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CN117325169A - A control method for lower limb rehabilitation robot with initial state learning - Google Patents

A control method for lower limb rehabilitation robot with initial state learning Download PDF

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CN117325169A
CN117325169A CN202311388890.3A CN202311388890A CN117325169A CN 117325169 A CN117325169 A CN 117325169A CN 202311388890 A CN202311388890 A CN 202311388890A CN 117325169 A CN117325169 A CN 117325169A
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CN117325169B (en
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黄丽敏
张敏
贺敏
郭毅锋
范大坤
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Abstract

本发明公开了一种带初态学习的下肢康复机器人控制方法,涉及辅助医疗康复机器人控制技术领域,包括:构建下肢康复机器人的迭代学习控制器;构建输出误差模型;采集下肢康复机器人的髋关节与膝关节的离散数据信息;构建迭代学习控制律的计算方程,并进行迭代学习,得到最终的迭代学习控制律作为第一系统输入条件;构建初始偏差的计算方程,并进行迭代学习,得到最终的初始偏差作为第二系统输入条件;将第一系统输入条件和第二系统输入条件输入迭代学习控制器,输出得到带初态学习的控制策略。本发明能够很好地处理因起步位置不一或重复性训练而导致的初态偏移问题,修正初始偏差,使下肢康复机器人系统在有初态偏移时输出轨迹也能跟踪上期望轨迹。

The invention discloses a control method for a lower limb rehabilitation robot with initial state learning, and relates to the technical field of auxiliary medical rehabilitation robot control. It includes: constructing an iterative learning controller of the lower limb rehabilitation robot; constructing an output error model; and collecting hip joints of the lower limb rehabilitation robot. and the discrete data information of the knee joint; construct the calculation equation of the iterative learning control law, and perform iterative learning, and obtain the final iterative learning control law as the first system input condition; construct the calculation equation of the initial deviation, and perform iterative learning to obtain the final The initial deviation is used as the input condition of the second system; the input condition of the first system and the input condition of the second system are input into the iterative learning controller, and the control strategy with initial state learning is output. The invention can well handle the problem of initial state deviation caused by different starting positions or repetitive training, correct the initial deviation, and enable the output trajectory of the lower limb rehabilitation robot system to track the desired trajectory even when there is an initial deviation.

Description

一种带初态学习的下肢康复机器人控制方法A control method for lower limb rehabilitation robot with initial state learning

技术领域Technical field

本发明涉及辅助医疗康复机器人控制技术领域,具体而言,涉及一种带初态学习的下肢康复机器人控制方法。The invention relates to the technical field of auxiliary medical rehabilitation robot control, and specifically to a control method for a lower limb rehabilitation robot with initial state learning.

背景技术Background technique

目前,脑损伤、脊髓损伤患者数量呈增长趋势,但多数患者在挽救生命后遗留了步行功能障碍的问题。针对患者步态康复,传统治疗为一名医护人员辅助一位患者进行高强度、重复性的步态训练,康复效果仅为肉眼评判,无法得到实时反馈数据,且康复治疗师人员严重不足。康复机器人作为医工结合的产物,不仅能够实时反馈步态数据、量化康复指标,并且适用于高强度、重复性训练工作,解放康复治疗师的双手。下肢康复机器人通过辅助患者进行重复性步态功能训练,刺激并重塑神经系统,使患者恢复正常行走能力,提高脑卒中、脊髓损伤、脑外伤、下肢肌肉等骨骼相关疾病患者的步行功能。At present, the number of patients with brain injuries and spinal cord injuries is increasing, but most patients still have walking dysfunction after saving their lives. For patients' gait rehabilitation, traditional treatment requires a medical staff to assist a patient in performing high-intensity and repetitive gait training. The rehabilitation effect can only be judged by the naked eye, and real-time feedback data cannot be obtained, and there is a serious shortage of rehabilitation therapists. As a product of the combination of medicine and engineering, rehabilitation robots can not only feed back gait data and quantify rehabilitation indicators in real time, but are also suitable for high-intensity and repetitive training work, freeing the hands of rehabilitation therapists. Lower limb rehabilitation robots assist patients in repetitive gait function training, stimulate and reshape the nervous system, restore patients to normal walking ability, and improve the walking function of patients with skeletal-related diseases such as stroke, spinal cord injury, brain trauma, and lower limb muscles.

针对下肢康复机器人系统的重复性、非线性及模型不够精确等特点,迭代学习控制算法因其能在重复中学习、适用于非线性及不需要精确的模型等优点而被广泛应用。如利用迭代学习控制算法,建立下肢康复机器人系统的随动控制模型,跟踪下肢髋关节与膝关节的期望轨迹,来提高人机系统的随动性能;超前采样时间迭代学习的下肢康复机器人轨迹跟踪控制方法;无模型自适应迭代学习控制算法;自适应迭代学习控制算法等等。In view of the repeatability, nonlinearity and inaccurate model of the lower limb rehabilitation robot system, the iterative learning control algorithm is widely used because it can learn through repetition, is suitable for nonlinearity and does not require accurate models, and is widely used. For example, the iterative learning control algorithm is used to establish the follow-up control model of the lower limb rehabilitation robot system and track the expected trajectories of the lower limb hip and knee joints to improve the follow-up performance of the human-machine system; iterative learning of the lower limb rehabilitation robot trajectory tracking in advance of the sampling time Control method; model-free adaptive iterative learning control algorithm; adaptive iterative learning control algorithm, etc.

但是上述控制方法均是在初始状态与期望初始状态一致的条件下进行的,没有考虑初态偏移的情况,若初始状态存在误差,随着迭代次数的增加,虽然最终的跟踪曲线走势与期望目标轨迹大致相同,但是始终与期望目标轨迹存在偏差,控制效果不佳,此种情况非常容易对患者造成二次伤害。However, the above control methods are all carried out under the condition that the initial state is consistent with the expected initial state, and the initial state deviation is not considered. If there is an error in the initial state, as the number of iterations increases, although the final tracking curve trend is consistent with the expected The target trajectory is roughly the same, but there is always a deviation from the expected target trajectory, and the control effect is poor. This situation can easily cause secondary harm to the patient.

发明内容Contents of the invention

本发明在于一种带初态学习的下肢康复机器人迭代学习控制方法,解决患者利用下肢康复机器人系统训练时存在的初始角度偏移、系统收敛速度低等问题,有效地实现下肢康复机器人系统在有初始误差的情况下,依然能够快速准确地跟踪上期望运动轨迹,提高康复效果。The invention is an iterative learning control method for a lower limb rehabilitation robot with initial state learning, which solves the problems of initial angle deviation and low system convergence speed when patients use the lower limb rehabilitation robot system for training, and effectively realizes the lower limb rehabilitation robot system with In the case of initial errors, the desired motion trajectory can still be tracked quickly and accurately, improving the rehabilitation effect.

本发明采取的技术方案如下:The technical solutions adopted by the present invention are as follows:

一种带初态学习的下肢康复机器人控制方法,包括以下步骤:A control method for lower limb rehabilitation robots with initial state learning, including the following steps:

S1、构建下肢康复机器人动力学方程 S1. Construct the dynamic equation of lower limb rehabilitation robot

根据下肢康复机器人动力学方程构建下肢康复机器人的迭代学习控制器Constructing an iterative learning controller for lower limb rehabilitation robots based on the dynamic equations of lower limb rehabilitation robots

其中,为xk(t)的导数,xk(t)表示第k次迭代时的系统状态,uk(t)表示第k次迭代时的系统输入,yk(t)表示第k次迭代时的系统输出;in, is the derivative of x k (t), x k (t) represents the system state at the k-th iteration, u k (t) represents the system input at the k-th iteration, y k (t) represents the k-th iteration system output;

D(θ)是惯性矩阵;是离心力和科里奥利力矩阵;G(θ)是重力矩阵;Tθ表示关节力矩矩阵;Td为误差和扰动;/>为下肢关节角度,θ1、θ2分别为髋关节角度和膝关节角度;/>为下肢关节角速度,/>分别为髋关节角速度继和膝关节角速度;/>为下肢关节角加速度,/>分别为髋关节角加速度和膝关节角加速度;D(θ) is the inertia matrix; is the centrifugal force and Coriolis force matrix; G(θ) is the gravity matrix; T θ represents the joint moment matrix; T d is the error and disturbance;/> is the joint angle of the lower limb, θ 1 and θ 2 are the hip joint angle and knee joint angle respectively;/> is the joint angular velocity of the lower limbs,/> are the hip joint angular velocity and knee joint angular velocity respectively;/> is the joint angular acceleration of the lower limbs,/> are the hip joint angular acceleration and knee joint angular acceleration respectively;

S2、根据下肢康复机器人的目标轨迹和下肢康复机器人的控制输出构建输出误差模型;S2. Construct an output error model based on the target trajectory of the lower limb rehabilitation robot and the control output of the lower limb rehabilitation robot;

S3、采集下肢康复机器人的髋关节与膝关节的离散数据信息,包括不同时间点下肢康复机器人的下肢关节角度数据;S3. Collect discrete data information of the hip joint and knee joint of the lower limb rehabilitation robot, including lower limb joint angle data of the lower limb rehabilitation robot at different time points;

S4、根据下肢康复机器人的下肢关节角度,基于迭代学习控制器和输出误差模型得到迭代学习控制律的计算方程,基于迭代学习控制律的计算方程进行迭代学习,达到迭代次数后,得到最终的迭代学习控制律作为第一系统输入条件;S4. According to the lower limb joint angle of the lower limb rehabilitation robot, the calculation equation of the iterative learning control law is obtained based on the iterative learning controller and the output error model. Based on the calculation equation of the iterative learning control law, iterative learning is performed. After the number of iterations is reached, the final iteration is obtained. Learning the control law as the first system input condition;

S5、根据下肢康复机器人的下肢关节初态角度,基于迭代学习控制器和输出误差模型得到初始偏差的计算方程,基于初始偏差的计算方程进行迭代学习,达到迭代次数后,得到最终的初始偏差作为第二系统输入条件;S5. According to the initial angle of the lower limb joint of the lower limb rehabilitation robot, the calculation equation of the initial deviation is obtained based on the iterative learning controller and the output error model. Based on the calculation equation of the initial deviation, iterative learning is performed. After the number of iterations is reached, the final initial deviation is obtained as Second system input conditions;

S6、将第一系统输入条件和第二系统输入条件输入迭代学习控制器,输出得到控制下肢康复机器人运行的带初态学习的控制策略。S6. Input the first system input condition and the second system input condition into the iterative learning controller, and output the control strategy with initial state learning that controls the operation of the lower limb rehabilitation robot.

在本发明的一较佳实施方式中,输出误差模型为:In a preferred implementation of the present invention, the output error model is:

ek(t)=yd(t)-yk(t)e k (t)=y d (t)-y k (t)

其中,ek(t)表示下肢康复机器人第k次迭代时的跟踪误差,yd(t)表示下肢康复机器人的目标轨迹,yk(t)表示下肢康复机器人系统第k次运行的控制输出。Among them, e k (t) represents the tracking error of the lower limb rehabilitation robot in the k-th iteration, y d (t) represents the target trajectory of the lower limb rehabilitation robot, and y k (t) represents the control output of the k-th operation of the lower limb rehabilitation robot system. .

在本发明的一较佳实施方式中,步骤S3中,需利用分段三次多项式对下肢康复机器人的髋关节与膝关节的离散数据信进行步态数据拟合,得到两关节的连续曲线函数。In a preferred embodiment of the present invention, in step S3, it is necessary to use piecewise cubic polynomials to fit the discrete data of the hip joint and knee joint of the lower limb rehabilitation robot to gait data to obtain continuous curve functions of the two joints.

在本发明的一较佳实施方式中,步骤S4中得到的迭代学习控制律的计算方程为:In a preferred embodiment of the present invention, the calculation equation of the iterative learning control law obtained in step S4 is:

其中,ek+1(t)与分别表示下肢康复机器人系统第k+1次迭代时的跟踪误差及其误差导数,K和L是具有相应维数的迭代学习增益矩阵,uk+1(t)为第k+1次迭代学习后的系统输入,uk(t)为第k次迭代学习时的系统输入,当k=0时,uk(t)表示最初未迭代学习时的系统输入,系统输入包括下肢髋关节与膝关节的力矩。Among them, e k+1 (t) and Respectively represent the tracking error and its error derivative at the k+1 iteration of the lower limb rehabilitation robot system, K and L are iterative learning gain matrices with corresponding dimensions, u k+1 (t) is the k+1 iterative learning After the system input, u k (t) is the system input during the k-th iterative learning. When k = 0, u k (t) represents the system input during the initial non-iterative learning. The system input includes the hip joint and knee of the lower limbs. joint torque.

在本发明的一较佳实施方式中,步骤S4具体包括以下步骤:In a preferred embodiment of the present invention, step S4 specifically includes the following steps:

S41、采集下肢康复机器人第k+1次运行时的下肢关节角度数据;S41. Collect lower limb joint angle data during the k+1th run of the lower limb rehabilitation robot;

S42、基于下肢康复机器人的目标轨迹,下肢康复机器人第k次运行的控制输出和输出误差模型,计算下肢康复机器人系统第k+1次迭代时的跟踪误差ek+1(t)及其误差导数 S42. Based on the target trajectory of the lower limb rehabilitation robot, the control output and output error model of the kth operation of the lower limb rehabilitation robot, calculate the tracking error e k+1 (t) and its error in the k+1 iteration of the lower limb rehabilitation robot system. Derivative

S43、设置迭代学习增益矩阵K和L;S43. Set the iterative learning gain matrices K and L;

S44、将增益矩阵K和L,下肢康复机器人系统第k+1次迭代时的跟踪误差ek+1(t)及其误差导数以及第k次迭代学习时的系统输入uk(t)代入第一迭代学习控制律的计算方程,得到迭代学习控制律;S44. Combine the gain matrices K and L, the tracking error e k+1 (t) of the lower limb rehabilitation robot system at the k+1 iteration and its error derivative And the system input u k (t) during the k-th iterative learning is substituted into the calculation equation of the first iterative learning control law to obtain the iterative learning control law;

S45、循环步骤S41~S44,直至达到指定迭代次数结束,即得到最终的迭代学习控制律,将该最终的迭代学习控制律作为第一系统输入条件,在循环过程中,每次迭代用到的下肢关节角度均不同。S45. Loop steps S41 to S44 until the specified number of iterations is reached, that is, the final iterative learning control law is obtained. The final iterative learning control law is used as the first system input condition. During the loop process, each iteration uses The joint angles of the lower limbs are all different.

在本发明的一较佳实施方式中,步骤S5中得到的初始偏差的计算方程为:In a preferred embodiment of the present invention, the calculation equation of the initial deviation obtained in step S5 is:

xk+1(0)=xk(0)+M(0)Lek+1(0)x k+1 (0)=x k (0)+M(0)Le k+1 (0)

其中,xk+1(0)为系统第k+1次的迭代初态,xk(0)为系统第k次的迭代初态,M(0)为t=0时所得的值,L为系统迭代学习增益矩阵,ek+1(0)为系统第k+1次的迭代跟踪误差初值。Among them, x k+1 (0) is the k+1 iteration initial state of the system, x k (0) is the k-th iteration initial state of the system, and M (0) is when t=0 The obtained value, L is the iterative learning gain matrix of the system, and e k+1 (0) is the initial value of the k+1 iteration tracking error of the system.

在本发明的一较佳实施方式中,步骤S5具体包括以下步骤:In a preferred embodiment of the present invention, step S5 specifically includes the following steps:

S51、采集下肢康复机器人第k+1次运行时的迭代初态角度;S51. Collect the iteration initial state angle during the k+1th run of the lower limb rehabilitation robot;

S52、基于下肢康复机器人的目标轨迹,下肢康复机器人第k次运行的控制输出和输出误差模型,计算下肢康复机器人系统第k+1次的迭代跟踪误差初值;S52. Based on the target trajectory of the lower limb rehabilitation robot, the control output and output error model of the kth operation of the lower limb rehabilitation robot, calculate the initial value of the k+1 iteration tracking error of the lower limb rehabilitation robot system;

S53、设置迭代学习增益矩阵L;S53. Set the iterative learning gain matrix L;

S54、将增益矩阵L,下肢康复机器人系统第k+1次的迭代跟踪误差初值,以及第k+1次运行时的迭代初态角度代入初始偏差的计算方程,输出得到下肢康复机器人系统的第k+1次迭代得到的初始偏差;S54. Substitute the gain matrix L, the initial value of the k+1 iteration tracking error of the lower limb rehabilitation robot system, and the iterative initial state angle at the k+1th run into the calculation equation of the initial deviation, and output the result of the lower limb rehabilitation robot system. The initial deviation obtained at the k+1 iteration;

S55、循环步骤S51~S54,直至达到指定迭代次数结束,即得到最终的初始偏差,并作为第二系统输入条件,在每次迭代用到的下肢关节初态角度均不同。S55. Loop steps S51 to S54 until the specified number of iterations is reached. The final initial deviation is obtained and used as the input condition of the second system. The initial angles of the lower limb joints used in each iteration are different.

与现有技术相比,本发明的有益效果是:Compared with the prior art, the beneficial effects of the present invention are:

为带初态学习的迭代学习控制方法,能够很好地处理因起步位置不一或重复性训练而导致的初态偏移问题,修正初始偏差,使下肢康复机器人系统在有初态偏移时输出轨迹也能跟踪上期望轨迹,降低因初值偏移而导致的二次伤害,提升用户的体验感。It is an iterative learning control method with initial state learning, which can well handle the problem of initial state deviation caused by different starting positions or repetitive training, correct the initial deviation, and make the lower limb rehabilitation robot system when there is an initial state deviation. The output trajectory can also track the desired trajectory, reducing secondary damage caused by initial value deviation and improving the user experience.

为使本发明的上述目的、特征和优点能更明显易懂,下文特举本发明实施例,并配合所附附图,作详细说明如下。In order to make the above-mentioned objects, features and advantages of the present invention more obvious and understandable, embodiments of the present invention are given below and described in detail with reference to the accompanying drawings.

附图说明Description of drawings

为了更清楚地说明本发明实施例的技术方案,下面将对实施例中所需要使用的附图作简单地介绍,应当理解,以下附图仅示出了本发明的某些实施例,因此不应被看作是对范围的限定,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他相关的附图。In order to explain the technical solutions of the embodiments of the present invention more clearly, the drawings required to be used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and therefore do not It should be regarded as a limitation of the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without exerting creative efforts.

图1为本发明中使用的下肢康复机器人系统模型图;Figure 1 is a model diagram of the lower limb rehabilitation robot system used in the present invention;

图2为本发明一种带初态学习的下肢康复机器人控制框图;Figure 2 is a control block diagram of a lower limb rehabilitation robot with initial state learning according to the present invention;

图3为本发明中带初态学习的迭代学习控制的下肢髋关节与膝关节角度跟踪误差变化图;Figure 3 is a diagram showing changes in the tracking error of the hip joint and knee joint angles of the lower limbs using iterative learning control with initial state learning in the present invention;

图4为本发明中20次迭代后的下肢髋关节与膝关节的角度轨迹跟踪图及角度误差曲线图。Figure 4 is the angular trajectory tracking diagram and angle error curve diagram of the hip joint and knee joint of the lower limb after 20 iterations in the present invention.

具体实施方式Detailed ways

为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, rather than all embodiments.

请参照图1和图2,本发明提供了一种带初态学习的下肢康复机器人控制方法,具体包括如下步骤:Please refer to Figures 1 and 2. The present invention provides a lower limb rehabilitation robot control method with initial state learning, which specifically includes the following steps:

步骤1:采集人体下肢髋关节O与膝关节P的离散数据信息,利用分段三次多项式对它们进行数据拟合,得到两关节的曲线函数,即公式(1)与公式(2),并对拟合后的曲线函数进行误差分析,若误差太大,则重新进行数据拟合,传统的拟合方式为一个三角函数多项式,拟合较粗糙,本发明是用分段多项式进行拟合,误差较之前更低。通过误差分析,保证了髋关节与膝关节的拟合函数适用于下肢康复机器人系统轨迹跟踪目标曲线。Step 1: Collect the discrete data information of the hip joint O and knee joint P of the human lower limbs, use piecewise cubic polynomials to fit the data, and obtain the curve functions of the two joints, namely formula (1) and formula (2), and calculate The fitted curve function is subjected to error analysis. If the error is too large, data fitting is performed again. The traditional fitting method is a trigonometric function polynomial, and the fitting is rough. The present invention uses piecewise polynomials for fitting, and the error lower than before. Through error analysis, it is ensured that the fitting functions of the hip joint and knee joint are suitable for the trajectory tracking target curve of the lower limb rehabilitation robot system.

其中,t表示时间,下肢关节角度包括髋关节角度和膝关节角度,θ1表示髋关节角度,θ2表示膝关节角度。Among them, t represents time, the joint angle of the lower limb includes the hip joint angle and the knee joint angle, θ 1 represents the hip joint angle, and θ 2 represents the knee joint angle.

步骤2:建立下肢康复机器人系统模型,如附图1所示,O、P分别代表髋关节和膝关节,规定水平向右为x轴正方向;垂直向下为y轴正方向;两轴交点O表示坐标原点,也即髋关节;P表示膝关节;l1与l2分别表示大腿连杆和小腿连杆的长度;A与B分别为两连杆质心位置;d1与d2分别为连杆质心到髋关节与膝关节的长度;θ1与θ2分别为髋关节与膝关节的角度;根据正运动学及逆运动学得到下肢康复机器人系统模型的动力学方程如式(3)所示,并推出下肢康复机器人系统模型的系统状态方程如式(4)所示。Step 2: Establish a lower limb rehabilitation robot system model, as shown in Figure 1. O and P represent the hip joint and knee joint respectively. It is stipulated that horizontally to the right is the positive direction of the x-axis; vertically downward is the positive direction of the y-axis; the intersection of the two axes O represents the coordinate origin, that is, the hip joint; P represents the knee joint; l 1 and l 2 represent the lengths of the thigh link and calf link respectively; A and B are the positions of the center of mass of the two links respectively; d 1 and d 2 are respectively The length from the center of mass of the connecting rod to the hip joint and knee joint; θ 1 and θ 2 are the angles of the hip joint and knee joint respectively; according to the forward kinematics and inverse kinematics, the dynamic equation of the lower limb rehabilitation robot system model is obtained as Equation (3) is shown, and the system state equation of the lower limb rehabilitation robot system model is derived as shown in Equation (4).

其中, in,

D(θ)是惯性矩阵;是离心力和科里奥利力矩阵;G(θ)是重力矩阵;u(t)表示关节力矩矩阵;Td为误差和扰动;/>为下肢关节角度,包括髋关节角度θ1与膝关节角度θ2;/>为下肢关节角速度,包括髋关节角速度/>与膝关节角速度/>为下肢关节角加速度,包括髋关节角加速度/>与膝关节角加速度/> D(θ) is the inertia matrix; is the centrifugal force and Coriolis force matrix; G(θ) is the gravity matrix; u(t) represents the joint moment matrix; T d is the error and disturbance;/> is the joint angle of the lower limb, including the hip joint angle θ 1 and the knee joint angle θ 2 ;/> is the joint angular velocity of the lower limbs, including the hip joint angular velocity/> and knee joint angular velocity/> is the joint angular acceleration of the lower limbs, including the hip joint angular acceleration/> and knee joint angular acceleration/>

步骤3:针对下肢康复机器人系统存在初态误差而导致跟踪不上期望轨迹的问题设计迭代学习控制器,旨在实现下肢康复机器人系统在有初态偏移的情况下,实际输出轨迹仍能快速准确地跟踪上目标曲线。迭代学习控制器根据式(4)得到,如式(5)所示。Step 3: Design an iterative learning controller for the problem that the lower limb rehabilitation robot system cannot track the expected trajectory due to the initial state error. It aims to realize that the actual output trajectory of the lower limb rehabilitation robot system can still be fast even if there is an initial state deviation. Accurately track the upper target curve. The iterative learning controller is obtained according to equation (4), as shown in equation (5).

其中,下标k表示下肢康复机器人系统的第k次迭代学习控制,为xk(t)的导数,xk(t)表示第k次迭代时的系统状态,即髋关节与膝关节的角度与角速度,uk(t)表示第k次迭代时的系统输入,yk(t)表示第k次迭代时的系统输出。Among them, the subscript k represents the k-th iteration learning control of the lower limb rehabilitation robot system, is the derivative of x k (t), x k (t) represents the system state at the k-th iteration, that is, the angle and angular velocity of the hip joint and knee joint, u k (t) represents the system input at the k-th iteration, y k (t) represents the system output at the k-th iteration.

步骤4:构建输出误差模型如式(6)所示:Step 4: Construct the output error model as shown in Equation (6):

ek(t)=yd(t)-yk(t) (6)e k (t)=y d (t)-y k (t) (6)

其中,ek(t)表示下肢康复机器人系统第k次迭代时的跟踪误差,表示下肢康复机器人系统的目标轨迹,此处目标轨迹曲线已在步骤1中给出,即公式(1)与公式(2),yk(t)表示下肢康复机器人系统第k次运行时的控制输出,两者在步骤2与步骤3中均给出。Among them, e k (t) represents the tracking error of the lower limb rehabilitation robot system in the k-th iteration, Represents the target trajectory of the lower limb rehabilitation robot system. The target trajectory curve here has been given in step 1, that is, formula (1) and formula (2). y k (t) represents the control of the lower limb rehabilitation robot system during the kth run. The output, both given in steps 2 and 3.

步骤5:设计第一迭代学习控制律作为系统输入:Step 5: Design the first iterative learning control law as system input:

其中,ek+1(t)与分别表示下肢康复机器人系统第k+1次迭代时的跟踪误差及其误差导数,K和L是具有相应维数的迭代学习增益矩阵,uk+1(t)为第k+1次迭代学习后的系统输入,uk(t)为第k次迭代学习时的系统输入,当k=0时,uk(t)表示最初未迭代学习时的系统输入,系统输入包括下肢髋关节与膝关节的力矩。Among them, e k+1 (t) and Respectively represent the tracking error and its error derivative at the k+1 iteration of the lower limb rehabilitation robot system, K and L are iterative learning gain matrices with corresponding dimensions, u k+1 (t) is the k+1 iterative learning After the system input, u k (t) is the system input during the k-th iterative learning. When k = 0, u k (t) represents the system input during the initial non-iterative learning. The system input includes the hip joint and knee of the lower limbs. joint torque.

下面采用迭代学习控制律进行控制,保证下肢康复机器人系统能够跟踪上目标轨迹,具体过程如下:The following uses an iterative learning control law for control to ensure that the lower limb rehabilitation robot system can track the target trajectory. The specific process is as follows:

步骤5.1:采集下肢康复机器人第k+1次运行时的下肢关节角度θ1(k+1)、θ2(k+1)Step 5.1: Collect the lower limb joint angles θ 1(k+1) and θ 2(k+1) during the k+1th operation of the lower limb rehabilitation robot;

步骤5.2:根据式(6)推出ek+1(t)=yd(t)-yk+1(t),其中已在步骤1中给出,计算下肢康复机器人系统第k+1次迭代时的跟踪误差ek+1(t)及其误差导数/> Step 5.2: According to equation (6), derive e k+1 (t) = y d (t)-y k+1 (t), where As given in step 1, calculate the tracking error e k+1 (t) and its error derivative at the k+1 iteration of the lower limb rehabilitation robot system/>

步骤5.3:设置迭代学习增益矩阵K和L;Step 5.3: Set the iterative learning gain matrices K and L;

步骤5.4:将步骤5.3中增益矩阵K和L、步骤5.2中下肢康复机器人系统第k+1次迭代时的跟踪误差ek+1(t)及其误差导数以及第k次迭代学习时的系统输入uk(t)代入式(7),得到迭代学习控制律;Step 5.4: Combine the gain matrices K and L in step 5.3, the tracking error e k+1 (t) of the lower limb rehabilitation robot system at the k+1 iteration in step 5.2 and its error derivative And the system input u k (t) during the k-th iterative learning is substituted into equation (7) to obtain the iterative learning control law;

步骤5.5:循环以上步骤,直至达到所指定迭代次数结束,即得到最终的迭代学习控制律uk+1(t),将最终的迭代学习控制律uk+1(t)作为第一系统输入条件,在循环过程中,每次迭代用到的下肢关节角度均不同。Step 5.5: Loop the above steps until the specified number of iterations is reached, that is, the final iterative learning control law u k+1 (t) is obtained, and the final iterative learning control law u k+1 (t) is used as the first system input Condition, during the loop process, the lower limb joint angles used in each iteration are different.

步骤6:在运行步骤5的同时,对下肢康复机器人系统每次迭代的初始状态(即t=0)也采用初始偏差进行学习,保证下肢康复机器人系统在初态偏移的情况下依然能够跟踪上目标轨迹曲线。构建初始偏差的计算方程为:Step 6: While running step 5, the initial state of each iteration of the lower limb rehabilitation robot system (i.e. t=0) is also learned using the initial deviation to ensure that the lower limb rehabilitation robot system can still track even if the initial state shifts. upper target trajectory curve. The calculation equation to construct the initial deviation is:

xk+1(0)=xk(0)+M(0)Lek+1(0) (8)x k+1 (0)=x k (0)+M(0)Le k+1 (0) (8)

其中,xk+1(0)为系统第k+1次的迭代初态,xk(0)为系统第k次的迭代初态,M(0)为t=0时所得的值,L为系统迭代学习增益矩阵,ek+1(0)为系统第k+1次的迭代跟踪误差初值。Among them, x k+1 (0) is the k+1 iteration initial state of the system, x k (0) is the k-th iteration initial state of the system, and M (0) is when t=0 The obtained value, L is the iterative learning gain matrix of the system, and e k+1 (0) is the initial value of the k+1 iteration tracking error of the system.

具体迭代过程如下:The specific iteration process is as follows:

步骤6.1:采集下肢康复机器人第k+1次运行时的迭代初态角度θ1(k+1)(0)、θ2(k+1)(0);Step 6.1: Collect the iterative initial state angles θ 1(k+1)(0) and θ 2(k+1) (0) during the k+1th run of the lower limb rehabilitation robot;

步骤6.2:根据式(6)推出ek+1(0)=yd(0)-yk+1(0),其中yd(t)已在步骤1中给出,计算下肢康复机器人系统第k+1次的迭代跟踪误差初值ek+1(0);Step 6.2: According to equation (6), derive e k+1 (0)=y d (0)-y k+1 (0), where y d (t) has been given in step 1. Calculate the initial value of the k+1 iteration tracking error e k+1 (0) of the lower limb rehabilitation robot system;

步骤6.3:设置迭代初态学习增益矩阵L;Step 6.3: Set the iterative initial state learning gain matrix L;

步骤6.4:将M(0)、步骤6.3中的增益矩阵L、步骤6.2中下肢康复机器人系统第k+1次的迭代跟踪误差初值ek+1(0),以及系统第k次的迭代初值xk(0)代入方程(8),得到系统第k+1次迭代得到的初始偏差xk+1(0);Step 6.4: Combine M(0), the gain matrix L in step 6.3, the initial tracking error value e k+1 (0) of the k+1 iteration of the lower limb rehabilitation robot system in step 6.2, and the k-th iteration of the system. The initial value x k (0) is substituted into equation (8) to obtain the initial deviation x k+1 (0) obtained at the k+1 iteration of the system;

步骤6.5:循环以上步骤,直至达到所指定迭代次数结束,得到最终的迭代得到的初始偏差xk+1(0),并作为第二系统输入条件,在每次迭代用到的下肢关节初态角度均不同。Step 6.5: Loop the above steps until the specified number of iterations is reached. The initial deviation x k+1 (0) obtained by the final iteration is obtained, and is used as the input condition of the second system. The initial state of the lower limb joints used in each iteration is The angles are all different.

步骤7:将第一系统输入条件(第k+1次迭代学习后的系统输入uk+1(t))和第二系统输入条件(第k+1次的迭代初态xk+1(0))输入下肢康复机器人,即输入式(5),如图2所示,得到下肢康复机器人系统第k+1次运行的迭代学习控制输出yk+1(t),即控制下肢康复机器人运行的带初态学习的控制策略,包括下肢髋关节角度θ1与膝关节角度θ2,图2中,ek+1(t)表示下肢康复机器人系统第k+1次迭代时的跟踪误差;K和L是具有相应维数的迭代学习增益矩阵;表示对ek+1(t)进行求导,即下肢康复机器人系统第k+1次迭代时的跟踪误差导数ek+1(t);uk(t)为第k次迭代学习时的系统输入;uk+1(t)为第k+1次迭代学习后的系统输入;xk+1(0)为系统第k+1次的迭代初态;xk(0)为系统第k次的迭代初态;M(0)为t=0时所得的值;ek+1(0)为系统第k+1次的迭代跟踪误差初值;yd(t)表示下肢康复机器人系统的目标轨迹;yk+1(t)表示下肢康复机器人系统第k+1次运行时的控制输出。Step 7: Combine the input conditions of the first system (the system input u k+1 (t) after the k+1th iteration learning) and the input conditions of the second system (the initial state of the k+1 iteration x k+1 ( 0)) Input the lower limb rehabilitation robot, that is, input formula (5), as shown in Figure 2, and obtain the iterative learning control output y k+1 (t) of the k+1th operation of the lower limb rehabilitation robot system, that is, control the lower limb rehabilitation robot The running control strategy with initial state learning includes the lower limb hip joint angle θ 1 and knee joint angle θ 2 . In Figure 2, e k+1 (t) represents the tracking error at the k+1 iteration of the lower limb rehabilitation robot system. ;K and L are iterative learning gain matrices with corresponding dimensions; Indicates the derivation of e k+1 (t), that is, the tracking error derivative e k +1 (t) at the k+1 iteration of the lower limb rehabilitation robot system; u k (t) is the tracking error at the k-th iteration of learning. System input; u k+1 (t) is the system input after the k+1 iteration learning; x k+1 (0) is the k+1 iteration initial state of the system; x k (0) is the system’s k+1 iteration initial state Initial state of k iterations; M(0) is when t=0 The obtained value; e k+1 (0) is the initial value of the k+1 iteration tracking error of the system; y d (t) represents the target trajectory of the lower limb rehabilitation robot system; y k+1 (t) represents the lower limb rehabilitation robot The control output when the system runs for the k+1th time.

下面对本发明所述带初态学习的下肢康复机器人控制方法进行仿真实验。Next, a simulation experiment is conducted on the control method of the lower limb rehabilitation robot with initial state learning according to the present invention.

对初态偏移状态下的下肢康复机器人系统进行仿真与分析,来验证改进算法的有效性。附图3为下肢康复机器人在带初态学习的迭代学习控制下的关节角度跟踪误差变化图,其中,星线表示髋关节的角度跟踪误差曲线,圆圈线表示膝关节的角度跟踪误差曲线。从图中曲线走势看,髋关节与膝关节角度跟踪误差均随着迭代次数的增加呈逐渐下降趋势,表明改进算法可以有效地抑制初态误差的影响,在第8次迭代控制处,角度跟踪误差为0.2104°,之后系统输出误差逐渐趋近于零。验证了带初态学习的迭代学习控制策略能够克服初态误差所产生的影响。Simulate and analyze the lower limb rehabilitation robot system in the initial offset state to verify the effectiveness of the improved algorithm. Figure 3 is a graph showing changes in joint angle tracking errors of the lower limb rehabilitation robot under iterative learning control with initial state learning. The star line represents the angle tracking error curve of the hip joint, and the circle line represents the angle tracking error curve of the knee joint. Judging from the curve trend in the figure, the hip joint and knee joint angle tracking errors gradually decrease as the number of iterations increases, indicating that the improved algorithm can effectively suppress the impact of the initial state error. At the 8th iteration control point, the angle tracking The error is 0.2104°, and then the system output error gradually approaches zero. It is verified that the iterative learning control strategy with initial state learning can overcome the impact of initial state error.

附图4表示下肢康复机器人系统进行20次迭代学习控制后的轨迹跟踪效果,(a)图表示髋关节角度跟踪图;(b)图表示髋关节角度误差曲线;(c)图表示膝关节角度跟踪图;(d)图表示膝关节角度误差曲线。(a)与(c)图中,虚线表示髋关节与膝关节的目标曲线;实线表示下肢康复机器人系统髋关节与膝关节的实际输出曲线。从这4幅图可以看出,髋关节与膝关节的角度已经跟踪上系统的目标轨迹曲线,且最大角度误差不超过为0.3°。结果验证了带初态学习的迭代学习控制策略能够克服初态偏移的影响,有效地实现下肢康复机器人系统在有初始误差的情况下,依然能够快速准确地跟踪上期望运动轨迹,提高康复效果。Figure 4 shows the trajectory tracking effect of the lower limb rehabilitation robot system after 20 iterations of learning control. (a) shows the hip joint angle tracking chart; (b) shows the hip joint angle error curve; (c) shows the knee joint angle. Tracking graph; (d) graph shows the knee joint angle error curve. In the figures (a) and (c), the dotted lines represent the target curves of the hip and knee joints; the solid lines represent the actual output curves of the hip and knee joints of the lower limb rehabilitation robot system. It can be seen from these four pictures that the angles of the hip joint and the knee joint have tracked the target trajectory curve of the upper system, and the maximum angle error does not exceed 0.3°. The results verify that the iterative learning control strategy with initial state learning can overcome the impact of initial state deviation, effectively realizing that the lower limb rehabilitation robot system can still quickly and accurately track the desired motion trajectory despite initial errors, improving the rehabilitation effect. .

以上所述仅为本发明的优选实施例而已,并不用于限制本发明,对于本领域的技术人员来说,本发明可以有各种更改和变化。凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims (7)

1.一种带初态学习的下肢康复机器人控制方法,其特征在于,包括以下步骤:1. A control method for a lower limb rehabilitation robot with initial state learning, which is characterized by including the following steps: S1、构建下肢康复机器人动力学方程 S1. Construct the dynamic equation of lower limb rehabilitation robot 根据下肢康复机器人动力学方程构建下肢康复机器人的迭代学习控制器Constructing an iterative learning controller for lower limb rehabilitation robots based on the dynamic equations of lower limb rehabilitation robots 其中,为xk(t)的导数,xk(t)表示第k次迭代时的系统状态,uk(t)表示第k次迭代时的系统输入,yk(t)表示第k次迭代时的系统输出;in, is the derivative of x k (t), x k (t) represents the system state at the k-th iteration, u k (t) represents the system input at the k-th iteration, y k (t) represents the k-th iteration system output; D(θ)是惯性矩阵;是离心力和科里奥利力矩阵;G(θ)是重力矩阵;Tθ表示关节力矩矩阵;Td为误差和扰动;/>为下肢关节角度,θ1、θ2分别为髋关节角度和膝关节角度;为下肢关节角速度,/>分别为髋关节角速度继和膝关节角速度;/>为下肢关节角加速度,/>分别为髋关节角加速度和膝关节角加速度;D(θ) is the inertia matrix; is the centrifugal force and Coriolis force matrix; G(θ) is the gravity matrix; Tθ represents the joint moment matrix; T d is the error and disturbance;/> is the joint angle of the lower limb, θ 1 and θ 2 are the hip joint angle and knee joint angle respectively; is the joint angular velocity of the lower limbs,/> are the hip joint angular velocity and knee joint angular velocity respectively;/> is the joint angular acceleration of the lower limbs,/> are the hip joint angular acceleration and knee joint angular acceleration respectively; S2、根据下肢康复机器人的目标轨迹和下肢康复机器人的控制输出构建输出误差模型;S2. Construct an output error model based on the target trajectory of the lower limb rehabilitation robot and the control output of the lower limb rehabilitation robot; S3、采集下肢康复机器人的髋关节与膝关节的离散数据信息,包括不同时间点下肢康复机器人的下肢关节角度数据;S3. Collect discrete data information of the hip joint and knee joint of the lower limb rehabilitation robot, including lower limb joint angle data of the lower limb rehabilitation robot at different time points; S4、根据下肢康复机器人的下肢关节角度,基于迭代学习控制器和输出误差模型得到迭代学习控制律的计算方程,基于迭代学习控制律的计算方程进行迭代学习,达到迭代次数后,得到最终的迭代学习控制律作为第一系统输入条件;S4. According to the lower limb joint angle of the lower limb rehabilitation robot, the calculation equation of the iterative learning control law is obtained based on the iterative learning controller and the output error model. Based on the calculation equation of the iterative learning control law, iterative learning is performed. After the number of iterations is reached, the final iteration is obtained. Learning the control law as the first system input condition; S5、根据下肢康复机器人的下肢关节初态角度,基于迭代学习控制器和输出误差模型得到初始偏差的计算方程,基于初始偏差的计算方程进行迭代学习,达到迭代次数后,得到最终的初始偏差作为第二系统输入条件;S5. According to the initial angle of the lower limb joint of the lower limb rehabilitation robot, the calculation equation of the initial deviation is obtained based on the iterative learning controller and the output error model. Based on the calculation equation of the initial deviation, iterative learning is performed. After the number of iterations is reached, the final initial deviation is obtained as Second system input conditions; S6、将第一系统输入条件和第二系统输入条件输入迭代学习控制器,输出得到控制下肢康复机器人运行的带初态学习的控制策略。S6. Input the first system input condition and the second system input condition into the iterative learning controller, and output the control strategy with initial state learning that controls the operation of the lower limb rehabilitation robot. 2.根据权利要求1所述带初态学习的下肢康复机器人控制方法,其特征在于,输出误差模型为:2. The lower limb rehabilitation robot control method with initial state learning according to claim 1, characterized in that the output error model is: ek(t)=yd(t)-yk(t)e k (t)=y d (t)-y k (t) 其中,ek(t)表示下肢康复机器人第k次迭代时的跟踪误差,yd(t)表示下肢康复机器人的目标轨迹,yk(t)表示下肢康复机器人系统第k次运行的控制输出。Among them, e k (t) represents the tracking error of the lower limb rehabilitation robot in the k-th iteration, y d (t) represents the target trajectory of the lower limb rehabilitation robot, and y k (t) represents the control output of the k-th operation of the lower limb rehabilitation robot system. . 3.根据权利要求2所述带初态学习的下肢康复机器人控制方法,其特征在于,步骤S3中,需利用分段三次多项式对下肢康复机器人的髋关节与膝关节的离散数据信进行步态数据拟合,得到两关节的连续曲线函数。3. The lower limb rehabilitation robot control method with initial state learning according to claim 2, characterized in that, in step S3, it is necessary to use a piecewise cubic polynomial to perform gait on the discrete data information of the hip joint and knee joint of the lower limb rehabilitation robot. The data is fitted to obtain the continuous curve function of the two joints. 4.根据权利要求2或3所述带初态学习的下肢康复机器人控制方法,其特征在于,步骤S4中得到的迭代学习控制律的计算方程为:4. The lower limb rehabilitation robot control method with initial state learning according to claim 2 or 3, characterized in that the calculation equation of the iterative learning control law obtained in step S4 is: 其中,ek+1(t)与分别表示下肢康复机器人系统第k+1次迭代时的跟踪误差及其误差导数,K和L是具有相应维数的迭代学习增益矩阵,uk+1(t)为第k+1次迭代学习后的系统输入,uk(t)为第k次迭代学习时的系统输入,当k=0时,uk(t)表示最初未迭代学习时的系统输入,系统输入包括下肢髋关节与膝关节的力矩。Among them, e k+1 (t) and Respectively represent the tracking error and its error derivative at the k+1 iteration of the lower limb rehabilitation robot system, K and L are iterative learning gain matrices with corresponding dimensions, u k+1 (t) is the k+1 iterative learning After the system input, u k (t) is the system input during the k-th iterative learning. When k = 0, u k (t) represents the system input during the initial non-iterative learning. The system input includes the hip joint and knee of the lower limbs. joint torque. 5.根据权利要求4所述带初态学习的下肢康复机器人控制方法,其特征在于,步骤S4具体包括以下步骤:5. The lower limb rehabilitation robot control method with initial state learning according to claim 4, characterized in that step S4 specifically includes the following steps: S41、采集下肢康复机器人第k+1次运行时的下肢关节角度数据;S41. Collect lower limb joint angle data during the k+1th run of the lower limb rehabilitation robot; S42、基于下肢康复机器人的目标轨迹,下肢康复机器人第k次运行的控制输出和输出误差模型,计算下肢康复机器人系统第k+1次迭代时的跟踪误差ek+1(t)及其误差导数 S42. Based on the target trajectory of the lower limb rehabilitation robot, the control output and output error model of the kth operation of the lower limb rehabilitation robot, calculate the tracking error e k+1 (t) and its error in the k+1 iteration of the lower limb rehabilitation robot system. Derivative S43、设置迭代学习增益矩阵K和L;S43. Set the iterative learning gain matrices K and L; S44、将增益矩阵K和L,下肢康复机器人系统第k+1次迭代时的跟踪误差ek+1(t)及其误差导数以及第k次迭代学习时的系统输入uk(t)代入第一迭代学习控制律的计算方程,得到迭代学习控制律;S44. Combine the gain matrices K and L, the tracking error e k+1 (t) of the lower limb rehabilitation robot system at the k+1 iteration and its error derivative And the system input u k (t) during the k-th iterative learning is substituted into the calculation equation of the first iterative learning control law to obtain the iterative learning control law; S45、循环步骤S41~S44,直至达到指定迭代次数结束,即得到最终的迭代学习控制律,将该最终的迭代学习控制律作为第一系统输入条件,在循环过程中,每次迭代用到的下肢关节角度均不同。S45. Loop steps S41 to S44 until the specified number of iterations is reached, that is, the final iterative learning control law is obtained. The final iterative learning control law is used as the first system input condition. During the loop process, each iteration uses The joint angles of the lower limbs are all different. 6.根据权利要求2或3所述带初态学习的下肢康复机器人控制方法,其特征在于,步骤S5中得到的初始偏差的计算方程为:6. The lower limb rehabilitation robot control method with initial state learning according to claim 2 or 3, characterized in that the calculation equation of the initial deviation obtained in step S5 is: xk+1(0)=xk(0)+M(0)Lek+1(0)x k+1 (0)=x k (0)+M(0)Le k+1 (0) 其中,xk+1(0)为系统第k+1次的迭代初态,xk(0)为系统第k次的迭代初态,M(0)为t=0时所得的值,L为系统迭代学习增益矩阵,ek+1(0)为系统第k+1次的迭代跟踪误差初值。Among them, x k+1 (0) is the k+1 iteration initial state of the system, x k (0) is the k-th iteration initial state of the system, and M (0) is when t=0 The obtained value, L is the iterative learning gain matrix of the system, and e k+1 (0) is the initial value of the k+1 iteration tracking error of the system. 7.根据权利要求6所述带初态学习的下肢康复机器人控制方法,其特征在于,步骤S5具体包括以下步骤:7. The lower limb rehabilitation robot control method with initial state learning according to claim 6, characterized in that step S5 specifically includes the following steps: S51、采集下肢康复机器人第k+1次运行时的迭代初态角度;S51. Collect the iteration initial state angle during the k+1th run of the lower limb rehabilitation robot; S52、基于下肢康复机器人的目标轨迹,下肢康复机器人第k次运行的控制输出和输出误差模型,计算下肢康复机器人系统第k+1次的迭代跟踪误差初值;S52. Based on the target trajectory of the lower limb rehabilitation robot, the control output and output error model of the kth operation of the lower limb rehabilitation robot, calculate the initial value of the k+1 iteration tracking error of the lower limb rehabilitation robot system; S53、设置迭代学习增益矩阵L;S53. Set the iterative learning gain matrix L; S54、将增益矩阵L,下肢康复机器人系统第k+1次的迭代跟踪误差初值,以及第k+1次运行时的迭代初态角度代入初始偏差的计算方程,输出得到下肢康复机器人系统的第k+1次迭代得到的初始偏差;S54. Substitute the gain matrix L, the initial value of the k+1 iteration tracking error of the lower limb rehabilitation robot system, and the iterative initial state angle at the k+1th run into the calculation equation of the initial deviation, and output the result of the lower limb rehabilitation robot system. The initial deviation obtained at the k+1 iteration; S55、循环步骤S51~S54,直至达到指定迭代次数结束,即得到最终的初始偏差,并作为第二系统输入条件,在每次迭代用到的下肢关节初态角度均不同。S55. Loop steps S51 to S54 until the specified number of iterations is reached. The final initial deviation is obtained and used as the input condition of the second system. The initial angles of the lower limb joints used in each iteration are different.
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