CN114851171B - Gait track tracking control method of lower limb exoskeleton rehabilitation robot - Google Patents
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- 210000003141 lower extremity Anatomy 0.000 title claims abstract description 59
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- 230000005021 gait Effects 0.000 title claims abstract description 32
- 238000013461 design Methods 0.000 claims abstract description 8
- 210000004394 hip joint Anatomy 0.000 claims description 26
- 239000011159 matrix material Substances 0.000 claims description 24
- 210000000629 knee joint Anatomy 0.000 claims description 22
- 230000033001 locomotion Effects 0.000 claims description 19
- 230000006870 function Effects 0.000 claims description 13
- 210000002414 leg Anatomy 0.000 claims description 12
- 210000000689 upper leg Anatomy 0.000 claims description 9
- 238000004088 simulation Methods 0.000 claims description 7
- 230000000694 effects Effects 0.000 claims description 6
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- 210000000544 articulatio talocruralis Anatomy 0.000 claims description 5
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- 230000001133 acceleration Effects 0.000 claims description 4
- 238000005094 computer simulation Methods 0.000 claims description 4
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- 230000005484 gravity Effects 0.000 claims description 2
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- 238000006467 substitution reaction Methods 0.000 claims 1
- 238000010168 coupling process Methods 0.000 abstract 1
- 238000005859 coupling reaction Methods 0.000 abstract 1
- 238000010586 diagram Methods 0.000 description 4
- 206010019468 Hemiplegia Diseases 0.000 description 2
- 206010033892 Paraplegia Diseases 0.000 description 2
- 206010008190 Cerebrovascular accident Diseases 0.000 description 1
- 208000012661 Dyskinesia Diseases 0.000 description 1
- 206010017577 Gait disturbance Diseases 0.000 description 1
- 208000006011 Stroke Diseases 0.000 description 1
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/0006—Exoskeletons, i.e. resembling a human figure
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
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- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The gait track tracking control method of the lower limb exoskeleton rehabilitation robot comprises the following steps: 1) Aiming at an actual lower limb exoskeleton rehabilitation robot, establishing a lower limb exoskeleton rehabilitation robot dynamics model based on a Lagrange method, and discretizing the dynamics model according to a Lagrange system discretization criterion; 2) Based on the discrete dynamics model, designing a system discrete sliding mode surface and a discrete equivalent control law according to the expected control performance; 3) Designing a discrete self-adaptive sliding mode control law according to the discrete sliding mode surface and the discrete equivalent control law obtained in the step 2; 4) And constructing a discrete system controller based on the control law designed in the step 3. The invention provides a novel discrete sliding mode control law design method for guaranteeing control performance aiming at the gait track tracking control problem of a multi-input multi-output nonlinear strong-coupling lower limb exoskeleton rehabilitation robot, and the method has higher track tracking control precision and stronger robust performance.
Description
Technical Field
The invention belongs to the technical field of robot control, and particularly relates to a gait track tracking control method of a lower limb exoskeleton rehabilitation robot based on a novel discrete sliding mode control law.
Background
In recent years, in the progress of economic and rapid development and aging of the population, adults suffering from lower limb movement dysfunction such as lower limb hemiplegia and paraplegia due to diseases such as cerebral apoplexy and spinal cord injury have been increasing year by year. For patients with lower limb dyskinesia such as hemiplegia, paraplegia and the like, the subsequent rehabilitation effect is greatly improved by early intervention rehabilitation treatment. The lower limb exoskeleton rehabilitation robot is novel rehabilitation equipment capable of quantifying, lasting and standardizing rehabilitation training, can provide effective lower limb motor function assistance, promotes the remodeling of damaged nerve functions of patients, quantitatively evaluates the rehabilitation process and feeds back the rehabilitation progress.
The lower limb exoskeleton rehabilitation robot is a bionic robot worn on the lower limb of a human body, and the mechanical structure of the robot mainly comprises a rigid connecting rod, a servo motor and other components, wherein hip joints and knee joints of the lower limb exoskeleton are used as active joints and driven by the servo motor, and ankle joints are passive joints and are composed of spring components. Therefore, when the robot assists the lower limbs of the human body to carry out fixed gait track tracking training, the control system drives the motors at the hip joint and the knee joint to cooperatively move.
Aiming at the problem of motion control of a lower limb exoskeleton rehabilitation robot, a control method is generally required to be designed on the basis of building a lower limb exoskeleton robot dynamics model, so that motor input at joints is controlled to control the overall motion of the lower limb. However, in actual motion control, the control system is susceptible to model modeling errors and external disturbances, resulting in reduced gait trajectory tracking accuracy and abnormal gait during training. Aiming at the nonlinear system, the sliding mode variable structure control method has the advantages of simplicity in implementation, quick response, invariance to system parameter perturbation and interference and the like, so that the sliding mode variable structure control method is widely applied to robot control. However, the sliding mode variable structure control has the following problems in application: 1) In the control process, the invariance to interference is actually at the cost of high-frequency buffeting of a control quantity, however, the high-frequency buffeting easily excites the unmodeled characteristic of the system, and the dynamic quality of the system is adversely affected; 2) The existing engineering control is almost realized on the basis of a computer, and the computer controls the system under the discrete condition, but under the discrete condition, the system cannot generate an ideal sliding mode, so that the robustness of the control is reduced. Thus overcoming these problems while maintaining advantages in slip-form variable structure control applications.
Disclosure of Invention
For the problems, the invention designs a gait track tracking control method of a lower limb exoskeleton rehabilitation robot based on a discrete sliding mode control law.
In a discrete system realized based on a computer, because the accuracy of a dynamic model of the Euler method direct discretization is low, the lower limb exoskeleton rehabilitation robot is more susceptible to modeling errors and external interference under discrete control, so that gait track tracking control performance is reduced; 2) The use of the general discrete sliding mode control is easy to cause the phenomenon that the control input quantity is subjected to high-frequency buffeting, and the robustness of the controller is reduced.
In order to solve the technical problems, the gait track tracking control method of the lower limb exoskeleton rehabilitation robot provided by the invention comprises the following steps:
1. establishing a lower limb exoskeleton rehabilitation robot dynamics model based on a Lagrange method, and discretizing the dynamics model according to a Lagrange system discretization criterion;
2. designing a sliding die surface based on a discretized dynamics model of the lower limb exoskeleton rehabilitation robot;
3. designing an equivalent control law based on a discretization dynamics model and a sliding mode surface of the lower limb exoskeleton rehabilitation robot;
4. discrete self-adaptive system state arrival control law is designed based on a lower limb exoskeleton rehabilitation robot discretization dynamics model and a designed equivalent control law.
The invention has the beneficial effects that: 1) According to the invention, a new discretization dynamics model of the lower limb exoskeleton rehabilitation robot is established according to the discretization criterion of the Lagrange system, so that the accuracy of the discretization system is improved; 2) The novel self-adaptive discretization sliding mode control law is provided, and the robustness of a discrete control system is enhanced.
Drawings
FIG. 1 is a diagram of a dynamic model of a lower limb exoskeleton rehabilitation robot according to the present invention;
FIG. 2 is a diagram of the combined simulation effect of MATLAB2016a software and Opensim software of the present invention;
fig. 3 is a hip joint θ of the lower limb exoskeleton rehabilitation robot of the present invention 1 Tracking a motion trail and a result graph;
fig. 4 is a knee joint θ of the lower limb exoskeleton rehabilitation robot of the present invention 2 Tracking a motion trail and a result graph;
FIG. 5 is a diagram of a gait tracking error e of a lower limb exoskeleton rehabilitation robot based on a novel discrete sliding mode control law 1 and e2 Trajectory graph of (2);
FIG. 6 is a control input τ for gait track tracking control of a lower extremity exoskeleton rehabilitation robot based on a novel discrete sliding mode control law of the present invention 1 and τ2 Trajectory graph of (2);
fig. 7 is a flow chart of the method of the present invention.
Detailed Description
The technical scheme of the invention will be further described with reference to the accompanying drawings.
The invention discloses a gait track tracking control method of a lower limb exoskeleton rehabilitation robot based on a discrete sliding mode control law, which comprises the following specific steps:
1. and establishing a dynamic model of the lower limb exoskeleton rehabilitation robot based on the Lagrangian method, and discretizing the dynamic model according to a Lagrangian system discretization criterion. The method specifically comprises the following steps:
1.1 For simplifying the establishment of the inverse dynamic model and the design of the controller, the motion of the lower limb of the human body in the three-dimensional space can be simplified into multi-rigid-body plane motion on the sagittal plane, and the mechanical legs are symmetrical on the sagittal plane in the rehabilitation motion process, so that the exoskeleton mechanical legs can be simplified into a single-leg model for analysis. In rehabilitation training, the motion of the ankle joint has little influence on the motion of the whole human body, so that only the hip joint and the knee joint are considered as active joints and the ankle joint is considered as passive joints in the exoskeleton robot dynamic model. A two-link model of the mechanical leg dynamics model shown in fig. 1 is established, and a coordinate system shown in the figure is established by taking the rotation point of the hip joint as an origin. Let the mass of thigh rod in lower limb exoskeleton mechanical leg be m 1 Length l 1 The distance from the center of mass of the thigh to the hip joint is l c1 The weight of the shank is m 2 Length l 2 The distance from the center of mass of the lower leg to the knee joint is l c2 ，θ 1 Angle θ for exoskeleton hip joint to deviate from x-axis 2 For the angle of the knee joint offset from the hip joint,for exoskeleton joint angular velocity, ++>Is the angular acceleration of the exoskeleton joint.
The centroid coordinates of the thigh and shank in the exoskeleton system are set to (x) according to the coordinate system set up in fig. 1 c1 ,y c1 )，(x c2 ,y c2 ) The expression for deriving centroid coordinates is:
the total kinetic energy of the system is:
the total potential energy of the system is as follows:
the Lagrangian system function of the lower limb exoskeleton robot system can be obtained as follows:
the lagrangian kinetic equation for the exoskeleton system is:
wherein τ1 Representing the moment input quantity at the hip joint, τ 2 Representing the moment input at the knee joint.
The established system dynamics model is arranged into a matrix form as follows:
in the dynamic model, θ,Vectors representing joint position, joint angular velocity and joint angular acceleration of the hip joint and the knee joint, respectively, τ represents a driving moment vector of the joint, M (θ) is a symmetrical positive inertia matrix,/->For the Golgi force and centrifugal force coefficient matrix, G (θ) is a gravity term matrix, and the specific form of each parameter is as follows:
1.2 The continuous state dynamics model of the exoskeleton system is obtained by solving a dynamics equation based on a Lagrangian method, if the Euler method is directly used for approximate discretization, the model precision is not high, the discretization treatment is carried out on the lower limb exoskeleton dynamics model according to the discretization principle of the Lagrangian system, and the adopted discretization criterion is as follows:
where T represents the sampling period and k represents the sampling instant. After discretization, the following discretization kinetic equation can be obtained:
the parameters in the kinetic equation are expressed as follows:
among the above parameters, θ 1,k and θ2,k The rotation angle values of the hip joint and the knee joint at the time k are respectively shown, and />Respectively representing the rotation angular velocity values of the hip joint and the knee joint at the moment k, τ 1,k and τ2,k Respectively represent the hip joint at the moment kRotation moment value of knee joint, and parameter theta k+1 Can be approximately expressed as +.>After discretization, the state space expression of the dynamics model can be further obtained, so that +.>Representing system state variables, U k ＝[τ 1,k τ 2,k ] T Expressed as system control input variables, the state space expression is as follows:
X k+1 ＝F(X k )X k +B k U k +d (19)
wherein ,F(Xk ) Representing a state transition matrix, B k Representing a control matrix, d k ∈R 4×1 Representing the sum of the systematic modeling error part and the external interference, I 2×2 Expressed as a 2 x 2 identity matrix, 0 2×2 Represented as a zero matrix of 2 x 2.
2. Discrete sliding mode surface design based on lower limb exoskeleton rehabilitation robot discrete dynamics model is as follows:
defining an error variable:
wherein E represents gait track tracking error and X d (k) For gait reference trajectories, X (k) is the true gait trajectory. The selected sliding mode surface function is as follows:
wherein ,gain matrix for sliding mode surface function, c 1 and c2 Is a constant greater than zero.
3. The equivalent control law based on the discretization dynamics model and the sliding mode surface design of the lower limb exoskeleton rehabilitation robot is as follows:
modeling errors in the system model and external disturbances can be expressed as d= [0 0 0 0 ]] T And the ideal quasi-sliding mode band of the system satisfies s (k+1) =s (k) =0, the following is obtained according to the sliding mode surface function:
s(k+1)＝C T [X d (k+1)-F(X k )X k -B k U k ]＝0 (24)
the equivalent control inputs are:
u 1 (k)＝(C T B k ) -1 [C T X d (k+1)-C T F(X k )X k ] (25)
4. the novel discrete self-adaptive system state arrival control law based on the lower limb exoskeleton rehabilitation robot discrete dynamics model and the equivalent control law design is as follows:
when d is not equal to 0 0 0 0] T In order to eliminate the influence caused by system modeling errors and external disturbance, the novel discrete self-adaptive approach law of the invention can be used as follows:
s(k+1)＝Γ(k)Qs(k)-TΓ(k)Φ(k)|s(k)| α sgn[s(k)] (26)
wherein the adaptive parameter matrix and Parameter matrixAnd phi is 1 (k)＝δ|s 1 (k)|，Φ 2 (k)＝δ|s 2 (k) I (I); parameter matrixAnd delta is more than 0,0 is less than 1-q 1 T＜1，0＜1-q 2 T is less than 1,0 is less than alpha is less than 1. The system state arrival control law is obtained as:
u 2 (k)＝-(C T B k ) -1 [Γ(k)Qs(k)-TΓ(k)Φ(k)|s(k)| α sgn[s(k)]] (27)
the final control input is:
in order to explain the scheme and the advantages of the invention, the invention utilizes MATLAB2016a software and Opensim software to carry out joint simulation, and verifies the effect of the gait track tracking control method of the lower limb exoskeleton rehabilitation robot based on the novel discrete sliding mode control law.
Specific given parameters of the lower limb exoskeleton rehabilitation robot are as follows:
the reference gait trajectory in the simulation is a gait trajectory fitted according to a normal gait, wherein the movement trajectory functions of the hip joint and the knee joint are as follows:
the sliding mode surface function and the controller parameters are set as follows: c 1 ＝15，c 2 ＝25，m＝2，ε＝500，α＝0.5，δ＝160，q 1 ＝0.6，q 2 =0.6. In order to verify the robust performance of the discrete sliding mode controller designed by the invention, the system modeling error and external disturbance are set as d= [ 0.5 sin (t) -5sin (t)] T The discrete system sampling period is t=1 ms.
The combined simulation effect diagram is shown in fig. 2, the simulation results are shown in fig. 3, fig. 4 and fig. 5, and the lower limb exoskeleton rehabilitation robot can stably track the reference gait track under the condition that disturbance exists, the track error quickly goes to zero, and the actual motion track is smoother and has no jitter. As shown in fig. 6, under discrete control, the control input is relatively smooth without significant high frequency buffeting. The above results show that the discrete sliding mode control method designed by the invention can realize a better control effect.
The embodiments described in this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, but the scope of the present invention and the equivalents thereof as would occur to one skilled in the art based on the inventive concept.
Claims (5)
1. The gait track tracking control method of the lower limb exoskeleton rehabilitation robot comprises the following steps:
s1, establishing a discretization dynamics model of a lower limb exoskeleton rehabilitation robot based on a Lagrangian method, and discretizing the dynamics model according to a Lagrangian system discretization criterion;
s2, designing a sliding die surface based on a discretization dynamics model of the lower limb exoskeleton rehabilitation robot;
s3, designing an equivalent control law based on a discretization dynamics model and a sliding mode surface of the lower limb exoskeleton rehabilitation robot; the method specifically comprises the following steps:
the modeling error and external interference in the system model are expressed as d= [0 0 0 0 ]] T And the ideal quasi-sliding mode band of the system satisfies s (k+1) =s (k) =0, the following is obtained according to the sliding mode surface function:
s(k+1)＝C T [X d (k+1)-F(X k )X k -B k U k ]＝0 (24)
the equivalent control inputs are:
u 1 (k)＝(C T B k ) -1 [C T X d (k+1)-C T F(X k )X k ] (25)
s4, designing a discrete self-adaptive system state arrival control law based on a lower limb exoskeleton rehabilitation robot discretization dynamics model and a designed equivalent control law; the method specifically comprises the following steps:
when d is not equal to 0 0 0 0] T In order to eliminate the influence of system modeling errors and external disturbances, the discrete adaptive approach law is used as follows:
s(k+1)＝Γ(k)Qs(k)-TΓ(k)Φ(k)|s(k)| α sgn[s(k)] (26)
wherein the adaptive parameter matrix and Parameter matrixAnd phi is 1 (k)＝δ|s 1 (k)|，Φ 2 (k)＝δ|s 2 (k) I (I); parameter matrixAnd delta is more than 0,0 is less than 1-q 1 T＜1，0＜1-q 2 T is less than 1,0 is less than alpha is less than 1; the system state arrival control law is obtained as:
u 2 (k)＝-(C T B k ) -1 [Γ(k)Qs(k)-TΓ(k)Φ(k)|s(k)| α sgn[s(k)]] (27)
the final control input is:
2. the method for tracking and controlling gait track of lower limb exoskeleton rehabilitation robot according to claim 1, wherein the method comprises the following steps: the step S1 specifically comprises the following steps:
1.1 For simplifying the establishment of inverse dynamic models and the design of controllers, the motion of human lower limbs in a three-dimensional space is simplified into multi-rigid-body plane motion on a sagittal plane, and the mechanical legs are symmetrical on the sagittal plane in the rehabilitation motion process, so that the exoskeleton mechanical legs are simplified into a single-leg model for analysis; in rehabilitation training, the motion of the ankle joint has little influence on the motion of the whole human body, so that only the hip joint and the knee joint are considered as active joints and the ankle joint is considered as a passive joint in an exoskeleton robot dynamic model; establishing a two-link model of the mechanical leg dynamics model, and establishing a coordinate system by taking a rotation point of a hip joint as an origin; let the mass of thigh rod in lower limb exoskeleton mechanical leg be m 1 Length l 1 The distance from the center of mass of the thigh to the hip joint is l c1 The weight of the shank is m 2 Length l 2 The distance from the center of mass of the lower leg to the knee joint is l c2 ，θ 1 Angle θ for exoskeleton hip joint to deviate from x-axis 2 For the angle of the knee joint offset from the hip joint,for exoskeleton joint angular velocity, ++>Angular acceleration of the exoskeleton joint;
the center of mass coordinates of the thigh and shank in the exoskeleton system were set to (x c1 ,y c1 )，(x c2 ,y c2 ) The expression for deriving centroid coordinates is:
the total kinetic energy of the system is:
the total potential energy of the system is as follows:
the Lagrangian system function of the lower limb exoskeleton robot system is obtained as follows:
the lagrangian kinetic equation for the exoskeleton system is:
wherein τ1 Representing the moment input quantity at the hip joint, τ 2 Representing moment input quantity at knee joint; the established system dynamics model is arranged into a matrix form as follows:
in the dynamic model, θ,Vectors representing joint position, joint angular velocity and joint angular acceleration of the hip joint and the knee joint, respectively, τ represents a driving moment vector of the joint, M (θ) is a symmetrical positive inertia matrix,/->For the Golgi force and centrifugal force coefficient matrix, G (θ) is a gravity term matrix, and the specific form of each parameter is as follows:
1.2 The continuous state dynamics model of the exoskeleton system is obtained by solving a dynamics equation based on a Lagrange method, discretizing the lower limb exoskeleton dynamics model according to a discrete substitution principle of the Lagrange system, wherein the discretization criterion is as follows:
wherein T represents a sampling period, and k represents a sampling time; after discretization, the following discretization kinetic equation can be obtained:
the parameters in the kinetic equation are expressed as follows:
among the above parameters, θ 1,k and θ2,k The rotation angle values of the hip joint and the knee joint at the time k are respectively shown, and />Respectively representing the rotation angular velocity values of the hip joint and the knee joint at the moment k, τ 1,k and τ2,k Respectively represent the rotation moment values of the hip joint and the knee joint at the moment k, and the parameter theta k+1 Can be approximately expressed as +.>After discretization, the state space expression of the dynamics model can be further obtained, so that +.>Representing system state variables, U k ＝[τ 1,k τ 2,k ] T Expressed as system control input variables, the state space expression is as follows:
X k+1 ＝F(X k )X k +B k U k +d (19)
wherein ,F(Xk ) Representing a state transition matrix, B k Representing a control matrix, d k ∈R 4×1 Representing the sum of the systematic modeling error part and the external interference, I 2×2 Expressed as a 2 x 2 identity matrix, 0 2×2 Represented as a zero matrix of 2 x 2.
3. The method for tracking and controlling gait track of lower limb exoskeleton rehabilitation robot according to claim 1, wherein the method comprises the following steps: the step S2 specifically comprises the following steps:
defining an error variable:
wherein E represents gait track tracking error and X d (k) X (k) is the gait real track; the selected sliding mode surface function is as follows:
wherein ,gain matrix for sliding mode surface function, c 1 and c2 Is a constant greater than zero.
4. The method for tracking and controlling gait track of lower limb exoskeleton rehabilitation robot according to claim 1, wherein the method comprises the following steps: step S4, performing joint simulation by utilizing MATLAB2016a software and Opensim software, and verifying the effect of a gait track tracking control method of the lower limb exoskeleton rehabilitation robot;
the reference gait trajectory in the simulation is a gait trajectory fitted according to a normal gait, wherein the movement trajectory functions of the hip joint and the knee joint are as follows:
the sliding mode surface function and the controller parameters are set as follows: c 1 ＝15，c 2 ＝25，m＝2，ε＝500，α＝0.5，δ＝160，q 1 ＝0.6，q 2 =0.6; to verify the robust performance of the design discrete sliding mode controller, the system modeling error and external disturbance were set to d= [ 0.5 sin (t) -5sin (t)] T The discrete system sampling period is t=1 ms.
5. The gait track tracking control method of the lower limb exoskeleton rehabilitation robot according to claim 4, wherein the method comprises the following steps: specific given parameters of the lower limb exoskeleton rehabilitation robot are as follows:
m 1 the weight of thigh rods in the mechanical legs is 9.0kg; m is m 2 The weight of the shank rod in the mechanical leg is 5.0kg; l (L) 1 The length of the thigh rod in the mechanical leg is 0.45m; l (L) 2 The length of the shank rod in the mechanical leg is 0.4m; l (L) c1 The distance from the center of mass of the thigh to the hip joint is 0.25m; l (L) c2 The distance from the center of mass of the lower leg to the knee joint is 0.25m.
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