing S (p, q, r 0 ) The neural network estimation model of the man-machine system is further established, and a dynamics model for estimating structural changes of the man-machine system is further established; let X (t) represent the actual walking track of the rehabilitation training robot, X d (t) represents a training trajectory designated by a doctor, and a trajectory tracking error e is set 1 (t) and velocity tracking error e 2 (t) are respectively
e 1 (t)＝X(t)-X d (t) (3)
Wherein α represents a parameter to be designed, e 1 (t)＝[e 11 (t) e 12 (t) e 13 (t)] T Respectively representing x-axis, y-axis and rotation angleTracking error of the track of the direction, e 2 (t)＝[e 21 (t) e 22 (t) e 23 (t)] T Speed tracking errors in x-axis, y-axis and rotation angle directions are respectively indicated; design S (p, q, r) 0 ) The neural network estimation model of (a) is as follows:
wherein the method comprises the steps ofRepresentation->E= [ e = [ e ] pseudo-inverse matrix of (a) 1 (t) e 2 (t)] T Input vector representing network, +_>Represents an estimated value of the network weight, and Σ (e) = [ Σ ] 1 (e) Σ 2 (e) … Σ n (e)] T And sigma f (e) (f=1, 2, …, n) represents a gaussian function as follows:
wherein beta is j Sum sigma j Respectively representing the center and base width parameters of the f node function; setting the optimal estimation weight of the network delta * For a given small positive number ε 0 The design estimation error is as follows:
definition of the definitionRepresenting the weight estimation error, there is +.>Thus S (p, q, r) 0 ) The expression form of (a) is as follows:
further, according to the formulas (2) and (8), a kinetic model of the rehabilitation robot with structural change estimation is obtained as follows:
according to equations (3) (4) (9), a tracking error system is obtained as follows:
the design controller u (t) and the network estimation weights adapting to the structural changes are as follows:
wherein Ω represents a positive definite symmetric matrix of appropriate dimension, λ 2 ＞0,ρ 1 A value of > 0 indicates that the controller adjusts the parameter,representation B 1 A pseudo-inverse of (θ); the drive controller is obtained from equation (11):
the safe driving conditions for the design track tracking error are as follows:
when t 0 When the time controller drives for the first time:
t 0 ＝min{t＞0；|e 1r (t)|＞a 1r },r＝1,2,3 (13)
when t i When the time controller is driven (i is more than or equal to 1):
t i ＝min{t＞t i-1 ；||ξ(t)||≥ω(e 1 (t),e 2 (t))and|e 1r (t)|＞a 1r } (14)
as can be seen from equations (13) (14), when the track following error exceeds the bounded range a 1r The controller is composed of u (t i ) Drive update to u (t) i+1 ) Thereby realizing safe motion trail; wherein e 1r > 0 represents a trajectory tracking error bounded in x-axis, y-axis and rotation angle directions; and is also provided with
λ 1 ＞0,λ 2 > 0 is the controller tuning parameter;
when t is E [ t ] i ,t i+1 ) The tracking error system is represented as follows:
wherein the method comprises the steps ofSet variable->The form of ζ (t) is as follows:
according to an error system (16) of the time gap driven by the controller twice, a Lyapunov function is established as follows:
deriving equation (17) along error system (16), obtaining:
order theLipschitz constant of L > 0, can be obtained:
meanwhile, according to Young's inequality, for a given constant ρ 1 > 0, have
The formula (19) and (20) are substituted into the formula (18)
Substituting the controller formula (11) into formula (21) yields:
wherein the method comprises the steps ofThe gap xi (t) is set at the time of driving twice to satisfy the inequality
||ξ(t)||＜ω(e 1 (t),e 2 (t)) (23)
And substituting the formula (23) into the formula (22) to obtain
From (24), it can be seen thatSo that the gap tracking error system is asymptotically stable at the moment of the two driving; further, when ζ (t) does not satisfy the equation (23), the controller is configured by u (t) i ) Drive update to u (t) i+1 ) Thereby ensuring the stability of the tracking error system;
therefore, under the action of the safety driving controllers (11) (13) (14) with slowly-changing adaptive structures, the tracking error system (10) is asymptotically stable, and a bounded track tracking error is realized, so that the safety of a trainer is ensured.
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