CN111158238B - Force feedback equipment dynamics parameter estimation algorithm based on particle swarm optimization - Google Patents

Force feedback equipment dynamics parameter estimation algorithm based on particle swarm optimization Download PDF

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CN111158238B
CN111158238B CN202010019658.2A CN202010019658A CN111158238B CN 111158238 B CN111158238 B CN 111158238B CN 202010019658 A CN202010019658 A CN 202010019658A CN 111158238 B CN111158238 B CN 111158238B
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李春泉
何永华
杨峰
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Nanchang University
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Abstract

本发明提供了一种基于粒子群算法的力反馈设备动力学参数估计算法。具体为用一种改进的全面学习粒子群算法来更好的估计力反馈设备的动力学参数。主要包括以下步骤：步骤1，设定力反馈设备关节角理想运动轨迹；步骤2，对关节角理想运动轨迹进行位置跟踪；步骤3，对关节角运动轨迹和输入力矩采样；步骤4，利用ICLPSO算法估计力反馈设备参数。本发明通过使用四种策略：分层更新策略、位置学习策略、指导粒子学习策略、全局最优学习策略，有效地解决在传统PSO算法中存在的“两步向前，一步向后”问题以及早熟问题。与传统PSO算法对比，ICLPSO算法不仅收敛速度更快，而且获得的模型参数也更为精确，能够为各关节提供精确的力矩估计值，提升控制算法的性能。

Figure 202010019658

The invention provides a dynamic parameter estimation algorithm of force feedback device based on particle swarm algorithm. Specifically, an improved comprehensive learning particle swarm algorithm is used to better estimate the dynamic parameters of the force feedback device. It mainly includes the following steps: step 1, set the ideal motion trajectory of the joint angle of the force feedback device; step 2, perform position tracking on the ideal motion trajectory of the joint angle; step 3, sample the joint angle motion trajectory and input torque; step 4, use ICLPSO Algorithms estimate force feedback device parameters. The present invention effectively solves the "two-step forward, one-step backward" problem existing in the traditional PSO algorithm by using four strategies: a hierarchical update strategy, a position learning strategy, a guided particle learning strategy, and a global optimal learning strategy. Premature issues. Compared with the traditional PSO algorithm, the ICLPSO algorithm not only converges faster, but also obtains more accurate model parameters, which can provide accurate torque estimates for each joint and improve the performance of the control algorithm.

Figure 202010019658

Description

一种基于粒子群算法的力反馈设备动力学参数估计算法A Dynamic Parameter Estimation Algorithm for Force Feedback Equipment Based on Particle Swarm Optimization

技术领域technical field

本发明涉及力反馈设备参数的估计，具体为一种基于粒子群算法的力反馈设备动力学参数估计算法。The invention relates to the estimation of force feedback device parameters, in particular to a force feedback device dynamic parameter estimation algorithm based on particle swarm algorithm.

背景技术Background technique

由于力触觉在人类感觉中具有显著的地位，研究者们尝试将力触觉特性引入遥操作机器人、虚拟现实等研究领域，为操作者在人机交互的过程中提供力触觉反馈信息。例如，核电站发生事故时，需要通过遥操作机器人完成检测、维修等任务，此时视频监控面临严重干扰，操作者借助力触觉反馈信息，可以有效提高操作的准确性、可靠性。在虚拟手术中，医生在虚拟人体上进行实时手术仿真训练，增加力触觉反馈信息，可以大幅提高培训效率，缩短培训周期，减轻一系列成本开销。另外，力触觉也常常应用在深海作业、医疗康复机器人、微创手术以及游戏和教育中，给操作者提供真实的力感和触感。而力触觉的实现依赖于力反馈设备，因此，力反馈设备的性能尤为重要。通常来说，力反馈设备的性能与两方面的因素有关。一方面与结构、减速器、传感器等硬件的选取有关，另一方面控制算法也是影响其性能的关键因素。通过控制算法可以消除力反馈设备中的自身惯量、摩擦力、重力等因素的影响，能够改进系统的透明性以及力反馈的逼真性。因此，对力反馈设备及其相关的控制算法进行研究是非常有意义的，是当前乃至今后一段时期内研究的热点。Because haptic has a prominent position in human perception, researchers have tried to introduce haptic characteristics into research fields such as tele-robots and virtual reality, so as to provide haptic feedback information for operators in the process of human-computer interaction. For example, in the event of an accident in a nuclear power plant, tasks such as detection and maintenance need to be completed by teleoperated robots. At this time, video surveillance is facing serious interference. The operator can effectively improve the accuracy and reliability of the operation with the help of force-tactile feedback information. In virtual surgery, doctors perform real-time surgical simulation training on the virtual human body and add haptic feedback information, which can greatly improve the training efficiency, shorten the training cycle, and reduce a series of costs. In addition, force touch is often used in deep-sea operations, medical rehabilitation robots, minimally invasive surgery, games and education, providing operators with a real sense of force and touch. The realization of force touch depends on the force feedback device, therefore, the performance of the force feedback device is particularly important. Generally speaking, the performance of force feedback devices is related to two factors. On the one hand, it is related to the selection of hardware such as structure, reducer, and sensor, and on the other hand, the control algorithm is also a key factor affecting its performance. Through the control algorithm, the influence of the inertia, friction, gravity and other factors in the force feedback device can be eliminated, which can improve the transparency of the system and the fidelity of the force feedback. Therefore, it is very meaningful to study the force feedback device and its related control algorithm, and it is a research hotspot at present and even in the future.

研究力反馈设备控制算法的基础前提是分析力反馈设备的运动学和动力学。其中，动力学模型的精确建立，对于设备保持高速、高精度的运行以及改进控制器性能等方面都起着重要的作用，同时也能够降低设计的成本、减少研究时间。建立力反馈设备的关节动力学模型，需要得到该设备的动力学参数以及摩擦力参数，即确定各个关节的关节质量、惯性张量、质心、库伦摩擦力以及粘滞摩擦力等参数。然而，通常情况下，力反馈设备参数是未知或不准确的，并且设备在长期的使用过程中，会受到磨损、形变以及环境等因素的影响，导致参数产生偏差。因此，需要对动力学参数进行估计。如果参数估计的越准确，动力学模型的精度就会越高，这也就能使各关节力矩的估计值越精确，为操纵者提供一个更精准的力反馈。The basic premise of studying force feedback device control algorithm is to analyze the kinematics and dynamics of force feedback device. Among them, the accurate establishment of the dynamic model plays an important role in maintaining the high-speed and high-precision operation of the equipment and improving the performance of the controller, and can also reduce the design cost and research time. To establish a joint dynamics model of a force feedback device, it is necessary to obtain the dynamic parameters and friction parameters of the device, that is, to determine the parameters of each joint such as joint mass, inertia tensor, center of mass, Coulomb friction and viscous friction. However, in general, the parameters of force feedback equipment are unknown or inaccurate, and the equipment will be affected by factors such as wear, deformation and environment during long-term use, resulting in deviation of parameters. Therefore, kinetic parameters need to be estimated. If the parameters are estimated more accurately, the accuracy of the dynamic model will be higher, which will make the estimated value of each joint torque more accurate, and provide a more accurate force feedback for the operator.

获取力反馈设备参数的方法有：解体测量法，指通过将设备解体，然后测量设备的几何参数及其材料参数，然后得出其动力学参数的方法。该方法对设备关节质量、惯性张量、质心的获取是比较准确的。但操作复杂，可执行性低，并且参数值的结果容易受到设备的形状、材料等因素的影响，同时在解体过程中有可能会损伤或无法还原设备；CAD建模法，建立在计算机图形技术基础之上的，根据设备的结构图，利用相应的动力学模型，求解出设备的参数。能够便捷的获得独立的参数值，并且在设备的设计阶段就可以获得力反馈设备的参数值，然后根据参数值来计算机器人的动力学特性。但是该方法容易受到连杆材质不均匀等设备制造工艺的影响，使动力学参数存在一定的误差；估算方法，无论是解体测量法还是CAD建模法，除了存在上述问题外，都未考虑到设备在长期的使用过程中，会受到磨损、形变以及环境等因素的影响，导致模型参数产生偏差。Honegger等人提出一种利用非线性自适应控制算法(详见：Adaptive control of the hexaglide,a 6dof parallelmanipulator[C].Proceedings of International Conference on RoboticsandAutomation.IEEE,1997,1:543-548.)对动力学参数进行在线辨识，但是该方法无法保证参数收敛。由于粒子群算法具有简单易行、快速收敛的优点，Hossein Jahandideh等人利用粒子群算法(详见：Use ofPSO in Parameter Estimation of Robot Dynamics；PartOne:No Need for Parameterization[C].International Conference on SystemTheory.IEEE,2012.)对动力学参数进行估计，在该方法中，粒子各维度分别代表动力学模型的实际参数或者组合参数，根据假设的动力学模型，以力矩误差作为目标函数，对参数进行估计，相比于其它估计算法，PSO算法估计参数具有收敛速度快的特点。但估计的力矩误差较大，参数估计的效果较差，更容易陷入局部最优。The methods of obtaining the parameters of the force feedback device include: disintegration measurement method, which refers to the method of disassembling the device, then measuring the geometric parameters of the device and its material parameters, and then obtaining its dynamic parameters. This method is relatively accurate for the acquisition of equipment joint mass, inertia tensor and mass center. However, the operation is complicated, the practicability is low, and the results of the parameter values are easily affected by factors such as the shape and material of the equipment. At the same time, the equipment may be damaged or cannot be restored during the disassembly process. The CAD modeling method is based on computer graphics technology. On the basis, according to the structure diagram of the equipment, the corresponding dynamic model is used to solve the parameters of the equipment. Independent parameter values can be easily obtained, and the parameter values of the force feedback device can be obtained in the design stage of the device, and then the dynamic characteristics of the robot can be calculated according to the parameter values. However, this method is easily affected by the equipment manufacturing process such as the uneven material of the connecting rod, so that there are certain errors in the dynamic parameters; the estimation method, whether it is the disintegration measurement method or the CAD modeling method, has not taken into account the above problems except for the above problems. During the long-term use of the equipment, it will be affected by factors such as wear, deformation, and environment, resulting in deviations of model parameters. Honegger et al. proposed a nonlinear adaptive control algorithm (see: Adaptive control of the hexaglide, a 6dof parallelmanipulator [C]. Proceedings of International Conference on Robotics and Automation. IEEE, 1997, 1: 543-548.) However, this method cannot guarantee parameter convergence. Because particle swarm optimization has the advantages of simplicity, ease of operation and rapid convergence, Hossein Jahandideh et al. used particle swarm optimization (see: Use of PSO in Parameter Estimation of Robot Dynamics; PartOne: No Need for Parameterization [C]. International Conference on SystemTheory. IEEE, 2012.) to estimate the dynamic parameters. In this method, each dimension of the particle represents the actual parameters or combined parameters of the dynamic model. According to the assumed dynamic model, the torque error is used as the objective function to estimate the parameters. , compared with other estimation algorithms, the estimated parameters of the PSO algorithm have the characteristics of fast convergence. However, the estimated moment has a large error, the effect of parameter estimation is poor, and it is easier to fall into local optimum.

发明内容SUMMARY OF THE INVENTION

基于上述背景，本发明提供了一种基于粒子群算法的力反馈设备动力学参数估计算法。具体为用一种改进的全面学习粒子群(Improved Comprehensive LearningParticle Swarm Optimization,ICLPSO)算法来更好的估计力反馈设备的动力学参数。本发明是通过以下技术方案实现的。Based on the above background, the present invention provides a dynamic parameter estimation algorithm of a force feedback device based on a particle swarm algorithm. Specifically, an improved comprehensive learning particle swarm optimization (ICLPSO) algorithm is used to better estimate the dynamic parameters of the force feedback device. The present invention is achieved through the following technical solutions.

本发明所述的一种基于粒子群算法的力反馈设备动力学参数估计算法，按以下步骤：A kind of dynamic parameter estimation algorithm of force feedback device based on particle swarm algorithm according to the present invention, according to the following steps:

通用力反馈设备的动力学方程具体如下：The dynamic equation of the universal force feedback device is as follows:

Figure GDA0002770871000000031
Figure GDA0002770871000000031

Figure GDA0002770871000000032
Figure GDA0002770871000000032

其中，θ为关节角；

Figure GDA0002770871000000033
为关节角速度；
Figure GDA0002770871000000034
为关节角加速度；D为力反馈设备的惯性矩阵；C为离心力和科里奥利力矩阵；G为重力矩阵；Fc为库伦摩擦系数矩阵；Fv为黏滞摩擦系数矩阵；τ为关节力矩；ΔX为考虑建模不确定性而引入的补偿项。Among them, θ is the joint angle;
Figure GDA0002770871000000033
is the joint angular velocity;
Figure GDA0002770871000000034
is the joint angular acceleration; D is the inertia matrix of the force feedback device; C is the centrifugal force and Coriolis force matrix; G is the gravity matrix; F c is the Coulomb friction coefficient matrix; F v is the viscous friction coefficient matrix; τ is the joint Moment; ΔX is a compensation term introduced to account for modeling uncertainty.

需要估计的参数除了参数X外，还有补偿参数ΔX，如下所示：In addition to the parameter X, the parameters to be estimated also include the compensation parameter ΔX, as follows:

X＝[l1，l2,l3,ma，Iaxx，Iayy,Iazz，mbe，Ibexx,Ibeyy,Ibezz,mc,Icxx，Icyy,Iczz,l5,mdf，Idfxx,Idfyy,Idfzz,l6,Idf,Fc1,Fc2,Fc3,Fv1,Fv2,Fv3]X=[l 1 , l 2 , l 3 , m a , I axx , I ayy , I azz , m be , I bexx , I beyy , I bezz , m c , I cxx , I cyy , I czz , l 5 ,m df , I dfxx ,I dfyy ,I dfzz ,l 6 ,I df ,F c1 ,F c2 ,F c3 ,F v1 ,F v2 ,F v3 ]

ΔX＝[a1,b1,a2,b2,a3,b3]ΔX=[a 1 ,b 1 ,a 2 ,b 2 ,a 3 ,b 3 ]

其中：力反馈设备的模型分为A到G七段，X为力反馈设备的动力学参数；l1，l2分别是B段和A段的长度，l3是AB两段交点到C段的距离，l5是BE段的质心到原点的距离，l6是DF段质心到原点的距离；ma，mbe，mc,mdf分别是A段、BE段、C段和DF段的质量；Iaxx，Iayy,Iazz，Ibexx，Ibeyy,Ibezz,Icxx，Icyy,Iczz,Idfxx，Idfyy,Idfzz分别是A段、BE段、C段和DF段的惯性张量矩阵在三个轴的分量；Idf是DF段的惯性张量矩阵；Fc1,Fc2,Fc3是三个关节的库伦摩擦系数；Fv1,Fv2,Fv3是三个关节的粘滞摩擦系数，ΔX为考虑建模不确定性而引入的补偿项；a1,b1,a2,b2,a3,b3为三个关节补偿方程的系数。Among them: the model of the force feedback device is divided into seven sections from A to G, X is the dynamic parameter of the force feedback device; l 1 , l 2 are the lengths of the B and A sections respectively, and l 3 is the intersection of the two sections AB to the C section. l5 is the distance from the centroid of the BE segment to the origin, l6 is the distance from the centroid of the DF segment to the origin ; m a , m be , m c , m df are the A segment, the BE segment, the C segment and the DF segment, respectively quality; I axx , I ayy , I azz , I bexx , I beyy , I bezz , I cxx , I cyy , I czz , I dfxx , I dfyy , I dfzz are A segment, BE segment, C segment and DF respectively The components of the inertia tensor matrix of the segment in the three axes; I df is the inertia tensor matrix of the DF segment; F c1 , F c2 , F c3 are the Coulomb friction coefficients of the three joints; F v1 , F v2 , F v3 are The viscous friction coefficient of the three joints, ΔX is the compensation term introduced by considering the modeling uncertainty; a 1 , b 1 , a 2 , b 2 , a 3 , b 3 are the coefficients of the three joint compensation equations.

步骤1：设定力反馈设备关节角理想运动轨迹；Step 1: Set the ideal motion trajectory of the joint angle of the force feedback device;

力反馈设备具有N个可旋转的关节J1、J2…JN，对应的N个关节角为θ1、θ2…θN。设定N个关节角的理想运动轨迹分别为：角度θ1(t)、θ2(t)…θN(t)，角速度

Figure GDA0002770871000000035
Figure GDA0002770871000000036
角加速度
Figure GDA0002770871000000037
The force feedback device has N rotatable joints J 1 , J 2 ···J N , and the corresponding N joint angles are θ 1 , θ 2 ··· θ N . The ideal motion trajectories for setting N joint angles are: angle θ 1 (t), θ 2 (t)...θ N (t), angular velocity
Figure GDA0002770871000000035
Figure GDA0002770871000000036
Angular acceleration
Figure GDA0002770871000000037

步骤2：对关节角理想运动轨迹进行位置跟踪；Step 2: Perform position tracking on the ideal motion trajectory of the joint angle;

使用PID控制算法，控制力反馈设备的N个关节对理想轨迹进行位置跟踪，得到N个关节的输入力矩τ1、τ2…τN和角度θ1(t)、θ2(t)…θN(t)。利用非线性跟踪-微分器得到各关节的角速度

Figure GDA0002770871000000038
和角加速度
Figure GDA0002770871000000039
Using the PID control algorithm, the N joints of the control force feedback device perform position tracking on the ideal trajectory, and obtain the input torques τ 1 , τ 2 ... τ N and the angles θ 1 (t), θ 2 (t) ... θ of the N joints N (t). Using nonlinear tracking-differentiator to obtain the angular velocity of each joint
Figure GDA0002770871000000038
and angular acceleration
Figure GDA0002770871000000039

步骤3：对关节角运动轨迹和输入力矩采样；Step 3: Sampling the joint angular motion trajectory and input torque;

对运动轨迹：关节角度θ1(t)、θ2(t)…θN(t)，关节角速度

Figure GDA0002770871000000041
关节角加速度
Figure GDA0002770871000000042
以及输入的关节力矩τ1、τ2…τN进行
Figure GDA0002770871000000043
采样，其中T为采样时间，P为采样点数。得到采样轨迹：关节角度
Figure GDA0002770871000000044
关节角速度
Figure GDA0002770871000000045
和关节角加速度
Figure GDA0002770871000000046
及力矩
Figure GDA0002770871000000047
Figure GDA0002770871000000048
For motion trajectories: joint angles θ 1 (t), θ 2 (t)…θ N (t), joint angular velocity
Figure GDA0002770871000000041
joint angular acceleration
Figure GDA0002770871000000042
and the input joint moments τ 1 , τ 2 . . . τ N
Figure GDA0002770871000000043
Sampling, where T is the sampling time and P is the number of sampling points. Get sampled trajectory: joint angle
Figure GDA0002770871000000044
joint angular velocity
Figure GDA0002770871000000045
and joint angular acceleration
Figure GDA0002770871000000046
and torque
Figure GDA0002770871000000047
Figure GDA0002770871000000048

步骤4：用改进的全面学习粒子群ICLPSO算法估计力反馈设备参数；Step 4: Use the improved comprehensive learning particle swarm ICLPSO algorithm to estimate the parameters of the force feedback device;

(a)：将估计的参数

Figure GDA0002770871000000049
及关节角运动轨迹代入动力学方程中，计算得到估计的关节力矩，第i个关节、第p次采样的力矩
Figure GDA00027708710000000410
计算公式如下：(a): Parameters that will be estimated
Figure GDA0002770871000000049
And the joint angle motion trajectory is substituted into the dynamic equation, and the estimated joint moment is calculated, the moment of the i-th joint and the p-th sampling
Figure GDA00027708710000000410
Calculated as follows:

Figure GDA00027708710000000411
Figure GDA00027708710000000411

上式中，

Figure GDA00027708710000000412
为第i个关节、第p次采样得到的关节角度；
Figure GDA00027708710000000413
为第i个关节、第p次采样得到的关节角速度；
Figure GDA00027708710000000414
为第i个关节、第p次采样得到的关节角加速度；Fcip为第i个关节、第p次采样得到的库伦摩擦系数；Fvip第i个关节、第p次采样得到的粘滞摩擦系数；In the above formula,
Figure GDA00027708710000000412
is the joint angle obtained by the i-th joint and the p-th sampling;
Figure GDA00027708710000000413
is the joint angular velocity obtained by the i-th joint and the p-th sampling;
Figure GDA00027708710000000414
is the joint angular acceleration obtained by the i-th joint and the p-th sampling; F cip is the Coulomb friction coefficient obtained by the i-th joint and the p-th sampling; F vip is the viscous friction obtained by the i-th joint and the p-th sampling coefficient;

(b)：定义误差矩阵为计算测量的关节力矩τ与估计的关节力矩

Figure GDA00027708710000000415
之间的误差
Figure GDA00027708710000000416
Figure GDA00027708710000000417
得到误差矩阵E为：(b): Define the error matrix as calculating the measured joint moment τ and the estimated joint moment
Figure GDA00027708710000000415
error between
Figure GDA00027708710000000416
Figure GDA00027708710000000417
The error matrix E is obtained as:

Figure GDA00027708710000000418
Figure GDA00027708710000000418

定义目标函数：Define the objective function:

f＝||E||2 f=||E|| 2

(c)：设置ICLPSO算法的参数。粒子维度D；粒子的个数Q；最大迭代次数max_iteration；最大评价次数max_EFS；最大停滞次数max_PST；粒子搜索范围为[Hmin Hmax]；(c): Set the parameters of the ICLPSO algorithm. The particle dimension D; the number of particles Q; the maximum iteration number max_iteration; the maximum evaluation number max_EFS; the maximum stagnation number max_PST; the particle search range is [H min H max ];

①初始化ICLPSO算法的参数，粒子个数Q、粒子维度D、搜索边界[Hmin Hmax]、迭代次数iteration、评价次数EFS、各粒子停滞次数PST，随机初始化粒子位置H、速度V；②评价粒子的位置，得到各粒子的适应度值，更新各粒子的个体历史最优位置pb和种群在整个搜索过程中找到的最优位置gb(全局最优位置)，更新iteration和EFS；①Initialize the parameters of the ICLPSO algorithm, the number of particles Q, the particle dimension D, the search boundary [H min H max ], the iteration number iteration, the evaluation number EFS, the stagnation number PST of each particle, and randomly initialize the particle position H and velocity V; ② Evaluation The position of the particle, the fitness value of each particle is obtained, the individual historical optimal position pb of each particle and the optimal position gb (global optimal position) found by the population in the entire search process are updated, and iteration and EFS are updated;

③使用分层更新策略更新粒子速度V，更新粒子位置H，设置参数M＝Q/2，K＝Q/4；评价各粒子得到适应度值，更新各粒子的pb和gb，更新iteration和EFS；③Use the layered update strategy to update the particle velocity V, update the particle position H, set the parameters M=Q/2, K=Q/4; evaluate each particle to get the fitness value, update the pb and gb of each particle, update iteration and EFS ;

若粒子的f(pbi)＜f(S_pbM)，则粒子的速度使用下面的公式更新If the particle's f(pb i ) < f(S_pb M ), the particle's velocity is updated using the following formula

Figure GDA0002770871000000051
Figure GDA0002770871000000051

否则，粒子的速度使用下面的公式更新Otherwise, the velocity of the particle is updated using the following formula

Figure GDA0002770871000000052
Figure GDA0002770871000000052

Figure GDA0002770871000000053
Figure GDA0002770871000000053

其中，

Figure GDA0002770871000000054
是第i个粒子的d维速度；w是惯性权重，调节对解空间的搜索能力；
Figure GDA0002770871000000055
是第i个粒子的指导粒子在d维的位置；
Figure GDA0002770871000000056
是第i个粒子在d维的位置；gbd是粒子种群在d维找到的最优位置；pbi是个体的历史最优位置；S_pb为pb按适应度值从小到大排序后的位置；g_pb是pb产生的指导粒子；cn为S_pb中前K个位置的中心；c1和c2为加速度因子；r1和r2是0到1之间均匀分布的随机数；cnd为S_pb中前K个值在第d维位置的中心；in,
Figure GDA0002770871000000054
is the d-dimensional velocity of the ith particle; w is the inertia weight, which adjusts the search ability of the solution space;
Figure GDA0002770871000000055
is the position of the guiding particle of the ith particle in dimension d;
Figure GDA0002770871000000056
is the position of the i-th particle in dimension d; gb d is the optimal position found by the particle population in dimension d; pb i is the historical optimal position of the individual; S_pb is the position of pb sorted by fitness value from small to large; g_pb is the guiding particle generated by pb; cn is the center of the first K positions in S_pb; c 1 and c 2 are acceleration factors; r 1 and r 2 are random numbers uniformly distributed between 0 and 1; cn d is in S_pb The first K values are at the center of the d-dimensional position;

④使用位置学习策略对粒子位置H进行更新。每个粒子都有学习其他粒子的能力，学习其他粒子的概率为PLX＝0.25，如果0～1的随机数r3小于PLX，则在此维度上，粒子学习另一个粒子；④ Use the position learning strategy to update the particle position H. Each particle has the ability to learn other particles. The probability of learning other particles is PLX=0.25. If the random number r 3 from 0 to 1 is less than PLX, then in this dimension, the particle learns another particle;

⑤使用指导粒子学习策略对指导粒子进行更新。当粒子的停滞次数PST达到设置的最大停滞次数max_PST时，随机选择一个粒子的pb替代停滞粒子的个体指导粒子。另外，为了防止粒子过早的聚集在一起，损失种群的多样性。当粒子的pb更新时，指导粒子g_pb将会等于pb；⑤Using the guiding particle learning strategy to update the guiding particles. When the particle's stagnation times PST reaches the set maximum stagnation times max_PST, a particle's pb is randomly selected to replace the stagnant particle's individual guiding particle. In addition, to prevent premature aggregation of particles, the diversity of the population is lost. When the particle's pb is updated, the guide particle g_pb will be equal to pb;

⑥使用全局最优学习策略优化gb。在每次迭代时，随机选择一个维度r4，让gb直接学习pb中的一个随机粒子

Figure GDA0002770871000000057
⑥ Use the global optimal learning strategy to optimize gb. At each iteration, randomly select a dimension r 4 and let gb directly learn a random particle in pb
Figure GDA0002770871000000057

⑦判断算法是否满足结束条件，若满足找到使目标函数f最小的参数，此时的参数

Figure GDA00027708710000000612
为估计的最优模型参数，算法结束；若不满足，则继续跳到步骤2继续运行。⑦ Determine whether the algorithm satisfies the end condition. If it satisfies to find the parameter that minimizes the objective function f, the parameter at this time
Figure GDA00027708710000000612
For the estimated optimal model parameters, the algorithm ends; if it is not satisfied, continue to skip to step 2 to continue running.

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:

本发明通过使用四种策略：分层更新策略、位置学习策略、指导粒子学习策略、全局最优学习策略，有效地解决在传统PSO算法中存在的“两步向前，一步向后”问题以及早熟问题。与传统PSO算法对比，本算法不仅收敛速度更快，而且获得的模型参数也更为精确，能够为各关节提供精确的力矩估计值，提升控制算法的性能。The present invention effectively solves the "two-step forward, one-step backward" problem existing in the traditional PSO algorithm by using four strategies: a hierarchical update strategy, a position learning strategy, a guided particle learning strategy, and a global optimal learning strategy. Premature issues. Compared with the traditional PSO algorithm, this algorithm not only converges faster, but also obtains more accurate model parameters, which can provide accurate torque estimates for each joint and improve the performance of the control algorithm.

附图说明Description of drawings

图1为一种改进的全面学习粒子群ICLPSO算法流程图。Figure 1 is a flowchart of an improved comprehensive learning particle swarm ICLPSO algorithm.

具体实施方式Detailed ways

本发明将通过以下实例作进一步说明。The present invention will be further illustrated by the following examples.

步骤1：设定力反馈设备关节角理想运动轨迹；Step 1: Set the ideal motion trajectory of the joint angle of the force feedback device;

力反馈设备具有3个可旋转的关节J1、J2、J3，对应的3个关节角为θ1、θ2、θ3。设定3个关节角的理想运动轨迹分别为：角度θ1(t)、θ2(t)、θ3(t)，角速度

Figure GDA0002770871000000061
Figure GDA0002770871000000062
角加速度
Figure GDA0002770871000000063
具体如下：The force feedback device has three rotatable joints J 1 , J 2 , and J 3 , and the corresponding three joint angles are θ 1 , θ 2 , and θ 3 . The ideal motion trajectories of the three joint angles are set as: angle θ 1 (t), θ 2 (t), θ 3 (t), angular velocity
Figure GDA0002770871000000061
Figure GDA0002770871000000062
Angular acceleration
Figure GDA0002770871000000063
details as follows:

角度：θ1＝0.5sint θ2＝0.5sint θ3＝0.2sintAngle: θ 1 =0.5sint θ 2 =0.5sint θ 3 =0.2sint

角速度：

Figure GDA0002770871000000064
Figure GDA0002770871000000065
Figure GDA0002770871000000066
Angular velocity:
Figure GDA0002770871000000064
Figure GDA0002770871000000065
Figure GDA0002770871000000066

角加速度：

Figure GDA0002770871000000067
Figure GDA0002770871000000068
Figure GDA0002770871000000069
Angular acceleration:
Figure GDA0002770871000000067
Figure GDA0002770871000000068
Figure GDA0002770871000000069

步骤2：对关节角理想运动轨迹进行位置跟踪；Step 2: Perform position tracking on the ideal motion trajectory of the joint angle;

使用PID控制算法，控制力反馈设备的3个关节对理想轨迹进行位置跟踪，得到3个关节的输入力矩τ1、τ2、τ3和角度θ1(t)、θ2(t)、θ3(t)。利用非线性跟踪-微分器得到各关节的角速度

Figure GDA00027708710000000610
和角加速度
Figure GDA00027708710000000611
Using the PID control algorithm, control the three joints of the force feedback device to track the ideal trajectory, and obtain the input torques τ 1 , τ 2 , τ 3 and angles θ 1 (t), θ 2 (t), θ of the three joints 3 (t). Using nonlinear tracking-differentiator to obtain the angular velocity of each joint
Figure GDA00027708710000000610
and angular acceleration
Figure GDA00027708710000000611

步骤3：对关节角运动轨迹和输入力矩采样；Step 3: Sampling the joint angular motion trajectory and input torque;

对运动轨迹：关节角度θ1(t)、θ2(t)、θ3(t)，关节角速度

Figure GDA0002770871000000071
关节角加速度
Figure GDA0002770871000000072
以及输入的关节力矩τ1、τ2、τ3进行
Figure GDA0002770871000000073
采样，其中T＝30s，P＝200。得到采样轨迹：关节角度
Figure GDA0002770871000000074
关节角速度
Figure GDA0002770871000000075
Figure GDA0002770871000000076
和关节角加速度
Figure GDA0002770871000000077
及力矩
Figure GDA0002770871000000078
For motion trajectories: joint angles θ 1 (t), θ 2 (t), θ 3 (t), joint angular velocity
Figure GDA0002770871000000071
joint angular acceleration
Figure GDA0002770871000000072
and the input joint moments τ 1 , τ 2 , τ 3
Figure GDA0002770871000000073
Sampling, where T=30s, P=200. Get sampled trajectory: joint angle
Figure GDA0002770871000000074
joint angular velocity
Figure GDA0002770871000000075
Figure GDA0002770871000000076
and joint angular acceleration
Figure GDA0002770871000000077
and torque
Figure GDA0002770871000000078

步骤4：用改进的全面学习粒子群(ICLPSO)算法估计力反馈设备参数。Step 4: Estimate force feedback device parameters with an improved comprehensive learning particle swarm (ICLPSO) algorithm.

(a)：将估计的参数

Figure GDA00027708710000000717
及关节角运动轨迹代入动力学方程中，计算得到估计的关节力矩，第i个关节、第p次采样的力矩
Figure GDA00027708710000000718
计算公式如下：(a): Parameters to be estimated
Figure GDA00027708710000000717
And the joint angle motion trajectory is substituted into the dynamic equation, and the estimated joint moment is calculated, the moment of the i-th joint and the p-th sampling
Figure GDA00027708710000000718
Calculated as follows:

Figure GDA0002770871000000079
Figure GDA0002770871000000079

上式中，

Figure GDA00027708710000000710
为第i个关节、第p次采样得到的关节角度；
Figure GDA00027708710000000711
为第i个关节、第p次采样得到的关节角速度；
Figure GDA00027708710000000712
为第i个关节、第p次采样得到的关节角加速度In the above formula,
Figure GDA00027708710000000710
is the joint angle obtained by the i-th joint and the p-th sampling;
Figure GDA00027708710000000711
is the joint angular velocity obtained by the i-th joint and the p-th sampling;
Figure GDA00027708710000000712
is the joint angular acceleration obtained by the i-th joint and the p-th sampling

(b)：定义误差矩阵为计算测量的关节力矩τ与估计的关节力矩

Figure GDA00027708710000000713
之间的误差
Figure GDA00027708710000000714
Figure GDA00027708710000000715
得到误差矩阵E为：(b): Define the error matrix as calculating the measured joint moment τ and the estimated joint moment
Figure GDA00027708710000000713
error between
Figure GDA00027708710000000714
Figure GDA00027708710000000715
The error matrix E is obtained as:

Figure GDA00027708710000000716
Figure GDA00027708710000000716

定义目标函数：Define the objective function:

f＝||E||2 f=||E|| 2

(c)：设置ICLPSO算法的参数。粒子维度D＝34；粒子的个数Q＝34；最大迭代次数max_iteration＝10000；最大评价次数max_EFS＝340000；最大停滞次数max_PST＝7；粒子搜索范围为Hmin＝0.5H、Hmax＝2H(H为负时，上下边界互换)；(c): Set the parameters of the ICLPSO algorithm. The particle dimension D=34; the number of particles Q=34; the maximum iteration times max_iteration=10000; the maximum evaluation times max_EFS =340000; the maximum stagnation times max_PST =7; When H is negative, the upper and lower boundaries are interchanged);

①初始化ICLPSO算法的参数，粒子个数Q、粒子维度D、搜索边界[Hmin Hmax]、迭代次数iteration、评价次数EFS、各粒子停滞次数PST，随机初始化粒子位置H、速度V，②评价粒子的位置，得到各粒子的适应度值，更新各粒子的个体历史最优位置pb和种群在整个搜索过程中找到的最优位置gb(全局最优位置)，更新iteration和EFS；①Initialize the parameters of ICLPSO algorithm, particle number Q, particle dimension D, search boundary [H min H max ], iteration number iteration, evaluation number EFS, each particle stagnation number PST, randomly initialize particle position H, velocity V, ② evaluation The position of the particle, the fitness value of each particle is obtained, the individual historical optimal position pb of each particle and the optimal position gb (global optimal position) found by the population in the entire search process are updated, and iteration and EFS are updated;

③使用分层学习模式更新粒子速度V，设置参数M＝Q/2，K＝Q/4。更新粒子位置H，评价各粒子得到适应度值，更新各粒子的pb和gb，更新iteration和EFS；③Use the layered learning mode to update the particle velocity V, and set the parameters M=Q/2, K=Q/4. Update the particle position H, evaluate each particle to get the fitness value, update the pb and gb of each particle, update iteration and EFS;

若粒子的f(pbi)＜f(S_pbM)，则粒子的速度使用下面的公式更新If the particle's f(pb i ) < f(S_pb M ), the particle's velocity is updated using the following formula

Figure GDA0002770871000000081
Figure GDA0002770871000000081

否则，粒子的速度使用下面的公式更新Otherwise, the velocity of the particle is updated using the following formula

Figure GDA0002770871000000082
Figure GDA0002770871000000082

Figure GDA0002770871000000083
Figure GDA0002770871000000083

其中，

Figure GDA0002770871000000084
是第i个粒子的d维速度；w是惯性权重，调节对解空间的搜索能力；
Figure GDA0002770871000000085
是第i个粒子的指导粒子在d维的位置；
Figure GDA0002770871000000086
是第i个粒子在d维的位置；gbd是粒子种群在d维找到的最优位置；pbi是个体的历史最优位置；S_pb为pb按适应度值从小到大排序后的位置；g_pb是pb产生的指导粒子；cn为S_pb中前K个位置的中心；c1和c2为加速度因子；r1和r2是0到1之间均匀分布的随机数；cnd为S_pb中前K个值在第d维位置的中心。in,
Figure GDA0002770871000000084
is the d-dimensional velocity of the ith particle; w is the inertia weight, which adjusts the search ability of the solution space;
Figure GDA0002770871000000085
is the position of the guiding particle of the ith particle in dimension d;
Figure GDA0002770871000000086
is the position of the i-th particle in dimension d; gb d is the optimal position found by the particle population in dimension d; pb i is the historical optimal position of the individual; S_pb is the position of pb sorted by fitness value from small to large; g_pb is the guiding particle generated by pb; cn is the center of the first K positions in S_pb; c 1 and c 2 are acceleration factors; r 1 and r 2 are random numbers uniformly distributed between 0 and 1; cn d is in S_pb The first K values are at the center of the d-th dimension position.

④使用位置学习策略对粒子位置H进行更新。每个粒子都有学习其他粒子的能力，学习其他粒子的概率为PLX＝0.25，如果0～1的随机数r3小于PLX，则在此维度上，粒子学习另一个粒子；④ Use the position learning strategy to update the particle position H. Each particle has the ability to learn other particles. The probability of learning other particles is PLX=0.25. If the random number r 3 from 0 to 1 is less than PLX, then in this dimension, the particle learns another particle;

⑤使用指导粒子学习策略对指导粒子进行更新。当粒子的停滞次数PST达到设置的最大停滞次数max_PST时，随机选择一个粒子的pb替代停滞粒子的个体指导粒子。另外，为了防止粒子过早的聚集在一起，损失种群的多样性。当粒子的pb更新时，指导粒子g_pb将会等于pb；⑤Using the guiding particle learning strategy to update the guiding particles. When the particle's stagnation times PST reaches the set maximum stagnation times max_PST, a particle's pb is randomly selected to replace the stagnant particle's individual guiding particle. In addition, to prevent premature aggregation of particles, the diversity of the population is lost. When the particle's pb is updated, the guide particle g_pb will be equal to pb;

⑥使用全局最优学习策略优化gb。在每次迭代时，随机选择一个维度r4，让gb直接学习pb中的一个随机粒子

Figure GDA0002770871000000088
⑥ Use the global optimal learning strategy to optimize gb. At each iteration, randomly select a dimension r 4 and let gb directly learn a random particle in pb
Figure GDA0002770871000000088

⑦判断算法是否满足结束条件，若满足找到使目标函数f最小的参数，此时的参数

Figure GDA0002770871000000087
为估计的最优模型参数，算法结束；若不满足，则继续跳到步骤2继续运行。⑦ Determine whether the algorithm satisfies the end condition. If it satisfies to find the parameter that minimizes the objective function f, the parameter at this time
Figure GDA0002770871000000087
For the estimated optimal model parameters, the algorithm ends; if it is not satisfied, continue to skip to step 2 to continue running.

以上所述仅表达了本发明的优选实施方式，其描述较为具体和详细，但并不能因此而理解为对本发明专利范围的限制。应当指出的是，对于本领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变形、改进及替代，这些都属于本发明的保护范围。因此，本发明专利的保护范围应以所附权利要求为准。The above description only expresses the preferred embodiments of the present invention, and the description thereof is relatively specific and detailed, but should not be construed as a limitation on the scope of the patent of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications, improvements and substitutions can be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be subject to the appended claims.

Claims (1)

1. A force feedback device dynamics parameter estimation algorithm based on a particle swarm algorithm is characterized by comprising the following steps:
the general force feedback device's equations of dynamics are detailed below:
Figure FDA0002770870990000011
Figure FDA0002770870990000012
wherein θ is a joint angle;
Figure FDA0002770870990000013
is the joint angular velocity;
Figure FDA0002770870990000014
is the angular acceleration of the joint; d is an inertia matrix of the force feedback equipment; c is a centrifugal force and Coriolis force matrix; g is a gravity matrix; fcIs a coulomb friction coefficient matrix; fvIs a viscous friction coefficient matrix; tau is joint moment; Δ X is a compensation term introduced in view of modeling uncertainty;
the parameters to be estimated are, in addition to the parameter X, a compensation parameter Δ X, as follows:
X＝[l1，l2，l3，ma，Iaxx，Iayy，Iazz，mbe，Ibexx，Ibeyy，Ibezz，mc，Icxx，Icyy，Iczz，l5，mdf，
Idfxx，Idfyy，Idfzz，l6，Idf，Fc1，Fc2，Fc3，Fv1，Fv2，Fv3]
ΔX＝[a1，b1，a2，b2，a3，b3]
wherein: the model of the force feedback equipment is divided into seven sections A to G, and X is a kinetic parameter of the force feedback equipment; l1，l2Length of the B and A segments, respectively, l3Is the distance from the intersection of the two segments AB to the segment C, l5Is the distance from the centroid of the BE segment to the origin, l6Is the distance from the center of mass of the DF segment to the origin; m isa，mbe，mc，mdfThe quality of the A section, the BE section, the C section and the DF section respectively; i isaxx，Iayy，Iazz，Ibexx，Ibeyy，Ibezz，Icxx，Icyy，Iczz，Idfxx，Idfyy，IdfzzThe components of inertia tensor matrixes of the section A, the section BE, the section C and the section DF in three axes respectively; i isdfIs the inertia tensor matrix of the DF section; fd，Fc2，Fc3Is the coulomb friction coefficient of the three joints; fv1，Fv2，Fv3Is the viscous friction coefficient of three joints, and Δ X is a compensation term introduced in consideration of modeling uncertainty; a is1，b1，a2，b2，a3，b3Coefficients for three joint compensation equations;
step 1: setting an ideal motion track of a joint angle of the force feedback equipment;
the force feedback device has N rotatable joints J1、J2…JNCorresponding N joint angles are theta1、θ2…θN(ii) a Set N number of switchesThe ideal motion trajectories of the pitch angles are respectively: angle theta1(t)、θ2(t)…θN(t), angular velocity
Figure FDA0002770870990000015
Figure FDA0002770870990000016
Angular acceleration
Figure FDA0002770870990000017
Step 2: carrying out position tracking on the ideal motion track of the joint angle;
using a PID control algorithm to control N joints of the force feedback equipment to track the position of the ideal track to obtain the input torque tau of the N joints1、τ2…τNAnd angle theta1(t)、θ2(t)…θN(t) obtaining angular velocity of each joint by using a nonlinear tracking-differentiator
Figure FDA0002770870990000021
And angular acceleration
Figure FDA0002770870990000022
And step 3: sampling the joint angular motion track and the input torque;
for the motion track: angle theta of articulation1(t)、θ2(t)…θN(t), angular velocity of joint
Figure FDA0002770870990000023
Angular acceleration of joint
Figure FDA0002770870990000024
And the input joint moment tau1、τ2…τNTo carry out
Figure FDA0002770870990000025
Sampling, wherein T is sampling time, and P is the number of sampling points; obtaining a sampling track: joint angle
Figure FDA0002770870990000026
Angular velocity of joint
Figure FDA0002770870990000027
And angular acceleration of joint
Figure FDA0002770870990000028
And moment of force
Figure FDA0002770870990000029
Figure FDA00027708709900000210
And 4, step 4: estimating force feedback equipment parameters by using an improved comprehensive learning particle swarm ICLPSO algorithm;
(a) the method comprises the following steps Parameters to be estimated
Figure FDA00027708709900000211
Substituting the angular motion track of the joint into a kinetic equation, and calculating to obtain the estimated joint moment, the moment of the ith joint and the moment of the p-th sampling
Figure FDA00027708709900000212
The calculation formula is as follows:
Figure FDA00027708709900000213
in the above formula, the first and second carbon atoms are,
Figure FDA00027708709900000214
the angle of the joint obtained by sampling for the ith joint and the p th time is obtained;
Figure FDA00027708709900000215
the joint angular velocity obtained by sampling for the ith joint and the p th time;
Figure FDA00027708709900000216
the joint angular acceleration obtained by sampling for the ith joint and the p th time; fcipThe Coulomb friction coefficient is obtained for the ith joint and the p th sampling; fvipThe viscous friction coefficient obtained by sampling the ith joint and the p th time;
(b) the method comprises the following steps Defining an error matrix as calculating the measured joint moments tau and the estimated joint moments
Figure FDA00027708709900000220
Error between
Figure FDA00027708709900000217
Figure FDA00027708709900000218
The resulting error matrix E is:
Figure FDA00027708709900000219
defining an objective function:
f＝||E||2
(c) the method comprises the following steps Setting parameters of an ICLPSO algorithm: a particle dimension D; the number of particles Q; maximum number of iterations max _ iteration; maximum evaluation times max _ EFS; the maximum number of stalls max _ PST; particle search range of [ Hmin Hmax]；
Firstly, initializing parameters of ICLPSO algorithm, particle number Q, particle dimension D and search boundary [ Hmin Hmax]Iteration times iteration, evaluation times EFS, stagnation times PST of each particle, and random initialization of particle position H and velocity V;
evaluating the positions of the particles to obtain the fitness value of each particle, updating the individual historical optimal position pb of each particle and the optimal position gb found by the population in the whole searching process, and updating iteration and EFS;
updating the particle speed V and the particle position H by using a layered updating strategy, and setting a parameter M to be Q/2 and a parameter K to be Q/4; evaluating each particle to obtain a fitness value, updating pb and gb of each particle, and updating iteration and EFS;
if f (pb) of the particlei)＜f(S_pbM) The velocity of the particle is updated using the following formula
Figure FDA0002770870990000031
Otherwise, the velocity of the particle is updated using the following formula
Figure FDA0002770870990000032
Figure FDA0002770870990000033
Wherein,
Figure FDA0002770870990000034
is the d-dimensional velocity of the ith particle; w is the inertial weight, regulating the search capability on the solution space;
Figure FDA0002770870990000035
is the position of the guide particle of the ith particle in d dimension;
Figure FDA0002770870990000036
is the position of the ith particle in d dimension; gbdThe optimal position of the particle population found in d dimension; pbiIs the historical optimal position of an individual, S _ pb is the position of pb sorted from small to large according to fitness value, g _ pb is the guide particle generated by pb, cn is the center of the first K positions in S _ pb, c1And c2Is an acceleration factor, r1And r2Is 0 to1, random numbers uniformly distributed among the random numbers; cn (c)dThe first K values in S _ pb are at the center of the d-dimension position;
fourthly, updating the particle position H by using a position learning strategy; each particle has the ability to learn other particles, the probability of learning other particles is PLX is 0.25, if the random number r is 0-13Less than PLX, then in this dimension, the particle learns another particle;
updating the guide particles by using a guide particle learning strategy; randomly selecting pb of one particle to replace an individual guide particle of a stagnant particle when the stagnation number PST of the particle reaches a set maximum stagnation number max _ PST, and in addition, in order to prevent the particles from gathering together too early and losing the diversity of the population, when the pb of the particles is updated, the guide particle g _ pb is equal to pb;
sixthly, using a global optimal learning strategy to optimize the gb; at each iteration, a dimension r is randomly selected4Let gb directly learn a random particle in pb
Figure FDA0002770870990000041
Seventhly, judging whether the algorithm meets the end condition, if the algorithm meets the end condition, finding the parameter which enables the target function f to be minimum, and determining the parameter at the moment
Figure FDA0002770870990000042
The algorithm is ended for the estimated optimal model parameters; if not, continuously jumping to the step 2 to continuously operate.
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