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

Abstract

The present invention designs a rehabilitation robot control method based on probabilistic motion primitives and hidden semi-Markov, comprising the following steps: (1) Recording the motion information of the unaffected upper limbs for multiple times, including information such as arm end stiffness and trajectory. (2) Generalize the stiffness recorded in (1) by probabilistic motion primitives. (3) Use the hidden semi-Markov model to generalize the data recorded in (1) to generate trajectories. (4) Mirror the generalized trajectory. (5) Perform variable impedance control on the end of the rehabilitation robot through the mirrored information. The present invention uses probabilistic motion primitives and hidden semi-Markov for the first time to generate the control parameters of the rehabilitation robot, which can effectively use the patient's unaffected limb to assist the rehabilitation training. By imitating the motion of the unaffected limb to control the rehabilitation robot, a better Rehabilitation training effect, while improving rehabilitation efficiency, greatly reducing the workload of rehabilitation doctors.

Description

Rehabilitation Robot Control Method Based on Probabilistic Motion Primitives and Hidden Semi-Markov

technical field

The invention belongs to the field of machine imitation learning, and relates to a control method for a rehabilitation robot, in particular to a variable impedance control method for a rehabilitation robot based on Probabilistic Motion Primitives (ProMP) and Hidden Semi-Markov (HSMM), which optimizes the control method of the rehabilitation robot. Trajectory generation under mirror control.

Background technique

Rehabilitation robots are a combination of industrial robots and medical robots, mainly to meet the needs of medical nurses and rehabilitation, assist patients with limbs or joints with disabilities, so as to help patients recover. At present, it is mainly divided into two types: wearable type (exoskeleton type) and independent type.

The invention relates to a control method of an independent rehabilitation robot, which uses the motion data of the unaffected upper limb to teach for many times, and uses the method of machine imitation learning to calculate control parameters and control the movement of the rehabilitation robot.

In machine learning, how to make the machine generalize the taught motion data to generate the required control parameters is a big problem, and common methods can be solved by using probabilistic motion primitives. The probabilistic motion primitive is improved on the basis of the motion primitive. Through the operation of probability theory, the parameter vector is expressed in the form of probability distribution; it has the advantages of adapting to new targets and easy to adjust control parameters. The present invention utilizes probabilistic motion primitives to generalize muscle stiffness data

In human-machine teaching, Hidden Markov Models are often used to analyze state sequences, which assume that the next state is only related to the current state. The hidden semi-Markov model expresses the probability of a certain state by a time probability function, which can better express the time information. Using the formula of Gaussian linear regression, generalization to the taught motion data can be achieved. The invention uses the hidden semi-Markov method to generalize the taught position, speed and other data.

For independent upper limb rehabilitation robots, impedance control is one of the commonly used control methods. Its main advantages are high flexibility, good robustness to disturbances and uncertainties, and it is a common method to achieve force control. Therefore, it is very It is suitable for use in rehabilitation scenarios to avoid secondary injury to the patient's limbs. The significance of variable impedance control is that the stiffness value can be adjusted in a timely manner.

The present invention designs a variable impedance control method for a rehabilitation robot based on probability motion primitives and hidden semi-Markov, and uses probability motion primitives and hidden semi-Markovs for the first time to generate control parameters of the rehabilitation robot, which can effectively utilize the patient's health Side limb assisted rehabilitation training, by imitating the motion of the unaffected limb to control the rehabilitation robot, can achieve better rehabilitation training effect, improve rehabilitation efficiency, and greatly reduce the workload of rehabilitation doctors.

SUMMARY OF THE INVENTION

In view of the above background, the present invention proposes a variable impedance control method for a rehabilitation robot based on probabilistic motion primitives and hidden semi-Markov.

In order to achieve the above goals, the present invention adopts the following technical scheme: a variable impedance control method for a rehabilitation robot based on probabilistic motion primitives and hidden semi-Markov, which specifically includes the following steps:

(1) Record the motion information of the unaffected upper limb for multiple times, including the stiffness and trajectory of the arm end.

(2) Generalize the stiffness recorded in (1) by probabilistic motion primitives.

(3) Use the hidden semi-Markov model to generalize the data recorded in (1) to generate trajectories. The parameters of the hidden semi-Markov model are estimated by the maximum likelihood estimation algorithm (Expectation-Maximization), and then the control parameters are calculated by the Gaussian regression algorithm.

(4) Mirror the generalized trajectory.

(5) The end of the rehabilitation robot is controlled by variable impedance through the mirrored trajectory, the changing stiffness information and the multi-dimensional force sensor installed on the robotic arm.

For the step (1), the stiffness, position and velocity information recorded during teaching are written in vector form, as follows:

x _{D, t} = (x _{1, t} , . . . , x _{d, t} ) ^T

k _D,t =(k _1,t ,...,,k _d,t ) ^T

为轨迹的速度，k_D，t为刚度信息。Among them, D represents degrees of freedom, t represents time, x _{D, t} is the position of the trajectory,

is the velocity of the trajectory, k _{D, t} is the stiffness information.

To the described step (2), the following steps are included:

(a1) Determine the vector by the motion information extracted in (1)

y _t = (k _{1, t} , k _{2, t} , ..., k _{d, t} ) T = Ψ _t ω+∈ _y

Among them, k _{d, t} is the muscle stiffness data of d degrees of freedom, t=0, 1, ..., N is the time, y _t refers to the muscle stiffness data in (1), ω is the weight vector, ∈ _y is the Gaussian distribution noise with the expectation of 0, its variance is ∑ _y , φ _{i, t} is the time-dependent basis function, for repetitive regular motion, the basis function can be made as:

φ _{i, t} = b _i (z)/∑ _j b _j (z)

in,

where z(t) is an arbitrary time monotonically increasing function, h is the bandwidth, and c _i is the center of the ith basis function

(a2) According to the probabilistic motion primitive formula, there are:

代表高斯分布，θ＝(μ_ω，∑_ω)为该概率密度函数的参数；Ψ_t ^Tμ_ω和Ψ_t ^T∑_ωΨ_t+∑_y分别代表该高斯分布p(y_t；θ)的期望与方差。in

represents the Gaussian distribution, θ=(μ _ω , ∑ _ω ) is the parameter of the probability density function; Ψ _t ^T μ _ω and Ψ _t ^T ∑ _ω Ψ _t +∑ _y represent the Gaussian distribution p(y _t ; θ), respectively Expectation and variance.

其中μ_ω ^*，∑_ω ^*为极大似然估计得出的数值，即为(a2)中模型的参数0；

即为运用概率运动原语得出的肌刚度，用以对机械臂进行控制。(a3) For the stiffness data extracted by teaching, use the maximum likelihood estimation algorithm to extract the parameters of the model in (a2) to obtain μ _ω ^* , ∑ _ω ^* ; and let the control parameters

Among them μ _ω ^* , ∑ _ω ^* is the value obtained by the maximum likelihood estimation, that is, the parameter 0 of the model in (a2);

It is the muscle stiffness obtained by using the probabilistic motion primitive to control the robotic arm.

For the step (3), the following sub-steps are included:

(b1) Establish a hidden semi-Markov model for each degree of freedom of the joint, where the hidden semi-Markov model Θ can be expressed as:

为第i个状态持续时间的概率密度函数的参数，服从高斯分布，μ_i，∑_i为第i个状态能够被成功观测到的概率密度函数的参数，对此，有：Among them, π _i is the probability that the ith state is the initial state, a _{i, j} is the probability of transitioning from state j to the next state i, and K is the total number of states;

is the parameter of the probability density function of the i-th state duration, obeying the Gaussian distribution, μ _i , ∑ _i is the parameter of the probability density function that the i-th state can be successfully observed, for this, there are:

η为设置在2-3之间的常数，T_max为示教数据向量的总采样数，where t=1, 2, ..., t _max ,

η is a constant set between 2-3, T _max is the total number of samples of the taught data vector,

In each time t of the i-th state, the observed data obeys a Gaussian distribution, and μ _i and ∑ _i are the expectation and variance of the distribution, respectively. For this, there are:

为t时刻观测到的位置与速度值，

in,

are the position and velocity values observed at time t,

为位置的期望，

为速度的期望；∑_i为协方差矩阵，其中

分别为对应的协方差；μ _i is the expectation of the joint Gaussian distribution, where

expectations for the location,

is the expectation of speed; ∑ _i is the covariance matrix, where

are the corresponding covariances, respectively;

和

分布中的参数进行计算，得出参数值

和μ_i，∑_i (b2) Using the maximum likelihood estimation algorithm, for each degree of freedom

and

The parameters in the distribution are calculated to obtain the parameter values

and μ _i , ∑ _i

(b3) For the probability of being in the i-th state at time t, there is a formula:

where x ₁ is the initial position, π _i is the probability that the i-th state is the initial state, a _{i, t} is the probability that the i-th state is at time t

和

有：(b4) Using the Gauss regression formula, calculate the control parameters

and

Have:

为机械臂的轨迹在t时刻的速度，并通过初始位置积分，即可得到在t时刻的轨迹

in,

is the velocity of the trajectory of the robotic arm at time t, and by integrating the initial position, the trajectory at time t can be obtained

To described step (5), utilize the control parameters calculated in (2) and (3), there are:

为期望的位置与速度向量，可由(3)导出；x_msr，

为当前的位置与速度向量，τ_dyn用于补偿系统的动态力，如重力和科里奥利力等。通过检测使用者手臂的力信号，根据阻抗控制的公式，输出相应的力矩。where Kj is a diagonal _matrix of (k1 _,t ^* ,k2 _,t ^* ,...,kd _,t ^* ) elements where Kj is the main diagonal, _Dj is the corresponding damping matrix, and _τcmd is the mechanical arm force information;

is the desired position and velocity vector, which can be derived from (3); x _msr ,

is the current position and velocity vector, τ _dyn is used to compensate the dynamic forces of the system, such as gravity and Coriolis force. By detecting the force signal of the user's arm, the corresponding torque is output according to the formula of impedance control.

Beneficial effects of the present invention:

The present invention uses probability motion primitives in machine learning and hidden semi-Markov to generate the control parameters of the rehabilitation robot, and uses the method of variable impedance control. Compared with the traditional method of direct data extraction and control, the present invention has higher flexibility and better protection. The patient's limbs are protected from secondary injuries, and a better rehabilitation training effect can be achieved.

Description of drawings

FIG. 1 is a flow chart of the control method of a rehabilitation robot based on probabilistic motion primitives and hidden semi-Markov in 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 of the present invention.

Detailed ways

The present invention will be further clarified below with reference to the accompanying drawings and specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present 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) Record the motion information of the unaffected upper limb for multiple times, including the stiffness and trajectory of the arm end.

(2) Generalize the stiffness recorded in (1) by probabilistic motion primitives.

(3) Use the hidden semi-Markov model to generalize the data recorded in (1) to generate trajectories. The parameters of the hidden semi-Markov model are estimated by the maximum likelihood estimation algorithm (Expectation-Maximization), and then the control parameters are calculated by the Gaussian regression algorithm.

(4) Mirror the generalized trajectory.

(5) The end of the rehabilitation robot is controlled by variable impedance through the mirrored trajectory, the changing stiffness information and the multi-dimensional force sensor installed on the robotic arm.

For the step (1), the stiffness, position and velocity information recorded during teaching are written in vector form, as follows:

x _{D, t} = (x ₁ , t, . . . , x _{d, t} ) ^T

k _D,t =(k _1,t ,...,k _d,t ) ^T

为轨迹的速度，k_D，t为刚度信息。Among them, D represents degrees of freedom, t represents time, x _{D, t} is the position of the trajectory,

is the velocity of the trajectory, k _{D, t} is the stiffness information.

To the described step (2), the following steps are included:

(a1) Through the motion information extracted in (1), determine the vector

y _t = (k _{1, t} , k _{2, t,} ..., k _{d, t} ) ^T = Ψ _t ω+∈ _y

Among them, k _{d, t} is the muscle stiffness data of d degrees of freedom, t=0, 1, ..., N is the time, y _t refers to the muscle stiffness data in (1), ω is the weight vector, ∈ _y is the Gaussian distribution noise with the expectation of 0, and its variance is ∑y, φ _{i, and t} is the time-dependent basis function. For repetitive regular motion, the basis function can be made as:

φ _{i, t} = b _i (z)/∑ _j b _j (z)

in,

where z(t) is an arbitrary time monotonically increasing function, h is the bandwidth, and c _i is the center of the ith basis function

(a2) According to the probabilistic motion primitive formula, there are:

代表高斯分布，θ＝(μ_ω，∑_ω)为该概率密度函数的参数；Ψ_t ^Tμ_ω和Ψ_t ^T∑_ωΨ_t+∑_y分别代表该高斯分布p(y_t；θ)的期望与方差。in

represents the Gaussian distribution, θ=(μ _ω , ∑ _ω ) is the parameter of the probability density function; Ψ _t ^T μ _ω and Ψ _t ^T ∑ _ω Ψ _t +∑ _y represent the Gaussian distribution p(y _t ; θ), respectively Expectation and variance.

其中μ_ω ^*，∑_ω ^*为极大似然估计得出的数值，即为(a2)中模型的参数θ；

即为运用概率运动原语得出的肌刚度，用以对机械臂进行控制。(a3) For the stiffness data extracted by teaching, use the maximum likelihood estimation algorithm to extract the parameters of the model in (a2) to obtain μ _ω ^* , ∑ _ω ^* ; and let the control parameters

Among them μ _ω ^* , ∑ _ω ^* is the value obtained by the maximum likelihood estimation, that is, the parameter θ of the model in (a2);

It is the muscle stiffness obtained by using the probabilistic motion primitive to control the robotic arm.

For the step (3), the following sub-steps are included:

(b1) Establish a hidden semi-Markov model for each degree of freedom of the joint, where the hidden semi-Markov model Θ can be expressed as:

为第i个状态持续时间的概率密度函数的参数，服从高斯分布，μ_i，∑_i为第i个状态能够被成功观测到的概率密度函数的参数，对此，有：Among them, π _i is the probability that the ith state is the initial state, a _{i, j} is the probability of transitioning from state j to the next state i, and K is the total number of states;

is the parameter of the probability density function of the i-th state duration, obeying the Gaussian distribution, μ _i , ∑ _i is the parameter of the probability density function that the i-th state can be successfully observed, for this, there are:

η为设置在2-3之间的常数，T_max为示教数据向量的总采样数，where t=1, 2, ..., t _max ,

η is a constant set between 2-3, T _max is the total number of samples of the taught data vector,

In each time t of the i-th state, the observed data obeys a Gaussian distribution, and μ _i and ∑ _i are the expectation and variance of the distribution, respectively. For this, there are:

为t时刻观测到的位置与速度值，

in,

are the position and velocity values observed at time t,

为位置的期望，

为速度的期望；∑_i为协方差矩阵，其中

分别为对应的协方差；μ _i is the expectation of the joint Gaussian distribution, where

expectations for the location,

is the expectation of speed; ∑ _i is the covariance matrix, where

are the corresponding covariances, respectively;

和

分布中的参数进行计算，得出参数值

和μ_i，∑_i (b2) Using the maximum likelihood estimation algorithm, for each degree of freedom

and

The parameters in the distribution are calculated to obtain the parameter values

and μ _i , ∑ _i

(b3) For the probability of being in the i-th state at time t, there is a formula:

where x ₁ is the initial position, π _i is the probability that the i-th state is the initial state, a _{i, t} is the probability that the i-th state is at time t

和

有：(b4) Using the Gauss regression formula, calculate the control parameters

and

Have:

为机械臂的轨迹在t时刻的速度，并通过初始位置积分，即可得到在t时刻的轨迹

in,

is the velocity of the trajectory of the robotic arm at time t, and by integrating the initial position, the trajectory at time t can be obtained

To described step (5), utilize the control parameters calculated in (2) and (3), there are:

元素的对角阵，D_j为相应的阻尼矩阵，τ_cmd为机械臂的力信息；

为期望的位置与速度向量，可由(3)导出；x_msr，

为当前的位置与速度向量，τ_dyn用于补偿系统的动态力，如重力和科里奥利力等。通过检测使用者手臂的力信号，根据阻抗控制的公式，输出相应的力矩。where K _j is the dominant diagonal

The diagonal matrix of elements, D _j is the corresponding damping matrix, τ _cmd is the force information of the manipulator;

is the desired position and velocity vector, which can be derived from (3); x _msr ,

is the current position and velocity vector, τ _dyn is used to compensate the dynamic forces of the system, such as gravity and Coriolis force. By detecting the force signal of the user's arm, the corresponding torque is output according to the formula of impedance control.

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:

x_D，t＝(x_1，t，...，x_d，t)^T

k_D，t＝(k_1，t，...，k_d，t)^T

wherein D represents a degree of freedom, t represents time, x_D，tIn order to be the position of the track,

is the velocity of the track, k_D，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)

y_t＝(k_1，t，k_2，t，...，k_d，t)^T＝Ψ_tω+∈_y

Wherein k is_d，tMuscle stiffness data for d degrees of freedom, t 0, 1_tRefers to the muscle stiffness data in step (1), omega is a weight vector, epsilon_yA Gaussian distribution noise of variance sigma is expected to be 0_y，φ_i，tFor time-dependent basis functions, for repetitive regular movements, the basis functions can be:

φ_i，t＝b_i(z)/∑_jb_j(z)

wherein,

where z (t) is an arbitrary monotonically increasing function of time, h is the bandwidth, c_iIs the center of the ith basis function;

(a2) according to the probability motion primitive formula, there are:

wherein

Representing a Gaussian distribution, θ ═ (. mu.) ═_ω，∑_ω) Parameters of the probability motion primitive formula; Ψ_t ^Tμ_ωAnd Ψ_t ^T∑_ωΨ_t+∑_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 mu_ω ^*，∑_ω ^*(ii) a And order the control parameters

Wherein mu_ω ^*，∑_ω ^*Obtaining a value for the maximum likelihood estimation, which is the parameter θ of the model in step (a 2);

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:

wherein, pi_iIs the probability that the ith state is the initial state, a_i，jK is the total number of states, which is the probability of transitioning from state j to the next state i;

parameters of the probability density function for the ith state duration obeying a Gaussian distribution, μ_i，∑_iFor the parameters of the probability density function that the ith state can be successfully observed, for this, there are:

wherein t is 1, 2_max，

Eta is a constant set between 2 and 3, T_maxTo 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, μ_i，∑_iRespectively, the expectation and variance of the distribution, for which there are:

wherein,

for the position and velocity values observed at time t,

μ_iis the expectation of a joint Gaussian distribution, wherein

In order to be able to anticipate the position,

is a desire for speed; sigma_iIs a covariance matrix, wherein

Respectively corresponding covariance;

(b2) using maximum likelihood estimation algorithms for each degree of freedom

And

calculating parameters in the distribution to obtain parameter values

And mu_i，∑_i；

(b3) For the probability at the ith state at time t, there is the formula:

wherein x₁Is an initial position, pi_iIs the probability that the ith state is the initial state, α_i，tIs the probability at the ith state at time t;

(b4) calculating control parameters using a Gaussian regression formula

And

comprises the following steps:

wherein,

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

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

Wherein K_jIs the main diagonal line of (k)_1，t ^*，k_2，t ^*，...，k_d，t ^*) Diagonal array of elements, D_jFor the corresponding damping matrix, τ_cmdForce information for the mechanical arm;

the desired position and velocity vector can be derived by the step (3); x is the number of_msr，

For the current position and velocity vector, τ_dynThe 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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