CN115805594B - Composite optimization method for track and configuration of reconfigurable rope-driven lower limb rehabilitation robot - Google Patents

Composite optimization method for track and configuration of reconfigurable rope-driven lower limb rehabilitation robot Download PDF

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CN115805594B
CN115805594B CN202310069010.XA CN202310069010A CN115805594B CN 115805594 B CN115805594 B CN 115805594B CN 202310069010 A CN202310069010 A CN 202310069010A CN 115805594 B CN115805594 B CN 115805594B
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张彬
周煜
尚伟伟
丛爽
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University of Science and Technology of China USTC
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Abstract

The invention provides a composite optimization method for tracks and configurations of a reconfigurable rope-driven lower limb rehabilitation robot, and belongs to the field of rehabilitation robot control. The method comprises the following steps: step 1, establishing a muscle acting force model according to the characteristics of the lower limbs of the human body and the skeletal muscle acting relationship of the lower limbs in the flexion and extension movements; step 2, according to the model in the step 1, establishing an overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot; step 3, setting muscle normalization acting as an optimization target based on the muscle acting force model in the step 1, fitting a training track by adopting a Fourier series, and carrying out optimization solving on the training track parameters; and 4, selecting the energy consumption of the reconfigurable rope-driven lower limb rehabilitation robot as an optimization target according to the overall dynamics model and the optimal training track parameters, and performing optimization solution on traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot. The robot training track and traction configuration parameters which are most suitable for rehabilitation patients can be given according to different rehabilitation requirements.

Description

Composite optimization method for track and configuration of reconfigurable rope-driven lower limb rehabilitation robot
Technical Field
The invention relates to the field of rehabilitation robots, in particular to a composite optimization method for a training track and a traction configuration of a reconfigurable rope-driven lower limb rehabilitation robot.
Background
Different from the traditional exoskeleton type rehabilitation robot, the rope drives the lower limb rehabilitation robot to drag the lower limb of the patient to be rehabilitated to move by adjusting the length of each rope, so that the patient is helped to finish rehabilitation training. Thanks to the flexibility of the rope, the rope-driven lower limb rehabilitation robot can avoid damage to limbs caused by collision in assisting a patient to perform rehabilitation training, and is safer compared with the traditional exoskeleton-type rehabilitation robot. However, due to the complex scenes faced by rehabilitation training, the aiming crowd is various, the common rope-driven lower limb rehabilitation robot is difficult to meet the complex requirements of rehabilitation training, and the universality is poor.
The reconfigurable rope drives the lower limb rehabilitation robot to realize the self structural change by introducing the sliding blocks and the guide rail mechanisms so as to adapt to various rehabilitation training requirements. The robot training trajectory and traction configuration need to be customized for different scenarios and patients so that the patients get the best training results. However, the general optimization method only optimizes the traction configuration of the robot from a mechanical angle or only optimizes the training track from a rehabilitation angle, but as the traction configuration and the training track are not considered jointly by the optimization, the problem that the motion track and the configuration parameters of the robot which are most suitable for a rehabilitation patient cannot be given according to different rehabilitation requirements exists.
Therefore, how to perform composite optimization on the training track and the traction configuration to meet the rehabilitation requirement is a problem that needs to be solved at present.
In view of this, the present invention has been made.
Disclosure of Invention
Based on the problems existing in the prior art, the invention aims to provide a composite optimization method for the track and the configuration of a reconfigurable rope-driven lower limb rehabilitation robot, which can provide robot training track parameters and traction configuration parameters which are most suitable for rehabilitation patients according to different rehabilitation requirements.
The embodiment of the invention provides a composite optimization method for tracks and configurations of a reconfigurable rope-driven lower limb rehabilitation robot, which comprises the following steps of:
step 1, establishing a muscle acting force model according to the characteristics of the lower limbs of the human body and the skeletal muscle acting relationship of the lower limbs;
step 2, establishing an overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot according to the skeletal muscle action relation and the muscle acting force model of the lower limb;
step 3, setting muscle normalization acting as an optimization target according to the muscle acting force model established in the step 1, fitting a training track of the reconfigurable rope-driven lower limb rehabilitation robot by adopting a Fourier series, and carrying out optimization solving on the training track parameters to obtain optimal training track parameters;
and 4, setting the energy consumption of the reconfigurable rope-driven lower limb rehabilitation robot as an optimization target according to the overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot established in the step 2 and the optimal training track parameters obtained in the step 3, and carrying out optimization solution on the traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot to obtain the optimal traction configuration parameters.
Compared with the prior art, the composite optimization method for the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot has the beneficial effects that:
the method is characterized in that the reconfigurable rope-driven lower limb rehabilitation robot is combined with rehabilitation training requirements, an optimization target is set from the angles of rehabilitation training and robots, dynamic modeling is carried out on the reconfigurable rope-driven lower limb rehabilitation robot and the whole lower limb based on a skeletal muscle schematic diagram of the lower limb of a human body, muscle acting force modeling and dynamic modeling, and the problems of complex, fuzzy and abstract rehabilitation training optimization are detailed and concrete, so that the reconfigurable rope-driven lower limb rehabilitation robot can play a role in actual rehabilitation training. Aiming at different rehabilitation scenes and different rehabilitation patients, only part of variables are needed to be modified to provide required training track parameters and traction configuration parameters, so that the rehabilitation device has good universality, and the problems caused by different requirements in actual rehabilitation training are greatly relieved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a composite optimization method of a track and a configuration of a reconfigurable rope-driven lower limb rehabilitation robot provided by an embodiment of the invention.
Fig. 2 is a schematic diagram of skeletal muscle affecting lower limb flexion and extension movements provided by an embodiment of the present invention.
Fig. 3 is a schematic diagram of a muscle force model provided by an embodiment of the present invention.
Fig. 4 is a schematic diagram of rehabilitation training performed by the reconfigurable rope-driven lower limb rehabilitation robot according to the embodiment of the invention.
Fig. 5 is a specific flowchart of a composite optimization method according to an embodiment of the present invention.
The muscle group names corresponding to the labels in fig. 1 and 2 are: 1-ilium psoas; 2-femoral muscle group including lateral, medial and intermediate muscles of the femur; 3-rectus; 4-a posterior thigh muscle group including the semimembranous muscle, biceps femoris long head and semitendinosus; 5-gastrocnemius, popliteal and biceps femoris brachium;
each labeled in fig. 4: 41-a first motor; 42-winding drum; 43-a second motor; 44-screw rod; 45-guide rails; 46-a slider; 47-pulleys; 48-rope connection means.
Detailed Description
The technical scheme in the embodiment of the invention is clearly and completely described below in combination with the specific content of the invention; it will be apparent that the described embodiments are only some embodiments of the invention, but not all embodiments, which do not constitute limitations of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
The terms that may be used herein will first be described as follows:
the term "and/or" is intended to mean that either or both may be implemented, e.g., X and/or Y are intended to include both the cases of "X" or "Y" and the cases of "X and Y".
The terms "comprises," "comprising," "includes," "including," "has," "having" or other similar referents are to be construed to cover a non-exclusive inclusion. For example: including a particular feature (e.g., a starting material, component, ingredient, carrier, formulation, material, dimension, part, means, mechanism, apparatus, step, procedure, method, reaction condition, processing condition, parameter, algorithm, signal, data, product or article of manufacture, etc.), should be construed as including not only a particular feature but also other features known in the art that are not explicitly recited.
The term "consisting of … …" is meant to exclude any technical feature element not explicitly listed. If such term is used in a claim, the term will cause the claim to be closed, such that it does not include technical features other than those specifically listed, except for conventional impurities associated therewith. If the term is intended to appear in only a clause of a claim, it is intended to limit only the elements explicitly recited in that clause, and the elements recited in other clauses are not excluded from the overall claim.
Unless specifically stated or limited otherwise, the terms "mounted," "connected," "secured," and the like should be construed broadly to include, for example: the connecting device can be fixedly connected, detachably connected or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the terms herein above will be understood by those of ordinary skill in the art as the case may be.
The terms "center," "longitudinal," "transverse," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," etc. refer to an orientation or positional relationship based on that shown in the drawings, merely for ease of description and to simplify the description, and do not explicitly or implicitly indicate that the apparatus or element in question must have a particular orientation, be constructed and operated in a particular orientation, and therefore should not be construed as limiting the present disclosure.
As shown in fig. 1, the embodiment of the invention provides a composite optimization method for a track and a configuration of a reconfigurable rope-driven lower limb rehabilitation robot, which comprises the following steps:
step 1, establishing a muscle acting force model according to the characteristics of the lower limbs of the human body and the skeletal muscle acting relationship of the lower limbs;
step 2, establishing an overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot according to the skeletal muscle action relation and the muscle acting force model of the lower limb;
step 3, setting muscle normalization acting as an optimization target according to the muscle acting force model established in the step 1, fitting a training track of the reconfigurable rope-driven lower limb rehabilitation robot by adopting a Fourier series, and carrying out optimization solving on the training track parameters to obtain optimal training track parameters;
and 4, setting the energy consumption of the reconfigurable rope-driven lower limb rehabilitation robot as an optimization target according to the overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot established in the step 2 and the optimal training track parameters obtained in the step 3, and carrying out optimization solution on the traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot to obtain the optimal traction configuration parameters.
Referring to fig. 4, in the above method, the reconfigurable rope driven lower limb rehabilitation robot is a robot which winds and unwinds each rope wound on each reel by m reels 42 driven by m first motors 41 and pulls limb movement by changing the length of the m ropes;
the traction configuration of the reconfigurable rope-driven lower limb rehabilitation robot comprises the following steps: the position of a rope leading-out point and the position of a rope connecting point are changed by driving a sliding block 46 to freely move along a guide rail 45 through m lead screws 44 driven by m second motors 43, and the rope is wound on a pulley 47 of the sliding block 46 and is connected with the sliding block 46; the location of the rope attachment point is changed by manually changing the location of the rope attachment means 48 at the leg attachment point. Preferably, the rope connection means 48 employs rope fastening straps.
According to the related study, the flexion and extension movements of the leg are mainly affected by the five muscle groups as shown in fig. 2, which can be abstracted into two parts affecting the hip joint movement and affecting the knee joint movement according to the joints of the corresponding actions, and the leg can thus be regarded as a two-bar linkage with two virtual muscles. Based on this, in step 1 of the above method, a muscle effort model is built according to the skeletal muscle action relationship of the lower limb and the human lower limb in the following manner, including:
considering the legs as two links with two virtual muscles according to the acting joints of the muscles affecting the leg flexion and extension movements, wherein one virtual muscle affects the hip joint movements and the other virtual muscle affects the knee joint movements; the device comprises an active controllable contraction unit CE, a passive series elastic unit SE and a passive parallel elastic damping unit PE; the active controllable contraction unit CE is controlled by the nerve body fluid regulating system to actively generate acting force; the passive series elastic unit SE and the passive parallel elastic damping unit PE are influenced by the length of muscle fiber and the change speed to passively generate acting force; in rehabilitation training, the reconfigurable rope drives the lower limb rehabilitation robot to pull the lower limb to make the lower limb passively follow the movement, and ignoring the active controllable contraction unit CE, the initial muscle acting force meets the following conditions:
f m ＝f SE +f PE (1)
in the above formula (1), f m Representing the force of the muscle; f (f) SE Representing the force of the passive series elastic element SE; f (f) PE Representing the acting force of the passive parallel elastic damping units PE; f (f) SE And f PE The following respectively satisfy:
Figure GDA0004159868020000051
in the above formula (2), deltal m Representing the amount of change in length of the muscle relative to the original length of the muscle during exercise;
Figure GDA0004159868020000052
indicating the rate of change of muscle length; a, a SE 、b SE 、a PE 、b PE Respectively representing physiological parameters corresponding to the passive series elastic element SE and the passive parallel elastic damping element PE, wherein the parameters are obtained from physiological research, a SE Take a value of 0.158, b SE The value is 232.6, a PE Take the value of 64.7, b PE The value is 23.95; c represents the damping coefficient of the passive parallel elastic damping unit PE, and the index part
Figure GDA0004159868020000053
And->
Figure GDA0004159868020000054
The first-order taylor expansion is performed at the initial state of the muscle to obtain:
Figure GDA0004159868020000055
wherein Deltal m0 When the variable quantity of the length of the muscle relative to the original length of the muscle in the initial state of the muscle is represented and the higher order infinitely small is ignored, the formula (2) can be approximated as:
Figure GDA0004159868020000056
in the above formula (4), k SE And k PE Respectively represent the elastic coefficients of the approximate rear SE part and the PE part, f SE 0 And f PE 0 Representing the forces of the SE and PE elements, respectively, in the initial state of the muscle, satisfying the following conditions:
Figure GDA0004159868020000061
substituting the formulas (4) - (5) into the formula (6) for simplification to obtain a muscle acting force model as shown in the formula (6):
Figure GDA0004159868020000062
in the above formula (6), k=k SE +k PE An elastic coefficient representing the whole muscle; f (f) m0 ＝f SE 0 +f PE 0 Indicating the force at the initial state of the muscle.
In step 2 of the above method, as shown in fig. 4, according to the skeletal muscle action relationship and muscle acting force model of the lower limb, an overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot is established in the following manner, including:
by establishing the global coordinate G system, ignoring the rope mass and assuming that the rope is always tensioned without sagging, the pulley moves only up and down in the Z-axis direction, the patient's thighs and calves are considered to be evenly distributed with mass, there is only motion in the Y-O-Z plane, then there is:
G P p ＝[x p ，y p ，z z ] (7)
Figure GDA0004159868020000063
Figure GDA0004159868020000071
Figure GDA0004159868020000072
Figure GDA0004159868020000073
Figure GDA0004159868020000074
in the above formulae (7) to (12), G P p and G P k respectively representing the coordinates of the rotation center of the hip joint and the rotation center of the knee joint under a global coordinate system G; x is x p 、y p And z p Respectively representing coordinate components of the hip joint in the XYZ direction of a global coordinate system G; G P a representing coordinates of the position of the shank end in a global coordinate system G; l (L) 1 And l 2 Respectively representing the length of the thigh and the length of the shank; joint angle θ of hip joint 1 Defined as the angle of the thigh to the X-O-Y plane; joint angle θ of knee joint 2 Defined as the angle formed by the thigh extension line and the shank; G A i representing coordinates of the position of the i-th rope lead-out point in a global coordinate system G; x is x Ai And y Bi Respectively representing coordinate components of the ith rope leading-out point in the XY direction; h is a i Representing the coordinate component of the i-th rope leading-out point in the Z direction, namely the height of the sliding block; G B i representing the position of the connection point of the ith rope on the leg of the person at global coordinates
Coordinates under G; l (L) Bi Representation of G B i Distance to the corresponding joint; G C i representing coordinates of the position of the virtual muscle on the leg of the person under a global coordinate system G; l (L) Ci Representation of G C i Distance to the corresponding joint;
kinetic energy E of thigh 1 And kinetic energy E of lower leg 2 The method comprises the following steps of:
Figure GDA0004159868020000081
Figure GDA0004159868020000082
in the above formulas (13) and (14), m 1 And m 2 Respectively representing the mass of the thigh and the mass of the shank; i 1 And I 2 The moment of inertia of the center of mass of the thigh and the moment of inertia of the center of mass of the calf are represented respectively;
Figure GDA0004159868020000083
and->
Figure GDA0004159868020000084
Respectively representing the angular velocity of the hip joint and the angular velocity of the knee joint; v 2D The speed representing the center of mass of the calf satisfies:
Figure GDA0004159868020000085
then formula (14) is:
Figure GDA0004159868020000086
the general potential energy of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot meets the following conditions:
Figure GDA0004159868020000087
in the above equation (17), if g is the gravitational acceleration, the lagrangian function L satisfies:
Figure GDA0004159868020000091
according to the Lagrangian equation:
Figure GDA0004159868020000092
in the above formula (19), τ 1 And τ 2 The moment at the hip joint and the moment at the knee joint are represented, and the overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot can be obtained after the (19) is simplified as shown in the formula (20):
Figure GDA0004159868020000093
while
Figure GDA0004159868020000101
And also satisfies the following:
τ＝τ c +τ m (21)
in the above formula (21), τ c Representing the moment generated by the rope tension; τ m Representing the moment generated by the muscle force, which satisfies respectively:
Figure GDA0004159868020000102
in the above formula (22), f mi A vector representing muscle force; f (f) ci A vector representing rope tension; u (u) mi And u ci Representing the corresponding distance vectors, respectively, which satisfy:
Figure GDA0004159868020000103
Figure GDA0004159868020000111
in the step 3, muscle normalization acting is set as an optimization target, a training track is fitted by adopting a Fourier series, and the training track is optimized and solved. In rehabilitation training, one training action is performed multiple times, so that the rehabilitation track is periodic. Since the muscle force is only related to the joint angle and the angular velocity, the first-half track and the second-half track are overlapped in one period, and only the half track of one period is optimized. Based on this, in step 3 of the above method, the method includes the steps of fitting the training track of the reconfigurable rope driven lower limb rehabilitation robot by adopting the following manner and performing optimization solution on the training track to obtain an optimal training track, and includes:
in a motion cycle of the training track of the rehabilitation training, the first half training track and the second half training track are overlapped, and the Fourier series is adopted to fit the half training track of the motion cycle, so that the joint angle theta of the ith joint i (t) satisfies:
Figure GDA0004159868020000112
in the above formula (25), ω is the frequency of the periodic motion, and the variable to be optimized is expressed as:
x 1 ＝[a 11 ，...，a 15 ，b 11 ，...，b 15 ，a 21 ，...，a 25 ，b 21 ，...，b 25 ] (26)
in rehabilitation training, normalization of muscle energy, which is the work done by the muscle in unit time, is used as an optimization target of a training track, and the recruitment degree of the muscle is represented and is an important evaluation index of rehabilitation training, wherein the normalization of the muscle energy is defined as:
Figure GDA0004159868020000113
in the above formula (27), f mi Representing the force of the ith muscle; l (L) mi Represents the length of the ith muscle; θ ireach Represents the maximum joint angle actually reached by the ith joint in the training process, satisfies theta ireach ＝maxθ i (t)；θ istart Represents the initial joint angle at the beginning of training and satisfies theta istart ＝θ i (0) The method comprises the steps of carrying out a first treatment on the surface of the The mathematical description of the optimization objective is:
Figure GDA0004159868020000121
in the above formula (28), θ 1min Represents the theoretical minimum joint angle of the hip joint; θ 1max Represents the theoretical maximum joint angle of the hip joint; θ 2min Represents the theoretical minimum joint angle of the knee joint; θ 2max Representing a theoretical maximum joint angle of the knee joint; t represents a movement period;
step-by-step solving optimization (28) by adopting a particle swarm optimization algorithm to finally obtain the optimal training track parameter x 1best 。
In step 4 of the above method, setting the energy consumption of the reconfigurable rope-driven lower limb rehabilitation robot as an optimization target according to the overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot established in step 2 and the optimal training track parameters obtained in step 3, and performing optimization solution on the traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot to obtain the optimal traction configuration parameters, wherein the method comprises the following steps:
rope of lower limb rehabilitation robot driven by reconfigurable rope does work W c As an optimization target, the optimization target is defined as:
E c ＝∑∫f ci dl cablei (29)
in the above formula (29), f ci Representing the acting force of the ith rope of the reconfigurable rope driven lower limb rehabilitation robot; l (L) cablei Representing the length of an ith rope of the reconfigurable rope driven lower limb rehabilitation robot; traction configuration parameter x of reconfigurable rope-driven lower limb rehabilitation robot 2 Divided into rope leading-out points A i Height h of (2) i And the rope connecting point C on the leg i Distance to the corresponding joint l Ci Two parts, the traction configuration parameter x 2 Is defined as:
Figure GDA0004159868020000131
for each rope, it can be connected to thigh or shank, 2 total 4 The possible traction configurations are, for each traction configuration, optimized to obtain the optimal traction configuration parameter x under that traction configuration 2best ' the globally optimal traction configuration and the corresponding traction configuration parameter x can be obtained by comparing 16 results 2best ’；
In rehabilitation training, in order to protect rehabilitation patients, the knee joint and the hip joint of the patients are prevented from being stressed by too large radial force, and equivalent resultant force Sigma f is formed at the hip joint and the knee joint in the X-axis direction ipx Sum sigma f ikx Should be zero, i.e. satisfy the constraint:
Figure GDA0004159868020000132
thus, the mathematical description of the optimization is as follows:
Figure GDA0004159868020000141
in the above formula (32), h imin Representing the lowest position of the i-th rope lead-out point; h is a imax The highest position of the i-th rope lead-out point; l (L) Cimin The i-th rope connection point is the nearest distance to the joint; l (L) Cimax The i-th rope connection point is the furthest distance from the joint; x is x 1best Solving an optimization problem (28) to obtain optimal training track parameters;
and (3) solving the optimization type (32) step by adopting a particle swarm optimization algorithm, and finally obtaining the optimal traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot.
An optimization algorithm flow chart of the composite optimization method of the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot is shown in fig. 5.
In summary, the compound optimization method of the embodiment of the invention starts from the physiological point of the human body, builds a muscle acting force model based on the skeletal muscle acting relation of the lower limb flexion and extension movement, and makes linear approximation on the muscle acting force to simplify the complexity of the follow-up optimization solution. And carrying out dynamic modeling on the lower limbs and the whole robot by using a Lagrangian potential function method to obtain a constraint relation between the rope tension and the rehabilitation track. Based on the model, the maximum muscle normalization acting is selected as an optimization target to perform optimization solution on the training track parameters, after the optimal training track is obtained, the minimum rope acting is selected as an optimization target to perform optimization solution on the robot traction configuration parameters, and finally the optimal training track parameters and the optimal robot traction configuration parameters are obtained by a patient.
In order to clearly show the technical scheme and the technical effects, the method for optimizing the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot in a composite mode is described in detail in the following.
Example 1
The embodiment provides a composite optimization method for tracks and configurations of a reconfigurable rope-driven lower limb rehabilitation robot, the reconfigurable rope-driven lower limb rehabilitation robot controlled by the method is shown in fig. 4, and the reconfigurable rope-driven lower limb rehabilitation robot is used for winding and unwinding ropes wound on the reels through m reels driven by m motors, so that limb movement is pulled by changing the lengths of the m ropes. The traction configuration of the reconfigurable rope-driven lower limb rehabilitation robot is divided into two parts, namely the position of a rope leading-out point and the position of a rope connecting point, the sliding block is driven to freely move along the guide rail by m lead screws driven by m motors, so that the position of the rope leading-out point is changed, and the position of the connecting point of a rope on a leg is changed by manually changing the position of a rope fixing device.
The optimizing method comprises the following steps:
step 1, establishing a muscle acting force model according to skeletal muscle schematic diagrams of lower limbs of a human body and the lower limbs. The flexion and extension movements of the legs are mainly affected by the five muscle groups as shown in fig. 2, and according to the action joints of the muscles affecting the flexion and extension movements of the legs, the legs are regarded as two links with two virtual muscles, one virtual muscle affecting hip joint movements and the other virtual muscle affecting knee joint movements. Each virtual muscle can be considered as being composed of: the device comprises an active controllable contraction unit CE, a passive series elastic unit SE and a passive parallel elastic damping unit PE; the active controllable contraction unit CE is controlled by the nerve body fluid regulating system to actively generate acting force; the passive series elastic unit SE and the passive parallel elastic damping unit PE are influenced by the length of muscle fiber and the change speed to passively generate acting force; in rehabilitation training, the reconfigurable rope drives the lower limb rehabilitation robot to pull the lower limb to make the lower limb passively follow the movement, and ignoring the active controllable contraction unit CE, the initial muscle acting force meets the following conditions:
f m ＝f SE +f PE (1)
in the above formula (1), f m Representing the force of the muscle; f (f) SE Representing the force of the passive series elastic element SE; f (f) PE Representing the acting force of the passive parallel elastic damping units PE; f (f) SE And f PE The following respectively satisfy:
Figure GDA0004159868020000161
in the above formula (2), deltal m Representing the amount of change in length of the muscle relative to the original length of the muscle during exercise;
Figure GDA0004159868020000162
indicating the rate of change of muscle length; a, a SE 、b SE 、a PE 、b PE Representing physiological parameters corresponding to the passive series elastic element SE and the passive parallel elastic damping element PE, wherein the parameters can be obtained from physiological research; c represents the damping coefficient of the passive parallel elastic damping unit PE, the index part +.>
Figure GDA0004159868020000163
And->
Figure GDA0004159868020000164
The first-order taylor expansion is performed at the initial state of the muscle to obtain:
Figure GDA0004159868020000165
wherein Deltal m0 When the variable quantity of the length of the muscle relative to the original length of the muscle in the initial state of the muscle is represented and the higher order infinitely small is ignored, the formula (2) can be approximated as:
Figure GDA0004159868020000166
in the above formula (4), k SE And k PE Respectively represent the elastic coefficients of the approximate rear SE part and the PE part, f SE 0 And f PE 0 Representing the forces of the SE and PE elements, respectively, in the initial state of the muscle, satisfying the following conditions:
Figure GDA0004159868020000171
and substituting the formulas (4) - (5) into the formula (6) for simplification to obtain a muscle acting force model as shown in the formula (6).
Figure GDA0004159868020000172
(6) Where k=k SE +k PE Representing the elastic coefficient of the whole muscle, f m0 ＝f SE 0 +f PE 0 Indicating the force at the initial state of the muscle.
And 2, establishing an overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot according to the skeleton-muscle schematic diagram and the muscle acting force model. As shown in fig. 4, a global coordinate G system is established, ignoring rope quality, assuming that the rope is always taut without sagging, the pulley moves only up and down in the Z-axis direction, the patient's thighs and calves are considered to be evenly distributed in quality, there is only motion in the Y-O-Z plane. Then there are:
G P p ＝[x p ，y p ，z p ] (7)
Figure GDA0004159868020000173
Figure GDA0004159868020000181
Figure GDA0004159868020000182
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Figure GDA0004159868020000183
Figure GDA0004159868020000184
wherein the method comprises the steps of G P p And G P k representing the rotation center of the hip joint and the rotation center of the knee joint in a global coordinate system G respectivelyCoordinates; x is x p 、y p And z p Respectively representing coordinate components of the hip joint in the XYZ direction of a global coordinate system G; G P a representing coordinates of the position of the shank end in a global coordinate system G; l (L) 1 And l 2 Respectively representing the length of the thigh and the length of the shank; joint angle θ of hip joint 1 Defined as the angle of the thigh to the X-O-Y plane; joint angle θ of knee joint 2 Defined as the angle formed by the thigh extension line and the shank; G A i representing coordinates of the position of the i-th rope lead-out point in a global coordinate system G; x is x Ai And y Bi Respectively representing coordinate components of the ith rope leading-out point in the XY direction; h is a i Representing the coordinate component of the i-th rope leading-out point in the Z direction, namely the height of the sliding block; G B i representing the coordinates of the position of the connection point of the ith rope on the leg of the person under the global coordinate system G; l (L) Bi Representation of G B i Distance to the corresponding joint; G C i representing coordinates of the position of the virtual muscle on the leg of the person under a global coordinate system G; l (L) Ci Representation of G C i Distance to the corresponding joint;
kinetic energy E of thigh 1 And kinetic energy E of lower leg 2 The method comprises the following steps of:
Figure GDA0004159868020000191
Figure GDA0004159868020000192
in the formulas (13) and (14), m 1 And m 2 Respectively representing the mass of the thigh and the mass of the shank, I 1 And I 2 Representing the moment of inertia of the center of mass of the thigh and the moment of inertia of the center of mass of the calf respectively,
Figure GDA0004159868020000193
and->
Figure GDA0004159868020000194
Respectively represent the angular velocity of the hip joint and the angular velocity of the knee joint, v 2D The speed representing the center of mass of the calf satisfies: />
Figure GDA0004159868020000195
Then formula (14) is:
Figure GDA0004159868020000196
the general potential energy of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot meets the following conditions:
Figure GDA0004159868020000197
in the above equation (17), if g is the gravitational acceleration, the lagrangian function L satisfies:
Figure GDA0004159868020000201
according to the Lagrangian equation:
Figure GDA0004159868020000202
in the above formula (19), τ 1 And τ 2 The moment at the hip joint and the moment at the knee joint are represented, the overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot is obtained after the (19) is simplified as shown in the formula (20):
Figure GDA0004159868020000203
while
Figure GDA0004159868020000211
And also satisfies the following:
τ＝τ c +τ m (21)
in the above formula (21), τ c Representing the moment generated by the rope tension; τ m Representing the moment generated by the muscle force, which satisfies respectively:
Figure GDA0004159868020000212
in the above formula (22), f mi A vector representing muscle force; f (f) ci A vector representing rope tension; u (u) mi And u ci Representing the corresponding distance vectors, respectively, which satisfy:
Figure GDA0004159868020000213
Figure GDA0004159868020000221
and 3, setting muscle normalization acting as an optimization target based on the skeletal muscle schematic diagram and the muscle acting force model of the lower limb in the step 1, fitting a training track by adopting a Fourier series, and carrying out optimization solving on the training track. In rehabilitation training, one training action is performed multiple times, so that the rehabilitation track is periodic. Since the muscle force is only related to the joint angle and the angular velocity, the first-half track and the second-half track are overlapped in one period, and only the half track of one period is optimized. The Fourier series is adopted to fit the motion track, the track is naturally periodic, the complexity of solving the optimization problem can be reduced to a certain extent, and the joint angle theta of the ith joint i (t) satisfies:
Figure GDA0004159868020000222
in the above formula (25), ω is the frequency of the periodic motion, and the variable to be optimized is expressed as:
x 1 ＝[a 11 ，...，a 15 ，b 11 ，...，b 15 ，a 21 ，...，a 25 ，b 21 ，... ， b 25 ] (26)
in muscle rehabilitation training, the degree of recruitment of muscle is represented by muscle energy, which is an important evaluation index of rehabilitation training, and is defined as the work performed by the muscle in unit time, so that the normalization of muscle energy is selected as an optimization target of a track, and is defined as follows:
Figure GDA0004159868020000223
in the above formula (27), f mi Representing the force of the ith muscle; l (L) mi Represents the length of the ith muscle; θ ireach Represents the maximum joint angle actually reached by the ith joint in the training process, satisfies theta ireach ＝maxθ i (t)；θ istart Represents the initial joint angle at the beginning of training and satisfies theta istart ＝θ i (0) The method comprises the steps of carrying out a first treatment on the surface of the The mathematical description of the optimization objective is:
Figure GDA0004159868020000231
in the above formula (28), θ 1min Represents the theoretical minimum joint angle of the hip joint; θ 1max Represents the theoretical maximum joint angle of the hip joint; θ 2min Represents the theoretical minimum joint angle of the knee joint; θ 2max Representing a theoretical maximum joint angle of the knee joint; t represents a movement period; step-by-step solving optimization (28) by adopting a particle swarm optimization algorithm to finally obtain the optimal training track parameter x 1best 。
Step 4, selecting a reconfigurable rope based on the overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot in the step 2 and the optimal training track obtained in the step 3And the energy consumption of the lower limb rehabilitation robot is driven as an optimization target, and the traction configuration of the reconfigurable rope-driven lower limb rehabilitation robot is optimized and solved. Obtaining the optimal track parameter x 1best And then, optimizing configuration parameters of the robot. In order to ensure that the robot has low energy consumption, the rope does work W in rehabilitation training c As an optimization target, the optimization target is defined as:
w c ＝∑∫f ci dl cabei (29)
in the above formula (29), f ci Representing the acting force of the ith rope of the reconfigurable rope driven lower limb rehabilitation robot; l (L) cablei Representing the length of an ith rope of the reconfigurable rope driven lower limb rehabilitation robot;
traction configuration parameter x of reconfigurable rope-driven lower limb rehabilitation robot 2 Divided into rope leading-out points A i Height h of (2) i And the rope connecting point C on the leg i Distance to the corresponding joint l Ci Two parts, the traction configuration parameter x 2 Is defined as:
Figure GDA0004159868020000241
for each rope, it can be connected to thigh or shank, 2 total 4 The possible traction configurations are, for each traction configuration, optimized to obtain the optimal configuration parameter x under that traction configuration 2best ' the globally optimal traction configuration and the corresponding configuration parameter x can be obtained by comparing 16 results 2best ’；
In rehabilitation training, in order to protect rehabilitation patients, the knee joint and the hip joint of the patients are prevented from being stressed by too large radial force, and equivalent resultant force Sigma f is formed at the hip joint and the knee joint in the X-axis direction ipx Sum sigma f ikx Should be zero, i.e. satisfy the constraint:
Figure GDA0004159868020000242
thus, the mathematical description of the optimization is as follows:
Figure GDA0004159868020000251
/>
in the above formula (32), h imin Representing the lowest position of the i-th rope lead-out point; h is a imax The highest position of the i-th rope lead-out point; l (L) Cimin The i-th rope connection point is the nearest distance to the joint; l (L) Cimax The i-th rope connection point is the furthest distance from the joint; x is x 1best Solving an optimal training track parameter obtained by an optimization formula (28); and (3) solving the optimization type (32) step by adopting a particle swarm optimization algorithm, and finally obtaining the optimal traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot.
A specific flow chart of the composite optimization method of the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot is shown in fig. 5.
In summary, the compound optimization method of the embodiment of the invention starts from the physiological point of the human body, builds a muscle acting force model based on the skeletal muscle schematic diagram of the lower limb, and makes linear approximation on the muscle acting force model to simplify the complexity of subsequent optimization solution. And carrying out dynamic modeling on the lower limbs and the whole robot by using a Lagrangian potential function method to obtain a constraint relation between the rope tension and the rehabilitation track. Based on the model, the maximum muscle normalization acting is selected as an optimization target to perform optimization solution on the training track parameters, after the optimal training track parameters are obtained, the minimum rope acting is selected as an optimization target to perform optimization solution on the robot traction configuration parameters, and finally the optimal training track parameters and the optimal robot traction configuration parameters are obtained by a patient. The composite optimization method for the training track and the traction configuration of the lower limb rehabilitation robot has at least the following beneficial effects:
(1) The method is characterized in that the reconfigurable rope-driven lower limb rehabilitation robot is deeply combined with the rehabilitation training requirements, an optimization target is set from the angles of rehabilitation training and robots, and the problems of complex, fuzzy and abstract rehabilitation training optimization are detailed and concrete by modeling muscle acting force and dynamic modeling of the reconfigurable rope-driven lower limb rehabilitation robot and the whole lower limb, so that the reconfigurable rope-driven lower limb rehabilitation robot can play a role in actual rehabilitation training.
(2) Aiming at different rehabilitation scenes and different rehabilitation patients, only part of variables are needed to be modified to provide the training track parameters and the traction configuration parameters required by the robot, so that the robot has good universality, and the problems caused by different requirements in actual rehabilitation training are greatly relieved.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. The composite optimization method for the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot is characterized by comprising the following steps of:
step 1, establishing a muscle acting force model according to the characteristics of the lower limbs of the human body and the skeletal muscle acting relationship of the lower limbs;
step 2, establishing an overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot according to the skeletal muscle action relation and the muscle acting force model of the lower limb; the reconfigurable rope driven lower limb rehabilitation robot is a robot which is characterized in that m winding drums driven by m first motors are used for winding and unwinding ropes wound on the winding drums, and the length of the m ropes is changed to draw limb movement; the traction configuration of the reconfigurable rope-driven lower limb rehabilitation robot comprises the following steps: the position of the rope leading-out point and the position of the rope connecting point are changed by driving the sliding block to freely move along the guide rail through m lead screws driven by m second motors; the position of the rope connection point is changed by manually changing the position of the rope connection means at the position of the connection point on the leg;
step 3, setting muscle normalization acting as an optimization target according to the muscle acting force model established in the step 1, fitting a training track of the reconfigurable rope-driven lower limb rehabilitation robot by adopting a Fourier series, and carrying out optimization solving on the training track parameters to obtain optimal training track parameters; in rehabilitation training, normalization of muscle energy is used as an optimization target of a training track parameter, the muscle energy is the work done by the muscle in unit time, the recruitment degree of the muscle is represented and is an important evaluation index of the rehabilitation training, so the normalization of the muscle energy is selected as the optimization target of the training track parameter, and the optimization target is defined as follows:
Figure FDA0004167091950000011
in the above formula (27), f mi Representing the force of the ith muscle; l (L) mi Represents the length of the ith muscle; θ ireach Represents the maximum joint angle actually reached by the ith joint in the training process, satisfies theta ireach ＝maxθ i (t)；θ istart Represents the initial joint angle at the beginning of training and satisfies theta istart ＝θ i (0)；
And 4, setting the energy consumption of the reconfigurable rope-driven lower limb rehabilitation robot as an optimization target according to the overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot established in the step 2 and the optimal training track parameters obtained in the step 3, and carrying out optimization solution on the traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot to obtain the optimal traction configuration parameters.
2. The method for compositely optimizing the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot according to claim 1, wherein in the step 1, a muscle acting force model is built according to the skeletal muscle acting relationship of the lower limb characteristics of the human body and the lower limb in the following manner, and the method comprises the following steps:
considering the legs as two links with two virtual muscles according to the acting joints of the muscles affecting the leg flexion and extension movements, wherein one virtual muscle affects the hip joint movements and the other virtual muscle affects the knee joint movements; each virtual muscle is considered to be composed of: the device comprises an active controllable contraction unit CE, a passive series elastic unit SE and a passive parallel elastic damping unit PE; the active controllable contraction unit CE is controlled by the nerve body fluid regulating system to actively generate acting force; the passive series elastic unit SE and the passive parallel elastic damping unit PE are influenced by the length of muscle fiber and the change speed to passively generate acting force; in rehabilitation training, the reconfigurable rope drives the lower limb rehabilitation robot to pull the lower limb to make the lower limb passively follow the movement, and ignoring the active controllable contraction unit CE, the initial muscle acting force meets the following conditions:
f m ＝f SE +f PE (1)
in the above formula (1), f m Representing the force of the muscle; f (f) SE Representing the force of the passive series elastic element SE; f (f) PE Representing the acting force of the passive parallel elastic damping units PE; f (f) SE And f PE The following respectively satisfy:
Figure FDA0004167091950000021
Figure FDA0004167091950000022
in the above formula (2), deltal m Representing the amount of change in length of the muscle relative to the original length of the muscle during exercise; i.e m Indicating the rate of change of muscle length; a, a SE 、b SE 、a PE 、b PE Respectively representing physiological parameters, a, corresponding to the passive series elastic unit SE and the passive parallel elastic damping unit PE SE Take a value of 0.158, b SE The value is 232.6, a PE Take the value of 64.7, b PE The value is 23.95; c represents the damping coefficient of the passive parallel elastic damping unit PE, and the index part
Figure FDA0004167091950000023
And
Figure FDA0004167091950000024
the first-order taylor expansion is performed at the initial state of the muscle to obtain:
Figure FDA0004167091950000031
wherein Deltal m0 When the variable quantity of the length of the muscle relative to the original length of the muscle in the initial state of the muscle is represented and the higher order infinitely small is ignored, the formula (2) can be approximated as:
f SE ＝k SE Δl m +f SE 0 ；
f PE ＝k PE Δl m +cl m +f PE 0 (4)
in the above formula (4), k SE And k PE Respectively represent the elastic coefficients of the approximate rear SE part and the PE part, f SE 0 And f PE 0 Representing the forces of the SE and PE elements, respectively, in the initial state of the muscle, satisfying the following conditions:
Figure FDA0004167091950000032
Figure FDA0004167091950000033
Figure FDA0004167091950000034
Figure FDA0004167091950000035
substituting the formulas (4) - (5) into the formula (6) for simplification to obtain a muscle acting force model as shown in the formula (6):
f m ＝kΔl m +ci m +f m0 (6)
in the above formula (6), k=k SE +k PE Representing the elastic coefficient of the whole muscle, f m0 ＝f SE 0 +f PE 0 Indicating the force at the initial state of the muscle.
3. The method for compositely optimizing the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot according to claim 2, wherein in the step 2, an overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot is built according to the skeletal muscle action relationship and the muscle acting force model of the lower limb in the following manner, and the method comprises the following steps:
by establishing the global coordinate G system, ignoring the rope mass and assuming that the rope is always tensioned without sagging, the pulley moves only up and down in the Z-axis direction, the patient's thighs and calves are considered to be evenly distributed with mass, there is only motion in the Y-O-Z plane, then there is:
G P p ＝[x p ，y p ，z p ] (7)
Figure FDA0004167091950000041
Figure FDA0004167091950000042
Figure FDA0004167091950000043
Figure FDA0004167091950000044
Figure FDA0004167091950000051
in the above formulae (7) to (12), G P p and G P k respectively representing the coordinates of the rotation center of the hip joint and the rotation center of the knee joint under a global coordinate system G; x is x p 、y p And z p Respectively representing coordinate components of the hip joint in the XYZ direction of a global coordinate system G; G P a representing coordinates of the position of the shank end in a global coordinate system G; l (L) 1 And l 2 Respectively representing the length of the thigh and the length of the shank; joint angle θ of hip joint 1 Defined as the angle of the thigh to the X-O-Y plane; joint angle θ of knee joint 2 Defined as the angle formed by the thigh extension line and the shank; G A i representing coordinates of the position of the i-th rope lead-out point in a global coordinate system G; x is x Ai And y Bi Respectively representing coordinate components of the ith rope leading-out point in the XY direction; h is a i Representing the coordinate component of the i-th rope leading-out point in the Z direction, namely the height of the sliding block; G B i representing the coordinates of the position of the connection point of the ith rope on the leg of the person under the global coordinate system G; l (L) Bi Representation of G B i Distance to the corresponding joint; G C i representing coordinates of the position of the virtual muscle on the leg of the person under a global coordinate system G; l (L) Ci Representation of G C i Distance to the corresponding joint;
kinetic energy E of thigh 1 And kinetic energy E of lower leg 2 The method comprises the following steps of:
Figure FDA0004167091950000052
Figure FDA0004167091950000053
in the above formulas (13) and (14), m 1 And m 2 Respectively representing the mass of the thigh and the mass of the shank; i 1 And I 2 The moment of inertia of the center of mass of the thigh and the moment of inertia of the center of mass of the calf are represented respectively;
Figure FDA0004167091950000054
and->
Figure FDA0004167091950000055
Respectively representing the angular velocity of the hip joint and the angular velocity of the knee joint; v 2D The speed representing the center of mass of the calf satisfies:
Figure FDA0004167091950000061
then formula (14) is:
Figure FDA0004167091950000062
the general potential energy of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot meets the following conditions:
Figure FDA0004167091950000063
in the above equation (17), if g is the gravitational acceleration, the lagrangian function L satisfies:
Figure FDA0004167091950000064
according to the Lagrangian equation:
Figure FDA0004167091950000065
Figure FDA0004167091950000066
in the above formula (19), τ 1 And τ 2 The moment at the hip joint and the moment at the knee joint are represented, the overall dynamics model of the lower limb and the reconfigurable rope driven lower limb rehabilitation robot is obtained after the (19) is simplified, and is shown as a formula (20):
Figure FDA0004167091950000071
while
Figure FDA0004167091950000072
And also satisfies the following:
τ＝τ c +τ m (21)
in the above formula (21), τ c Representing the moment generated by the rope tension; τ m Representing the moment generated by the muscle force, which satisfies respectively:
Figure FDA0004167091950000081
Figure FDA0004167091950000082
in the above formula (22), f mi A vector representing muscle force; f (f) ci A vector representing rope tension; u (u) mi And u ci Representing the corresponding distance vectors, respectively, which satisfy:
Figure FDA0004167091950000083
Figure FDA0004167091950000084
4. the method for compositely optimizing the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot according to claim 3, wherein in the step 3, the training track of the reconfigurable rope-driven lower limb rehabilitation robot is fitted by adopting fourier series and the training track parameters are optimized and solved to obtain the optimal training track parameters, and the method comprises the following steps:
in a motion cycle of the training track of the rehabilitation training, the first half training track and the second half training track are overlapped, and the Fourier series is adopted to fit the half training track of the motion cycle, so that the joint angle theta of the ith joint i (t) satisfies:
Figure FDA0004167091950000091
in the above formula (25), ω is the frequency of the periodic motion, and the variable to be optimized is expressed as:
x 1 ＝[a 11 ，...，a 15 ，b 11 ，...，b 15 ，a 21 ，...，a 25 ，b 21 ，...，b 25 ] (26)
the mathematical description of the optimization objective of equation (27) above is:
Figure FDA0004167091950000092
Figure FDA0004167091950000093
in the above formula (28), θ 1min Represents the theoretical minimum joint angle of the hip joint; θ 1max Represents the theoretical maximum joint angle of the hip joint; θ 2min Represents the theoretical minimum joint angle of the knee joint; θ 2max Representing a theoretical maximum joint angle of the knee joint; t represents a movement period;
step-by-step solving and optimizing the above-mentioned method by adopting particle swarm optimization algorithm(28) Finally obtaining the optimal training track parameter x 1best 。
5. The method for compositely optimizing the track and the configuration of the reconfigurable rope-driven lower limb rehabilitation robot according to claim 4, wherein in the step 4, the energy consumption of the reconfigurable rope-driven lower limb rehabilitation robot is set as an optimization target according to the overall dynamics model of the lower limb and the reconfigurable rope-driven lower limb rehabilitation robot established in the step 2 and the optimal training track parameters obtained in the step 3, and the optimizing solution of the traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot is performed to obtain the optimal traction configuration parameters, and the method comprises the following steps:
rope of lower limb rehabilitation robot driven by reconfigurable rope does work W c As an optimization target, the optimization target is defined as:
W c ＝∑∫f ci dl cablei (29)
in the above formula (29), f ci Representing the acting force of the ith rope of the reconfigurable rope driven lower limb rehabilitation robot; l (L) cablei Representing the length of an ith rope of the reconfigurable rope driven lower limb rehabilitation robot;
traction configuration parameter x of reconfigurable rope-driven lower limb rehabilitation robot 2 Divided into rope leading-out points A i Height h of (2) i And the rope is connected with the point c on the leg i Distance to the corresponding joint l ci Two parts, the traction configuration parameter x 2 Is defined as:
Figure FDA0004167091950000101
for each rope, it can be connected to thigh or shank, 2 total 4 Optimizing and solving to obtain optimal traction configuration parameters x under each traction configuration 2best’ Comparing 16 results to obtain the overall optimal traction configuration and traction configuration parameter x 2best’ ；
In rehabilitation training, to protect rehabilitation patientsThe patient's knee joint and hip joint are prevented from being subjected to too large radial force, and the equivalent resultant force Sigma f at the hip joint and knee joint in the X-axis direction ipx Sum sigma f ikx Should be zero, i.e. satisfy the constraint:
∑f ipx ＝0
∑f ikx ＝0 (31)
thus, the mathematical description of the optimization objective is:
Figure FDA0004167091950000111
Figure FDA0004167091950000112
in the above formula (32), h imin Representing the lowest position of the i-th rope lead-out point; h is a imax The highest position of the i-th rope lead-out point; l (L) Cimin The i-th rope connection point is the nearest distance to the joint; l (L) Cimax The i-th rope connection point is the furthest distance from the joint; x is x 1best Solving an optimal training track parameter obtained by an optimization formula (28);
and (3) solving the optimization type (32) step by adopting a particle swarm optimization algorithm, and finally obtaining the optimal traction configuration parameters of the reconfigurable rope-driven lower limb rehabilitation robot.
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