CN113057850B - Recovery robot control method based on probability motion primitive and hidden semi-Markov - Google Patents

Recovery robot control method based on probability motion primitive and hidden semi-Markov Download PDF

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CN113057850B
CN113057850B CN202110264726.6A CN202110264726A CN113057850B CN 113057850 B CN113057850 B CN 113057850B CN 202110264726 A CN202110264726 A CN 202110264726A CN 113057850 B CN113057850 B CN 113057850B
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markov
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CN113057850A (en
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徐宝国
汪逸飞
邓乐莹
王欣
宋爱国
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Southeast University
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H1/00—Apparatus for passive exercising; Vibrating apparatus ; Chiropractic devices, e.g. body impacting devices, external devices for briefly extending or aligning unbroken bones
    • A61H1/02—Stretching or bending or torsioning apparatus for exercising
    • A61H1/0274—Stretching or bending or torsioning apparatus for exercising for the upper limbs
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H2201/00—Characteristics of apparatus not provided for in the preceding codes
    • A61H2201/16—Physical interface with patient
    • A61H2201/1602—Physical interface with patient kind of interface, e.g. head rest, knee support or lumbar support
    • A61H2201/1635—Hand or arm, e.g. handle
    • A61H2201/1638—Holding means therefor
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H2201/00—Characteristics of apparatus not provided for in the preceding codes
    • A61H2201/50—Control means thereof
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H2201/00—Characteristics of apparatus not provided for in the preceding codes
    • A61H2201/50—Control means thereof
    • A61H2201/5007—Control means thereof computer controlled
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H2201/00—Characteristics of apparatus not provided for in the preceding codes
    • A61H2201/50—Control means thereof
    • A61H2201/5058—Sensors or detectors
    • A61H2201/5061—Force sensors

Abstract

The invention designs a rehabilitation robot control method based on probability motion primitives and hidden semi-Markov, which comprises the following steps: (1) and recording the motion information of the upper limbs on the healthy side for a plurality of times, wherein the motion information comprises the rigidity, the track and the like of the tail ends of the arms. (2) And generalizing the rigidity recorded in the step (1) through the probability motion primitive. (3) Generalizing the data recorded in (1) using a hidden semi-Markov model to generate a trajectory. (4) The generalized tracks are mirrored. (5) And carrying out variable impedance control on the tail end of the rehabilitation robot through the information after the mirror image. The invention uses the probability motion primitive and the hidden semi-Markov to generate the control parameters of the rehabilitation robot for the first time, can effectively utilize the side-healthy limb of the patient to assist the rehabilitation training, controls the rehabilitation robot by simulating the motion of the side-healthy limb, can achieve better rehabilitation training effect, simultaneously improves the rehabilitation efficiency, and greatly reduces the workload of the rehabilitation doctor.

Description

Recovery robot control method based on probability motion primitive and hidden semi-Markov
Technical Field
The invention belongs to the field of machine simulation learning, relates to a rehabilitation robot control method, and particularly relates to a rehabilitation robot variable impedance control method based on probabilistic motion primitives (ProMP) and hidden semi Markov (HSMM), which optimizes the track generation of a rehabilitation robot under mirror image control.
Background
The rehabilitation robot is the combination of industrial robot and medical robot, mainly is in order to meet medical care personnel and recovered demand, and the auxiliary patient moves the sick limb or the joint that has the trouble to reach the recovered purpose of help patient. At present, the wearable type (exoskeleton type) and the independent type are mainly divided.
The invention relates to a control method of an independent rehabilitation robot, which calculates control parameters and controls the motion of the rehabilitation robot by teaching motion data of upper limbs on healthy sides for many times and by using a machine simulation learning method.
In machine learning, how to generate required control parameters by using motion data of machine generalization teaching is a big problem, and a common method can be solved by using probability motion primitives. The probability motion primitive is improved on the basis of the motion primitive, and the parameter vector is represented in a probability distribution mode through the operation of probability theory; the method has the advantages of being adaptive to new targets, easy to adjust control parameters and the like. The present invention generalizes muscle stiffness data using probabilistic motion primitives
In human-machine teaching, hidden markov models are often used to analyze a sequence of states, which assumes that the next state is only related to the current state. The hidden semi-Markov model expresses the probability of a certain state staying by a time probability function, so that time information can be better expressed. Generalization of the taught motion data can be achieved by using a formula of gaussian linear regression. The present invention generalizes data such as a taught position and velocity by using a hidden semi-Markov method.
For an independent upper limb rehabilitation robot, impedance control is one of the common control modes, the main advantages of the independent upper limb rehabilitation robot are high flexibility and good robustness to disturbance and uncertainty, and the independent upper limb rehabilitation robot is a common mode for realizing force control, so the independent upper limb rehabilitation robot is very suitable for being applied to a rehabilitation scene to avoid secondary damage to limbs of a patient. The significance of the variable impedance control is that the stiffness value can be adjusted in time.
The invention designs a variable impedance control method of a rehabilitation robot based on probabilistic motion primitives and hidden semi-Markov, which is used for generating control parameters of the rehabilitation robot for the first time, can effectively utilize the side-caring limbs of a patient to assist rehabilitation training, controls the rehabilitation robot by simulating the motion of the side-caring limbs, can achieve better rehabilitation training effect, simultaneously improves the rehabilitation efficiency and greatly reduces the workload of a rehabilitation doctor.
Disclosure of Invention
Aiming at the background, the invention provides a rehabilitation robot variable impedance control method based on probabilistic motion primitive and hidden semi-Markov, which can simulate the motion of a healthy side upper limb to generate a rehabilitation motion track of the affected limb through machine learning.
In order to achieve the above purpose, the invention adopts the following technical scheme: a rehabilitation robot variable impedance control method based on probability motion primitives and hidden semi-Markov specifically comprises the following steps:
(1) and recording the motion information of the upper limbs on the healthy side for a plurality of times, wherein the motion information comprises the rigidity, the track and the like of the tail ends of the arms.
(2) And generalizing the rigidity recorded in the step (1) through the probability motion primitive.
(3) The data recorded in (1) is generalized using a hidden semi-markov model to generate a trajectory. The parameters of the hidden semi-Markov model are estimated by an extreme likelihood estimation algorithm (Expectation-Maximization), and then the control parameters are calculated by a Gaussian regression algorithm.
(4) The generalized tracks are mirrored.
(5) And performing variable impedance control on the tail end of the rehabilitation robot through the mirrored track, the changed rigidity information and the multi-dimensional force sensor arranged on the mechanical arm.
For the step (1), the information of the rigidity, the position and the speed recorded during the teaching is written into a vector form, and the method comprises the following steps:
xD，t＝(x1，t，...，xd，t)T
Figure GDA0003608053100000021
kD，t＝(k1，t，...，，kd，t)T
wherein D represents a degree of freedom, t represents time, xD，tIn order to be the position of the track,
Figure GDA0003608053100000022
is the velocity of the track, kD，tIs the stiffness information.
For the step (2), the method comprises the following sub-steps:
(a1) determining a vector by the motion information extracted in (1)
yt＝(k1，t，k2，t，...，kd，t)T＝Ψtω+∈y
Figure GDA0003608053100000023
Wherein k isd，tMuscle stiffness number for d degrees of freedomN is time, y is 0, 1tDenotes the muscle stiffness data in (1), ω is the weight vector, eyIs a Gaussian distribution noise with variance of sigmay，φi，tFor time-dependent basis functions, for repetitive regular movements, the basis functions can be:
φi，t＝bi(z)/∑jbj(z)
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003608053100000031
where z (t) is an arbitrary monotonically increasing function of time, h is the bandwidth, ciIs the center of the ith basis function
(a2) According to the probability motion primitive formula, there are:
Figure GDA0003608053100000032
wherein
Figure GDA0003608053100000033
Representing a Gaussian distribution, θ ═ (. mu.) ═ω，∑ω) Is a parameter of the probability density function; Ψt TμωAnd Ψt T∑ωΨt+∑yRespectively represent the Gaussian distribution p (y)t(ii) a θ) and variance.
(a3) For the stiffness data extracted by teaching, extracting the parameters of the model in the step (a2) by using a maximum likelihood estimation algorithm to obtain muω *，∑ω *(ii) a And order the control parameters
Figure GDA0003608053100000034
Wherein muω *，∑ω *The value obtained for the maximum likelihood estimation is the parameter 0 of the model in (a 2);
Figure GDA0003608053100000035
namely the muscle stiffness obtained by using the probability motion primitive, so as to control the mechanical arm.
For the step (3), the following substeps are included:
(b1) respectively establishing a hidden semi-Markov model for each degree of freedom of the joint, wherein the hidden semi-Markov model theta can be expressed by the following parameters:
Figure GDA0003608053100000036
wherein, piiIs the probability that the ith state is the initial state, ai，jK is the total number of states, which is the probability of transitioning from state j to the next state i;
Figure GDA0003608053100000037
parameters of the probability density function for the ith state duration obeying a Gaussian distribution, μi，∑iFor the parameters of the probability density function for which the i-th state can be successfully observed, there are:
Figure GDA0003608053100000041
wherein t is 1, 2max，
Figure GDA0003608053100000042
Eta is a constant set between 2 and 3, TmaxTo teach the total number of samples of the data vector,
at each time t of the ith state, the observed data obeys a Gaussian distribution, μi，∑iRespectively, the expectation and variance of the distribution, for which there are:
Figure GDA0003608053100000043
wherein the content of the first and second substances,
Figure GDA0003608053100000044
for the position and velocity values observed at time t,
Figure GDA0003608053100000045
μiis the expectation of a joint Gaussian distribution, wherein
Figure GDA0003608053100000046
In order to be able to anticipate the position,
Figure GDA0003608053100000047
is a desire for speed; sigmaiIs a covariance matrix, wherein
Figure GDA0003608053100000048
Respectively corresponding covariance;
(b2) using maximum likelihood estimation algorithms for each degree of freedom
Figure GDA0003608053100000049
And
Figure GDA00036080531000000410
calculating parameters in the distribution to obtain parameter values
Figure GDA00036080531000000411
And mui，∑i
(b3) For the probability at the ith state at time t, there is the formula:
Figure GDA00036080531000000412
Figure GDA00036080531000000413
Figure GDA00036080531000000414
wherein x1Is an initial position, niIs the probability that the ith state is the initial state, ai，tIs the probability at the ith state at time t
(b4) Calculating control parameters using a Gaussian regression formula
Figure GDA00036080531000000415
And
Figure GDA00036080531000000416
comprises the following steps:
Figure GDA00036080531000000417
wherein the content of the first and second substances,
Figure GDA0003608053100000051
the speed of the track of the mechanical arm at the time t is obtained, and the track at the time t can be obtained through initial position integration
Figure GDA0003608053100000052
In the step (5), the control parameters calculated in the step (2) and the step (3) include:
Figure GDA0003608053100000053
wherein KjIs the main diagonal line of (k)1，t *，k2，t *，...，kd，t *) Diagonal array of elements, DjFor the corresponding damping matrix, τcmdForce information for the mechanical arm;
Figure GDA0003608053100000054
the expected position and speed vector can be derived from (3); x is the number ofmsr，
Figure GDA0003608053100000055
For the current position and velocity vector, τdynThe dynamic force of the system is compensated, such as gravity, Coriolis force and the like. And outputting corresponding torque according to an impedance control formula by detecting a force signal of the arm of the user.
The invention has the beneficial effects that:
the invention uses the probability motion primitive and the hidden semi-Markov in the machine learning to generate the control parameter of the rehabilitation robot, and uses the variable impedance method to control, compared with the traditional method of directly extracting data to control, the flexibility is high, the limbs of the patient can be better protected from secondary damage, and the better rehabilitation training effect can be achieved.
Drawings
FIG. 1 is a flow chart of a rehabilitation robot control method based on probabilistic motion primitives and hidden semi-Markov models in accordance with the present invention.
Fig. 2 is a schematic diagram of impedance control in the rehabilitation robot control method based on probabilistic motion primitives and hidden semi-markov.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
As shown in the figure, a rehabilitation robot control method based on probabilistic motion primitives and hidden semi-markov specifically includes the following steps:
(1) and recording the motion information of the upper limbs on the healthy side for a plurality of times, wherein the motion information comprises the rigidity, the track and the like of the tail ends of the arms.
(2) And generalizing the rigidity recorded in the step (1) through the probability motion primitive.
(3) Generalizing the data recorded in (1) using a hidden semi-Markov model to generate a trajectory. The parameters of the hidden semi-Markov model are estimated by an extreme likelihood estimation algorithm (Expectation-Maximization), and then the control parameters are calculated by a Gaussian regression algorithm.
(4) The generalized tracks are mirrored.
(5) And performing variable impedance control on the tail end of the rehabilitation robot through the mirrored track, the changed rigidity information and the multi-dimensional force sensor arranged on the mechanical arm.
For the step (1), the information of the rigidity, the position and the speed recorded during the teaching is written into a vector form, and the method comprises the following steps:
xD，t＝(x1，t，...，xd，t)T
Figure GDA0003608053100000061
kD，t＝(k1，t，...，kd，t)T
wherein D represents a degree of freedom, t represents time, xD，tIn order to be the position of the track,
Figure GDA0003608053100000062
is the velocity of the track, kD，tIs the stiffness information.
For the step (2), the method comprises the following sub-steps:
(a1) determining a vector by the motion information extracted in (1)
yt＝(k1，t，k2，t，...，kd，t)T＝Ψtω+∈y
Figure GDA0003608053100000063
Wherein k isd，tMuscle stiffness data for d degrees of freedom, t 0, 1tDenotes the muscle stiffness data in (1), ω is the weight vector, eyIs a Gaussian distribution noise with a variance of Σ y, φi，tFor time-dependent basis functions, for repetitive regular movements, the basis functions can be:
φi，t＝bi(z)/∑jbj(z)
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003608053100000064
where z (t) is an arbitrary monotonically increasing function of time, h is bandwidth, ciIs the center of the ith basis function
(a2) According to the probability motion primitive formula, there are:
Figure GDA0003608053100000071
wherein
Figure GDA0003608053100000072
Represents a Gaussian distribution, and θ ═ is (μω，∑ω) Is a parameter of the probability density function; Ψt TμωAnd Ψt T∑ωΨt+∑yRespectively represent the Gaussian distribution p (y)t(ii) a θ) and variance.
(a3) For the stiffness data extracted by teaching, extracting the parameters of the model in the step (a2) by using a maximum likelihood estimation algorithm to obtain muω *，∑ω *(ii) a And order the control parameters
Figure GDA0003608053100000073
Wherein muω *，∑ω *Obtaining a value for the maximum likelihood estimation, namely a parameter theta of the model in (a 2);
Figure GDA0003608053100000074
namely the muscle stiffness obtained by using the probability motion primitive, so as to control the mechanical arm.
For the step (3), the following substeps are included:
(b1) respectively establishing a hidden semi-Markov model for each freedom degree of the joint, wherein the hidden semi-Markov model theta can be expressed by the following parameters:
Figure GDA0003608053100000075
wherein, piiIs the probability that the ith state is the initial state, ai，jK is the total number of states, which is the probability of transitioning from state j to the next state i;
Figure GDA0003608053100000076
parameters of the probability density function for the ith state duration, obeying a Gaussian distribution, μi，∑iFor the parameters of the probability density function for which the i-th state can be successfully observed, there are:
Figure GDA0003608053100000077
wherein t is 1, 2max，
Figure GDA0003608053100000078
Eta is a constant set between 2 and 3, TmaxTo teach the total number of samples of the data vector,
at each time t of the ith state, the observed data obeys a Gaussian distribution, μi，∑iRespectively, the expectation and variance of the distribution, for which there are:
Figure GDA0003608053100000079
wherein the content of the first and second substances,
Figure GDA0003608053100000081
for the position and velocity values observed at time t,
Figure GDA0003608053100000082
μiis the expectation of a joint Gaussian distribution, wherein
Figure GDA0003608053100000083
In order to be able to anticipate the position,
Figure GDA0003608053100000084
is a desire for speed; sigmaiIs a covariance matrix, wherein
Figure GDA0003608053100000085
Respectively corresponding covariance;
(b2) using maximum likelihood estimation algorithms for each degree of freedom
Figure GDA0003608053100000086
And
Figure GDA0003608053100000087
calculating parameters in the distribution to obtain parameter values
Figure GDA0003608053100000088
And mui，∑i
(b3) For the probability at the ith state at time t, there is the formula:
Figure GDA0003608053100000089
Figure GDA00036080531000000810
Figure GDA00036080531000000811
wherein x1Is an initial position, niIs the probability that the ith state is the initial state, ai，tIs the probability at the ith state at time t
(b4) Calculating control parameters using a Gaussian regression formula
Figure GDA00036080531000000812
And
Figure GDA00036080531000000813
comprises the following steps:
Figure GDA00036080531000000814
wherein the content of the first and second substances,
Figure GDA00036080531000000815
the speed of the track of the mechanical arm at the time t is obtained, and the track at the time t can be obtained through initial position integration
Figure GDA00036080531000000816
In the step (5), the control parameters calculated in the step (2) and the step (3) include:
Figure GDA00036080531000000817
wherein KjIs a main diagonal line of
Figure GDA00036080531000000818
Diagonal array of elements, DjFor the corresponding damping matrix, τcmdForce information for the mechanical arm;
Figure GDA00036080531000000819
the expected position and speed vector can be derived from (3); x is the number ofmsr，
Figure GDA0003608053100000091
For the current position and velocity vector, τdynThe dynamic force of the system is compensated, such as gravity, Coriolis force and the like. And outputting corresponding torque according to an impedance control formula by detecting a force signal of the arm of the user.

Claims (4)

1. A rehabilitation robot variable impedance control method based on probability motion primitives and hidden semi-Markov is characterized by comprising the following steps:
(1) recording the motion information of the upper limb on the healthy side for many times, writing the rigidity, position and speed information recorded during teaching into a vector form, comprising the following steps:
xD，t＝(x1，t，...，xd，t)T
Figure FDA0003608053090000011
kD，t＝(k1，t，...，kd，t)T
wherein D represents a degree of freedom, t represents time, xD，tIn order to be the position of the track,
Figure FDA0003608053090000012
is the velocity of the track, kD，tIs stiffness information;
(2) generalizing the rigidity recorded in the step (1) through a probability motion primitive;
(3) generalizing the data recorded in the step (1) by using a hidden semi-Markov model to generate a track, wherein parameters of the hidden semi-Markov model are estimated by an extreme likelihood estimation algorithm (Expectation-Maximization), and then control parameters are calculated by a Gaussian regression algorithm;
(4) mirroring the generalized tracks;
(5) and performing variable impedance control on the tail end of the rehabilitation robot through the mirrored track, the changed rigidity information and the multi-dimensional force sensor arranged on the mechanical arm.
2. The rehabilitation robot variable impedance control method based on probabilistic motion primitives and hidden semi-markov according to claim 1, wherein the step (2) comprises the following sub-steps:
(a1) determining a vector through the motion information extracted in the step (1)
yt＝(k1，t，k2，t，...，kd，t)T＝Ψtω+∈y
Figure FDA0003608053090000013
Wherein k isd，tMuscle stiffness data for d degrees of freedom, t 0, 1tRefers to the muscle stiffness data in step (1), omega is a weight vector, epsilonyA Gaussian distribution noise of variance sigma is expected to be 0y，φi，tFor time-dependent basis functions, for repetitive regular movements, the basis functions can be:
φi，t＝bi(z)/∑jbj(z)
wherein the content of the first and second substances,
Figure FDA0003608053090000021
where z (t) is an arbitrary monotonically increasing function of time, h is the bandwidth, ciIs the center of the ith basis function;
(a2) according to the probability motion primitive formula, there are:
Figure FDA0003608053090000022
wherein
Figure FDA0003608053090000023
Representing a Gaussian distribution, θ ═ (. mu.) ═ω，∑ω) Parameters of the probability motion primitive formula; Ψt TμωAnd Ψt T∑ωΨt+∑yRespectively represent the Gaussian distribution p (y)t(ii) a θ) expectation and variance;
(a3) for the stiffness data extracted by teaching, extracting the parameters of the model in the step (a2) by using a maximum likelihood estimation algorithm to obtain muω *，∑ω *(ii) a And order the control parameters
Figure FDA0003608053090000024
Wherein muω *，∑ω *Obtaining a value for the maximum likelihood estimation, which is the parameter θ of the model in step (a 2);
Figure FDA0003608053090000025
namely the muscle stiffness obtained by using the probability motion primitive, so as to control the mechanical arm.
3. The rehabilitation robot variable impedance control method based on probabilistic motion primitives and hidden semi-markov according to claim 2, wherein the step (3) comprises the following sub-steps:
(b1) respectively establishing a hidden semi-Markov model for each degree of freedom of the joint, wherein the hidden semi-Markov model theta can be expressed by the following parameters:
Figure FDA0003608053090000026
wherein, piiIs the probability that the ith state is the initial state, ai，jK is the total number of states, which is the probability of transitioning from state j to the next state i;
Figure FDA0003608053090000027
parameters of the probability density function for the ith state duration obeying a Gaussian distribution, μi，∑iFor the parameters of the probability density function that the ith state can be successfully observed, for this, there are:
Figure FDA0003608053090000031
wherein t is 1, 2max，
Figure FDA0003608053090000032
Eta is a constant set between 2 and 3, TmaxTo teach the total number of samples of the data vector,
at each time t of the ith state, the observed data obeys a Gaussian distribution, μi，∑iRespectively, the expectation and variance of the distribution, for which there are:
Figure FDA0003608053090000033
wherein the content of the first and second substances,
Figure FDA0003608053090000034
for the position and velocity values observed at time t,
Figure FDA0003608053090000035
μiis the expectation of a joint Gaussian distribution, wherein
Figure FDA0003608053090000036
In order to be able to anticipate the position,
Figure FDA0003608053090000037
is a desire for speed; sigmaiIs a covariance matrix, wherein
Figure FDA0003608053090000038
Respectively corresponding covariance;
(b2) using maximum likelihood estimation algorithms for each degree of freedom
Figure FDA0003608053090000039
And
Figure FDA00036080530900000310
calculating parameters in the distribution to obtain parameter values
Figure FDA00036080530900000311
And mui，∑i；
(b3) For the probability at the ith state at time t, there is the formula:
Figure FDA00036080530900000312
Figure FDA00036080530900000313
Figure FDA00036080530900000314
wherein x1Is an initial position, piiIs the probability that the ith state is the initial state, αi，tIs the probability at the ith state at time t;
(b4) calculating control parameters using a Gaussian regression formula
Figure FDA00036080530900000315
And
Figure FDA00036080530900000316
comprises the following steps:
Figure FDA0003608053090000041
wherein the content of the first and second substances,
Figure FDA0003608053090000042
the velocity of the track of the mechanical arm at the time t is integrated through an initial positionThe track at the time t can be obtained
Figure FDA0003608053090000043
4. The rehabilitation robot variable impedance control method based on probabilistic motion primitives and hidden semi-markov according to claim 3, wherein in the step (5), the adopted method is variable impedance control, and compliance control is realized by using the control parameters calculated in the steps (2) and (3) and through a corresponding strategy of the variable impedance control, wherein the variable impedance control satisfies the expression of
Figure FDA0003608053090000044
Wherein KjIs the main diagonal line of (k)1，t *，k2，t *，...，kd，t *) Diagonal array of elements, DjFor the corresponding damping matrix, τcmdForce information for the mechanical arm;
Figure FDA0003608053090000045
the desired position and velocity vector can be derived by the step (3); x is the number ofmsr，
Figure FDA0003608053090000046
For the current position and velocity vector, τdynThe dynamic force compensation system is used for compensating the dynamic force of the system, and outputting corresponding torque according to an impedance control formula by detecting a force signal of an arm of a user.
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