CN112549028A - Double-arm robot track planning method based on dynamic motion primitives and artificial potential field - Google Patents
Double-arm robot track planning method based on dynamic motion primitives and artificial potential field Download PDFInfo
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Abstract
Description
技术领域technical field
本发明属于机器人轨迹规划领域,具体涉及一种基于动态运动基元和人工势场的双臂机器人轨迹规划方法、系统、装置。The invention belongs to the field of robot trajectory planning, and in particular relates to a dual-arm robot trajectory planning method, system and device based on dynamic motion primitives and artificial potential fields.
背景技术Background technique
轨迹规划是机械臂控制的基础,是控制双臂机器人运动的关键技术之一,对机械臂工作效率、运动平稳性等都具有重要意义。常见的轨迹规划算法包括样条插值法、快速探索随机树(RRT)、人工势场法等。基于样条插值的轨迹规划方法含有时间常数,使得多自由度轨迹学习较为困难;快速探索随机树等基于统计的方法生成的轨迹连续性不好,在复杂环境中可能出现路径迂回和死锁,由于其搜索的盲目性,迭代的次数增加,其计算量大大增加,导致其实时性差,效率较低;人工势场法是轨迹规划算法中较为成熟且高效的规划方法,因其简单的数学模型被广泛使用,但其容易陷入局部极小值。基于此,本发明提出了一种基于动态运动基元和人工势场的双臂机器人轨迹规划方法。Trajectory planning is the basis of manipulator control and one of the key technologies to control the motion of dual-arm robots. It is of great significance to the work efficiency and motion stability of the manipulator. Common trajectory planning algorithms include spline interpolation, rapid exploration random tree (RRT), artificial potential field method, etc. The trajectory planning method based on spline interpolation contains a time constant, which makes multi-DOF trajectory learning difficult; the trajectory generated by statistical-based methods such as rapid exploration of random trees has poor continuity, and path detours and deadlocks may occur in complex environments. Due to the blindness of its search, the number of iterations increases, and the amount of calculation increases greatly, resulting in poor real-time performance and low efficiency; artificial potential field method is a relatively mature and efficient planning method in trajectory planning algorithms, because of its simple mathematical model is widely used, but it is prone to falling into local minima. Based on this, the present invention proposes a trajectory planning method for a dual-arm robot based on dynamic motion primitives and artificial potential fields.
发明内容SUMMARY OF THE INVENTION
为了解决现有技术中的上述问题,即为了解决现有机器人轨迹规划方法实时性差、泛化性差、效率低的问题,本发明第一方面,提出了一种基于动态运动基元和人工势场的双臂机器人轨迹规划方法,该方法包括:In order to solve the above problems in the prior art, that is, in order to solve the problems of poor real-time performance, poor generalization and low efficiency of the existing robot trajectory planning methods, the first aspect of the present invention proposes a method based on dynamic motion primitives and artificial potential fields. A dual-arm robot trajectory planning method, the method includes:
步骤S10,获取双臂机器人待路径规划的目标位置,作为输入数据;Step S10, obtaining the target position of the dual-arm robot to be planned by the path as input data;
步骤S20,基于所述输入数据,双臂机器人通过预构建的动态运动基元模型得到对应的规划路径,并沿该规划路径移动至所述目标位置;Step S20, based on the input data, the dual-arm robot obtains a corresponding planned path through a pre-built dynamic motion primitive model, and moves to the target position along the planned path;
其中,所述动态运动基元模型,其构建方法为:Wherein, the construction method of the dynamic motion primitive model is:
步骤A10,基于双臂机器人的D-H参数表,构建双臂机器人模型并通过蒙特卡洛算法求解双臂机器人的工作空间;Step A10, based on the D-H parameter table of the dual-arm robot, construct a dual-arm robot model and solve the workspace of the dual-arm robot through a Monte Carlo algorithm;
步骤A20,在所述工作空间中设置起始位置、目标位置及对应的示范路径,并实时采集双臂机器人沿所述示范路径移动时的轨迹运动数据,作为第一数据;所述轨迹运动数据包括位移、速度、加速度;Step A20, set the starting position, the target position and the corresponding demonstration path in the workspace, and collect the trajectory motion data when the dual-arm robot moves along the demonstration path in real time, as the first data; the trajectory motion data Including displacement, velocity, acceleration;
步骤A30,基于所述第一数据,通过预构建的第一模型,得到示范路径对应的非线性强迫项,作为第一强迫项;所述第一模型为不包含强迫项的离散运动的动态运动基元模型;Step A30, based on the first data, obtain a nonlinear forcing term corresponding to the demonstration path through a pre-built first model, as the first forcing term; the first model is a dynamic motion of discrete motion that does not include the forcing term primitive model;
步骤A40,基于所述第一强迫项,结合设定的学习路径的起始位置、目标位置,通过局部加权法获取每个基函数的最佳权重值,并构建所述学习路径对应的非线性强迫项,作为第二强迫项;Step A40, based on the first forcing term, combined with the starting position and target position of the set learning path, obtain the optimal weight value of each basis function through a local weighting method, and construct a nonlinear corresponding to the learning path. compulsion, as a second compulsion;
步骤A50,在所述第一模型中加入所述第二强迫项、预构建的加速度排斥项,构建带有避障功能的动态运动基元模型,作为最终构建的动态运动基元模型;所述加速度排斥项基于人工势场的负梯度构建。Step A50, adding the second forced term and the pre-built acceleration exclusion term to the first model, and constructing a dynamic motion primitive model with an obstacle avoidance function as the final dynamic motion primitive model; the The acceleration repulsion term is constructed based on the negative gradient of the artificial potential field.
在一些优选的实施方式中,所述不包含强迫项的离散运动的动态运动基元模型为:In some preferred embodiments, the dynamic motion primitive model of discrete motion that does not contain forced terms is:
其中,τ表示时间缩放因子,αy表示弹性常数,βy表示系统阻尼项,g表示目标位置,y、表示基元在运动过程中的位置、速度、加速度。Among them, τ represents the time scaling factor, α y represents the elastic constant, β y represents the system damping term, g represents the target position, y, Indicates the position, velocity, and acceleration of the primitive during motion.
在一些优选的实施方式中,所述示范路径对应的非线性强迫项为:In some preferred embodiments, the nonlinear forcing term corresponding to the exemplary path is:
其中,ftarget表示示范路径对应的非线性强迫项的实际值,ydemo、表示示范轨迹对应的基元在运动过程中位置、速度和加速度,y0、g0表示示范轨迹对应的起始位置、目标位置。Among them, f target represents the actual value of the nonlinear forced term corresponding to the demonstration path, y demo , It represents the position, velocity and acceleration of the primitive corresponding to the demonstration trajectory during the movement process, and y 0 and g 0 represent the starting position and target position corresponding to the demonstration trajectory.
在一些优选的实施方式中,“通过局部加权法获取每个基函数的最佳权重值”,其方法为:In some preferred embodiments, "obtaining the optimal weight value of each basis function through a local weighting method", the method is:
S=(ξ(1) ξ(2) ... ξ(p))T S=(ξ(1) ξ(2) ... ξ(p)) T
ξ=x(g1-y1)ξ=x(g 1 -y 1 )
其中,ψi表示服从中心为ci,方差为hi的高斯分布的基函数,ST表示,Γi表示,x表示相位变量,ωi表示第i个基函数的权重,i表示下标,T表示转置,y1、g1分别表示学习轨迹对应的起始位置、目标位置,p表示数量,为设定值。Among them, ψ i represents the basis function that obeys the Gaussian distribution whose center is c i and the variance is hi , S T represents, Γ i represents, x represents the phase variable, ω i represents the weight of the ith basis function, and i represents the subscript , T represents the transposition, y 1 and g 1 represent the starting position and target position corresponding to the learning trajectory, respectively, and p represents the quantity, which is the set value.
在一些优选的实施方式中,所述学习路径对应的非线性强迫项为:In some preferred embodiments, the nonlinear forced term corresponding to the learning path is:
其中,f表示学习路径对应的非线性强迫项的实际值,N表示基函数的个数。Among them, f represents the actual value of the nonlinear forced term corresponding to the learning path, and N represents the number of basis functions.
在一些优选的实施方式中,所述加速度排斥项为:In some preferred embodiments, the acceleration exclusion term is:
U(y)=Uatt(y)+Urep(y)U(y)=U att (y)+U rep (y)
其中,表示加速度排斥项对应的实际值,U(y)表示在点y处的势函数,Urep(y)、Uatt(y)表示在点y处的引力势、斥力势,表示引力增益,d(y,g1)表示当前点y到目标点g1之间的距离,η表示斥力增益,D(y)表示点y与最近障碍物之间的距离,Q表示障碍物距离作用阈值。in, represents the actual value corresponding to the acceleration repulsion term, U(y) represents the potential function at point y, U rep (y), U att (y) represent the gravitational potential and repulsion potential at point y, represents the gravitational gain, d(y, g 1 ) represents the distance between the current point y and the target point g 1 , η represents the repulsion gain, D(y) represents the distance between the point y and the nearest obstacle, and Q represents the obstacle Distance action threshold.
在一些优选的实施方式中,所述带有避障功能的动态运动基元模型为: In some preferred embodiments, the dynamic motion primitive model with obstacle avoidance function is:
本发明的第二方面,提出了一种基于动态运动基元和人工势场的双臂机器人轨迹规划系统,该系统包括位置获取模块、路径规划输出模块;In a second aspect of the present invention, a dual-arm robot trajectory planning system based on dynamic motion primitives and artificial potential fields is proposed, the system includes a position acquisition module and a path planning output module;
所述位置获取模块,配置为获取双臂机器人待路径规划的目标位置,作为输入数据;The position obtaining module is configured to obtain the target position of the dual-arm robot to be planned by the path as input data;
所述路径规划输出模块,配置为基于所述输入数据,双臂机器人通过预构建的动态运动基元模型得到对应的规划路径,并沿该规划路径移动至所述目标位置;The path planning output module is configured to, based on the input data, the dual-arm robot obtains a corresponding planned path through a pre-built dynamic motion primitive model, and moves to the target position along the planned path;
其中,所述动态运动基元模型,其构建方法为:Wherein, the construction method of the dynamic motion primitive model is:
步骤A10,基于双臂机器人的D-H参数表,构建双臂机器人模型并通过蒙特卡洛算法求解双臂机器人的工作空间;Step A10, based on the D-H parameter table of the dual-arm robot, construct a dual-arm robot model and solve the workspace of the dual-arm robot through a Monte Carlo algorithm;
步骤A20,在所述工作空间中设置起始位置、目标位置及对应的示范路径,并实时采集双臂机器人沿所述示范路径移动时的轨迹运动数据,作为第一数据;所述轨迹运动数据包括位移、速度、加速度;Step A20, set the starting position, the target position and the corresponding demonstration path in the workspace, and collect the trajectory motion data when the dual-arm robot moves along the demonstration path in real time, as the first data; the trajectory motion data Including displacement, velocity, acceleration;
步骤A30,基于所述第一数据,通过预构建的第一模型,得到示范路径对应的非线性强迫项,作为第一强迫项;所述第一模型为不包含强迫项的离散运动的动态运动基元模型;Step A30, based on the first data, obtain a nonlinear forcing term corresponding to the demonstration path through a pre-built first model, as the first forcing term; the first model is a dynamic motion of discrete motion that does not include the forcing term primitive model;
步骤A40,基于所述第一强迫项,结合设定的学习路径的起始位置、目标位置,通过局部加权法获取每个基函数的最佳权重值,并构建所述学习路径对应的非线性强迫项,作为第二强迫项;Step A40, based on the first forcing term, combined with the starting position and target position of the set learning path, obtain the optimal weight value of each basis function through a local weighting method, and construct a nonlinear corresponding to the learning path. compulsion, as a second compulsion;
步骤A50,在所述第一模型中加入所述第二强迫项、预构建的加速度排斥项,构建带有避障功能的动态运动基元模型,作为最终构建的动态运动基元模型;所述加速度排斥项基于人工势场的负梯度构建。Step A50, adding the second forced term and the pre-built acceleration exclusion term to the first model, and constructing a dynamic motion primitive model with an obstacle avoidance function as the final dynamic motion primitive model; the The acceleration repulsion term is constructed based on the negative gradient of the artificial potential field.
本发明的第三方面,提出了一种存储装置,其中存储有多条程序,所述程序适用于由处理器加载并执行以实现上述的基于动态运动基元和人工势场的双臂机器人轨迹规划方法。In a third aspect of the present invention, a storage device is provided, in which a plurality of programs are stored, and the programs are suitable for being loaded and executed by a processor to realize the above-mentioned dual-arm robot trajectory based on dynamic motion primitives and artificial potential fields. planning method.
本发明的第四方面,提出了一种处理装置,包括处理器、存储装置;处理器,适用于执行各条程序;存储装置,适用于存储多条程序;所述程序适用于由处理器加载并执行以实现上述的基于动态运动基元和人工势场的双臂机器人轨迹规划方法。In a fourth aspect of the present invention, a processing device is proposed, including a processor and a storage device; the processor is adapted to execute various programs; the storage device is adapted to store multiple programs; the programs are adapted to be loaded by the processor And execute to realize the above-mentioned dual-arm robot trajectory planning method based on dynamic motion primitives and artificial potential field.
本发明的有益效果:Beneficial effects of the present invention:
本发明提高了有机器人轨迹规划的实时性、泛化性以及效率。The invention improves the real-time performance, generalization and efficiency of robot trajectory planning.
(1)本发明只需采集一次轨迹样本数据进行训练,便获得动态运动基元模型权重参数,从而实现机器人自主轨迹规划。在此基础上,在机器人在完成新的任务时,只要修改运动的起点和目标点和相关参数便可,可以不用重新训练样本而保持原来样本轨迹的特性到达新的目标位置,而且该学习模型并非针对某一具体任务,其具有泛化推广的能力。(1) In the present invention, only one trajectory sample data is collected for training, and the weight parameters of the dynamic motion primitive model are obtained, thereby realizing the autonomous trajectory planning of the robot. On this basis, when the robot completes a new task, as long as the starting point, target point and related parameters of the movement are modified, it can maintain the characteristics of the original sample trajectory to reach the new target position without retraining the sample, and the learning model Rather than targeting a specific task, it has the ability to generalize.
(2)本发明将人工势场法应用到动态运动基元的方法中,即在具有稳定性质的二阶动力学系统中引入排斥加速度项,使得生成的轨迹点远离障碍物,如此生成的轨迹不但拥有预期的运动趋势,还可以同时达到避障的效果,提高了轨迹规划的效率和安全性。(2) The present invention applies the artificial potential field method to the method of dynamic motion primitives, that is, the repulsive acceleration term is introduced into the second-order dynamic system with stable properties, so that the generated trajectory points are far away from obstacles, and the trajectory thus generated is It not only has the expected movement trend, but also achieves the effect of obstacle avoidance at the same time, which improves the efficiency and safety of trajectory planning.
(3)本发明将人工势场法应用到动态运动基元的方法中,与快速探索随机树等基于概率采样的方法相比,本发明方法学习到的轨迹更加连续;与插值法相比,更易于实现多自由度耦合,可对多自由度轨迹进行模仿和学习,并且本方法的相关参数较少,调节参数也更为容易。(3) The present invention applies the artificial potential field method to the method of dynamic motion primitives. Compared with methods based on probability sampling such as rapid exploration of random trees, the trajectory learned by the method of the present invention is more continuous; It is easy to realize multi-degree-of-freedom coupling, which can imitate and learn multi-degree-of-freedom trajectories, and this method has fewer related parameters, and it is easier to adjust parameters.
附图说明Description of drawings
通过阅读参照以下附图所做的对非限制性实施例所做的详细描述,本申请的其他特征、目的和优点将会变得更明显。Other features, objects and advantages of the present application will become more apparent upon reading the detailed description of non-limiting embodiments taken with reference to the following drawings.
图1是本发明一种实施例的动态运动基元模型的构建过程的流程示意图;1 is a schematic flowchart of a construction process of a dynamic motion primitive model according to an embodiment of the present invention;
图2是本发明一种实施例的基于动态运动基元和人工势场的双臂机器人轨迹规划系统的框架示意图;2 is a schematic diagram of a framework of a dual-arm robot trajectory planning system based on dynamic motion primitives and artificial potential fields according to an embodiment of the present invention;
图3是本发明一种实施例的生成轨迹与示范轨迹的轨迹对比的示例图。FIG. 3 is an exemplary diagram illustrating the comparison of the generated trajectory and the trajectories of the exemplary trajectory according to an embodiment of the present invention.
具体实施方式Detailed ways
为使本发明的目的、技术方案和优点更加清楚,下面将结合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。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the objectives, technical solutions and advantages 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 accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not All examples. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
下面结合附图和实施例对本申请作进一步的详细说明。可以理解的是,此处所描述的具体实施例仅用于解释相关发明,而非对该发明的限定。另外还需要说明的是,为了便于描述,附图中仅示出了与有关发明相关的部分。The present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the related invention, but not to limit the invention. In addition, it should be noted that, for the convenience of description, only the parts related to the related invention are shown in the drawings.
需要说明的是,在不冲突的情况下,本申请中的实施例及实施例中的特征可以相互组合。It should be noted that the embodiments in the present application and the features of the embodiments may be combined with each other in the case of no conflict.
本发明的基于动态运动基元和人工势场的双臂机器人轨迹规划方法,包括以下步骤:The dual-arm robot trajectory planning method based on dynamic motion primitives and artificial potential fields of the present invention includes the following steps:
步骤S10,获取双臂机器人待路径规划的目标位置,作为输入数据;Step S10, obtaining the target position of the dual-arm robot to be planned by the path as input data;
步骤S20,基于所述输入数据,双臂机器人通过预构建的动态运动基元模型得到对应的规划路径,并沿该规划路径移动至所述目标位置;Step S20, based on the input data, the dual-arm robot obtains a corresponding planned path through a pre-built dynamic motion primitive model, and moves to the target position along the planned path;
其中,所述动态运动基元模型,其构建方法为:Wherein, the construction method of the dynamic motion primitive model is:
步骤A10,基于双臂机器人的D-H参数表,构建双臂机器人模型并通过蒙特卡洛算法求解双臂机器人的工作空间;Step A10, based on the D-H parameter table of the dual-arm robot, construct a dual-arm robot model and solve the workspace of the dual-arm robot through a Monte Carlo algorithm;
步骤A20,在所述工作空间中设置起始位置、目标位置及对应的示范路径,并实时采集双臂机器人沿所述示范路径移动时的轨迹运动数据,作为第一数据;所述轨迹运动数据包括位移、速度、加速度;Step A20, set the starting position, the target position and the corresponding demonstration path in the workspace, and collect the trajectory motion data when the dual-arm robot moves along the demonstration path in real time, as the first data; the trajectory motion data Including displacement, velocity, acceleration;
步骤A30,基于所述第一数据,通过预构建的第一模型,得到示范路径对应的非线性强迫项,作为第一强迫项;所述第一模型为不包含强迫项的离散运动的动态运动基元模型;Step A30, based on the first data, obtain a nonlinear forcing term corresponding to the demonstration path through a pre-built first model, as the first forcing term; the first model is a dynamic motion of discrete motion that does not include the forcing term primitive model;
步骤A40,基于所述第一强迫项,结合设定的学习路径的起始位置、目标位置,通过局部加权法获取每个基函数的最佳权重值,并构建所述学习路径对应的非线性强迫项,作为第二强迫项;Step A40, based on the first forcing term, combined with the starting position and target position of the set learning path, obtain the optimal weight value of each basis function through a local weighting method, and construct a nonlinear corresponding to the learning path. compulsion, as a second compulsion;
步骤A50,在所述第一模型中加入所述第二强迫项、预构建的加速度排斥项,构建带有避障功能的动态运动基元模型,作为最终构建的动态运动基元模型;所述加速度排斥项基于人工势场的负梯度构建。Step A50, adding the second forced term and the pre-built acceleration exclusion term to the first model, and constructing a dynamic motion primitive model with an obstacle avoidance function as the final dynamic motion primitive model; the The acceleration repulsion term is constructed based on the negative gradient of the artificial potential field.
为了更清晰地对本发明基于动态运动基元和人工势场的双臂机器人轨迹规划方法进行说明,下面结合附图对本发明方法一种实施例中各步骤进行展开详述。In order to more clearly describe the dual-arm robot trajectory planning method based on dynamic motion primitives and artificial potential fields of the present invention, each step in an embodiment of the method of the present invention will be described in detail below with reference to the accompanying drawings.
在下述实施例中,先对动态运动基元模型的构建过程进行详述,再对基于动态运动基元和人工势场的双臂机器人轨迹规划方法获取规划路径的过程进行详述。In the following embodiments, the construction process of the dynamic motion primitive model is first described in detail, and then the process of obtaining the planned path by the dual-arm robot trajectory planning method based on the dynamic motion primitive and the artificial potential field is described in detail.
1、动态运动基元模型的构建过程,如图1所示1. The construction process of the dynamic motion primitive model, as shown in Figure 1
步骤A10,基于双臂机器人的D-H参数表,构建双臂机器人模型并通过蒙特卡洛算法求解双臂机器人的工作空间;Step A10, based on the D-H parameter table of the dual-arm robot, construct a dual-arm robot model and solve the workspace of the dual-arm robot through a Monte Carlo algorithm;
在本实施例中,根据双臂机器人的D-H参数表,通过MATLAB中Robotic Toolbox工具包建立双臂机器人模型,并采用蒙特卡洛算法对双臂机器人工作空间进行求解计算,得到机器人的具体工作范围(即工作空间)。In this embodiment, according to the D-H parameter table of the dual-arm robot, a dual-arm robot model is established through the Robotic Toolbox toolkit in MATLAB, and the Monte Carlo algorithm is used to solve and calculate the workspace of the dual-arm robot to obtain the specific working range of the robot. (i.e. workspace).
步骤A20,在所述工作空间中设置起始位置、目标位置及对应的示范路径,并实时采集双臂机器人沿所述示范路径移动时的轨迹运动数据,作为第一数据;所述轨迹运动数据包括位移、速度、加速度;Step A20, set the starting position, the target position and the corresponding demonstration path in the workspace, and collect the trajectory motion data when the dual-arm robot moves along the demonstration path in real time, as the first data; the trajectory motion data Including displacement, velocity, acceleration;
在本实施例中,开启双臂机器人,在双臂机器人工作空间内设置起始位置和目标位置,并选择一条使双臂机器人能够从起始位置运动到目标位置,并可以避开障碍物的最优路径,即示范路径。In this embodiment, the dual-arm robot is turned on, the starting position and the target position are set in the working space of the dual-arm robot, and one is selected so that the dual-arm robot can move from the starting position to the target position and avoid obstacles. The optimal path is the demonstration path.
在双臂机器人运动过程中,实时采集双臂机器人沿示范路径移动时在笛卡尔坐标系中沿x-y-z三维方向的轨迹运动数据,轨迹运动数据包括位移、速度、加速度。During the movement of the dual-arm robot, the trajectory motion data along the x-y-z three-dimensional direction in the Cartesian coordinate system are collected in real time when the dual-arm robot moves along the demonstration path. The trajectory motion data includes displacement, velocity, and acceleration.
步骤A30,基于所述第一数据,通过预构建的第一模型,得到示范路径对应的非线性强迫项,作为第一强迫项;所述第一模型为不包含强迫项的离散运动的动态运动基元模型;Step A30, based on the first data, obtain a nonlinear forcing term corresponding to the demonstration path through a pre-built first model, as the first forcing term; the first model is a dynamic motion of discrete motion that does not include the forcing term primitive model;
在本实施例中,通过利用示范轨迹样本进行训练,获得动态运动基元模型参数,从而实现机器人自主轨迹规划。In this embodiment, the parameters of the dynamic motion primitive model are obtained by using the demonstration trajectory samples for training, so as to realize the autonomous trajectory planning of the robot.
动态运动基元模型DMP本质上是在一个具有稳定性质的二阶动力学系统中引入一系列高斯函数加权叠加的非线性函数项。由非线性函数来决定动态系统的运动过程,从而使系统达到目标吸引子状态。该方法以弹簧-质量-阻尼模型为基础,将其抽象为点吸引子系统。其中,不包含强迫项的离散运动的动态运动基元模型,如式(1)所示:The dynamic motion primitive model DMP is essentially a nonlinear function term that introduces a series of Gaussian functions weighted and superimposed in a stable second-order dynamic system. The motion process of the dynamic system is determined by the nonlinear function, so that the system can reach the target attractor state. The method is based on the spring-mass-damper model, which is abstracted as a point attraction subsystem. Among them, the dynamic motion primitive model of discrete motion without forced terms is shown in formula (1):
其中,τ表示时间缩放因子,用来调节典型系统的缩放速度,αy表示弹性常数,βy表示系统阻尼项,一般为βy=αy/4,使得系统到达临界阻尼状态,g表示目标位置,y、表示基元在运动过程中的位置、速度、加速度。Among them, τ represents the time scaling factor, which is used to adjust the scaling speed of the typical system, α y represents the elastic constant, β y represents the system damping term, generally β y = α y /4, so that the system reaches the critical damping state, g represents the target position, y, Indicates the position, velocity, and acceleration of the primitive during motion.
式(1)中的动态系统是只有一个点吸引子的二阶系统,因此该系统只能以一种特定的运动形式收敛到目标位置g,为了使系统能够按照我们想要的运动形式收敛到目标点,我们将非线性强迫项f引入到式(1)中,得到式(2)(3):The dynamic system in equation (1) is a second-order system with only one point attractor, so the system can only converge to the target position g in a specific motion form. At the target point, we introduce the nonlinear forcing term f into equation (1) to obtain equations (2) and (3):
其中,式(3)为调制时间的正则系统,x表示相位变量,αx表示正则系统参数,为x的一阶导数。Among them, formula (3) is the canonical system of modulation time, x represents the phase variable, α x represents the canonical system parameter, is the first derivative of x.
上述方案中设置初始参数包括目标位置g,弹性常数αy,系统阻尼项βy,时间缩放因子τ,f为非线性强迫项,使得系统生成任意非线性的复杂运动。根据式(2)可以逆向推导得出示范轨迹中非线性强迫项,如公式(4)所示:The initial parameters set in the above scheme include target position g, elastic constant α y , system damping term β y , time scaling factor τ, f is a nonlinear forcing term, so that the system can generate arbitrary nonlinear complex motion. According to equation (2), the nonlinear forcing term in the demonstration trajectory can be derived backwards, as shown in equation (4):
其中,ftarget表示示范路径对应的非线性强迫项的实际值,ydemo、表示示范轨迹对应的基元在运动过程中位置、速度和加速度,y0、g0表示示范轨迹对应的起始位置、目标位置。Among them, f target represents the actual value of the nonlinear forced term corresponding to the demonstration path, y demo , It represents the position, velocity and acceleration of the primitive corresponding to the demonstration trajectory during the movement process, and y 0 and g 0 represent the starting position and target position corresponding to the demonstration trajectory.
步骤A40,基于所述第一强迫项,结合设定的学习路径的起始位置、目标位置,通过局部加权法获取每个基函数的最佳权重值,并构建所述学习路径对应的非线性强迫项,作为第二强迫项;Step A40, based on the first forcing term, combined with the starting position and target position of the set learning path, obtain the optimal weight value of each basis function through a local weighting method, and construct a nonlinear corresponding to the learning path. compulsion, as a second compulsion;
在本实施例中,根据机器人的初始任务设定动态运动基元方法的相关初始参数,并给出机器人学习的起始位置和目标位置,以及所计算出的最佳权重值,如此便可通过动态运动基元模型生成一条学习轨迹,该轨迹具有示范轨迹的特性,即运动趋势与原示范轨迹基本相同。In this embodiment, the relevant initial parameters of the dynamic motion primitive method are set according to the initial task of the robot, and the starting position and target position of the robot learning and the calculated optimal weight value are given, so that the The dynamic motion primitive model generates a learning trajectory, which has the characteristics of the demonstration trajectory, that is, the motion trend is basically the same as the original demonstration trajectory.
其中,计算学习轨迹的非线性强迫项,如公式(5)(6)所示:Among them, the nonlinear forced term of the learning trajectory is calculated, as shown in formulas (5) and (6):
其中,f表示学习路径对应的非线性强迫项的实际值,N表示基函数的个数,ψi表示服从中心为ci,方差为hi的高斯分布的基函数,x表示相位变量,ωi表示第i个基函数的权重,i表示下标,T表示转置,y1、g1表示学习轨迹对应的起始位置、目标位置。Among them, f represents the actual value of the nonlinear forcing term corresponding to the learning path, N represents the number of basis functions, ψ i represents the basis function obeying a Gaussian distribution with center c i and variance hi , x represents the phase variable, ω i represents the weight of the ith basis function, i represents the subscript, T represents the transposition, and y 1 and g 1 represent the starting position and target position corresponding to the learning trajectory.
可以看出,基函数ψi通过加权相加,组合成强迫函数f。由于基函数ψi是非线性的,因此强迫函数f和整个动态运动基元系统也是非线性的。式(6)表明基函数ψi服从中心为ci,方差为hi的高斯分布。ωi为基函数权重,N为基函数个数,基函数个数越多,泛化目标轨迹越平滑。It can be seen that the basis functions ψ i are combined into a forcing function f through weighted addition. Since the basis function ψi is nonlinear, the forcing function f and the entire system of dynamic motion primitives are also nonlinear. Equation (6) shows that the basis function ψ i obeys a Gaussian distribution whose center is ci and whose variance is hi . ω i is the basis function weight, N is the number of basis functions, the more the number of basis functions, the smoother the generalized target trajectory.
基函数权重,其计算过程如公式(7)(8)(9)(10)所示:Basis function weight, its calculation process is shown in formula (7)(8)(9)(10):
S=(ξ(1) ξ(2) ... ξ(p))T (8)S=(ξ(1) ξ(2) ... ξ(p)) T (8)
ξ=x(g1-y1) (9)ξ=x(g 1 -y 1 ) (9)
其中,ψi表示服从中心为ci,方差为hi的高斯分布的基函数,i表示下标,T表示转置,y1、g1分别表示学习轨迹对应的起始位置、目标位置,p表示数量,为设定值。Among them, ψ i represents the basis function obeying the Gaussian distribution whose center is c i and the variance is hi, i represents the subscript, T represents the transposition, y 1 and g 1 represent the corresponding starting position and target position of the learning trajectory, respectively, p represents the quantity, which is the set value.
如图3所示,一条示范轨迹(黑色曲线),一条为学习轨迹(灰色曲线),该轨迹具有示范轨迹的特性,即运动趋势与原示范轨迹基本相同。As shown in FIG. 3 , one demonstration trajectory (black curve) and the other is the learning trajectory (grey curve), and the trajectory has the characteristics of the demonstration trajectory, that is, the movement trend is basically the same as the original demonstration trajectory.
步骤A50,在所述第一模型中加入所述第二强迫项、预构建的加速度排斥项,构建带有避障功能的动态运动基元模型,作为最终构建的动态运动基元模型;所述加速度排斥项基于人工势场的负梯度构建。Step A50, adding the second forced term and the pre-built acceleration exclusion term to the first model, and constructing a dynamic motion primitive model with an obstacle avoidance function as the final dynamic motion primitive model; the The acceleration repulsion term is constructed based on the negative gradient of the artificial potential field.
人工势场法是一种常见的在线避障方法。在本发明中,势场被定义在障碍物周围,同时势场的梯度对机器人产生排斥力。这种方法在移动机器人的运动规划中比较常见,也同样被用到机器人执行器中。Artificial potential field method is a common online obstacle avoidance method. In the present invention, the potential field is defined around the obstacle, and the gradient of the potential field produces a repulsive force on the robot. This approach is common in motion planning for mobile robots and is also used in robotic actuators.
本发明关注机械臂末端执行器的运动,相比于关节空间,在执行器空间中,障碍物的位置和势场更容易得到,因此,在执行其空间中使用DMPs只需要添加一个排斥项便可得到带有避障功能的动态运动基元模型。这个加法允许生成的运动路径被势函数的属性改变,每个障碍物在运动点处创建一个势场U(y),即 表示加速度排斥项对应的实际值。The present invention focuses on the motion of the end-effector of the manipulator. Compared with the joint space, the position and potential field of obstacles are easier to obtain in the actuator space. Therefore, the use of DMPs in the execution space only needs to add an exclusion term. A dynamic motion primitive model with obstacle avoidance function can be obtained. This addition allows the resulting motion path to be altered by the properties of the potential function, each obstacle creating a potential field U(y) at the point of motion, i.e. Indicates the actual value corresponding to the acceleration exclusion term.
在本实施例中,排斥加速度是人工势场的负梯度,它取决于末端执行器相对于障碍物的相对位置和速度,如此便使得生成的运动路径被势函数的属性改变。加入一个加速度排斥项的动态运动基元模型为式(11):In this embodiment, the repulsive acceleration is the negative gradient of the artificial potential field, which depends on the relative position and velocity of the end effector relative to the obstacle, so that the resulting motion path is changed by the properties of the potential function. The dynamic motion primitive model with an acceleration repulsion term added is equation (11):
我们可以根据实际任务需要将工作环境中的障碍物位置点设置为斥力场Urep(y),将任务目标点设置为引力场Uatt(y),则其运动过程中受到总力场U(y)的影响。在式中的附加项由势场的梯度给出,即某点y处的势函数U(y)为引力势和斥力势之和,如公式(12)所示:We can set the obstacle position point in the working environment as the repulsion field U rep (y) according to the actual task needs, and set the task target point as the gravitational field U att (y), then it will be affected by the total force field U ( y) impact. The additional term in Eq. is given by the gradient of the potential field, i.e. The potential function U(y) at a certain point y is the sum of the gravitational potential and the repulsive potential, as shown in formula (12):
U(y)=Uatt(y)+Urep(y) (12)U(y)=U att (y)+U rep (y) (12)
引力势函数,如式(13)所示:The gravitational potential function is shown in formula (13):
斥力势函数如式(14)所示:The repulsive potential function is shown in formula (14):
其中,表示加速度排斥项对应的实际值,U(y)表示在点y处的势函数,Urep(y)、Uatt(y)表示在点y处的引力势、斥力势,表示引力增益,d(y,g1)表示当前点y到目标点g1之间的距离,η表示斥力增益,D(y)表示点y与最近障碍物之间的距离,Q表示障碍物距离作用阈值,大于此距离的障碍物不会产生斥力影响。in, represents the actual value corresponding to the acceleration repulsion term, U(y) represents the potential function at point y, U rep (y), U att (y) represent the gravitational potential and repulsion potential at point y, represents the gravitational gain, d(y, g 1 ) represents the distance between the current point y and the target point g 1 , η represents the repulsion gain, D(y) represents the distance between the point y and the nearest obstacle, and Q represents the obstacle Threshold of distance action. Obstacles larger than this distance will not have repulsion effect.
在双臂机器人操作过程中,会出现障碍物与目标点距离相近的情况,在这种情况下,人工势场法会出现目标不可达的情况。针对这种情况,我们对斥力函数进行改进,在原斥力函数中,加入一个机器人与目标点之间的相对距离项,如上式(14),使得机器人向目标点运动过程中引力和斥力同时趋近于0,这样机器人到达目标点时所受合力为0,则人工势场法中的目标不可达的问题解决。During the operation of the dual-arm robot, there will be a situation where the distance between the obstacle and the target point is close. In this case, the artificial potential field method will cause the target to be unreachable. In view of this situation, we improve the repulsion function. In the original repulsion function, a relative distance term between the robot and the target point is added, as shown in the above formula (14), so that the gravitational force and the repulsive force approach simultaneously when the robot moves to the target point. is set to 0, so that the resultant force when the robot reaches the target point is 0, and the problem that the target cannot be reached in the artificial potential field method is solved.
如此便将人工势场法应用到动态运动基元的方法中,使得二阶系统中包含排斥加速度项,使得生成的轨迹点远离障碍物,如此生成的轨迹不但拥有预期的运动趋势,还可以同时达到避障的效果。In this way, the artificial potential field method is applied to the method of dynamic motion primitives, so that the repulsive acceleration term is included in the second-order system, so that the generated trajectory points are far away from obstacles, so the generated trajectory not only has the expected motion trend, but also can simultaneously achieve the effect of avoiding obstacles.
基于构建好的带有避障功能的动态运动基元模型,可以根据不同轨迹的起始位置、目标位置,计算不同轨迹的位移、速度、加速度信息,不用重新训练样本而保持原来样本轨迹的特性到达新的目标位置,而且该过程并非针对某一具体任务,具有泛化推广的能力。Based on the constructed dynamic motion primitive model with obstacle avoidance function, the displacement, velocity and acceleration information of different trajectories can be calculated according to the starting positions and target positions of different trajectories, and the characteristics of the original sample trajectories can be maintained without retraining the samples. Reach a new target position, and the process is not specific to a specific task, and has the ability to generalize.
2、基于动态运动基元和人工势场的双臂机器人轨迹规划方法2. Two-arm robot trajectory planning method based on dynamic motion primitives and artificial potential fields
步骤S10,获取双臂机器人待路径规划的目标位置,作为输入数据;Step S10, obtaining the target position of the dual-arm robot to be planned by the path as input data;
在本实施例中,获取双臂机器人待路径规划的目标位置。In this embodiment, the target position of the dual-arm robot for path planning is obtained.
步骤S20,基于所述输入数据,双臂机器人通过预构建的动态运动基元模型得到对应的规划路径,并沿该规划路径移动至所述目标位置。Step S20, based on the input data, the dual-arm robot obtains a corresponding planned path through a pre-built dynamic motion primitive model, and moves to the target position along the planned path.
在本实施例中,双臂机器人通过上述构建的带有避障功能的动态运动基元模型得到对应的规划路径,并沿该规划路径移动至目标位置。In this embodiment, the dual-arm robot obtains a corresponding planned path through the above constructed dynamic motion primitive model with an obstacle avoidance function, and moves to the target position along the planned path.
本发明第二实施例的一种基于动态运动基元和人工势场的双臂机器人轨迹规划系统,如图2所示,包括:位置获取模块100、路径规划输出模块200;A dual-arm robot trajectory planning system based on dynamic motion primitives and artificial potential fields according to the second embodiment of the present invention, as shown in FIG. 2 , includes: a
所述位置获取模块100,配置为获取双臂机器人待路径规划的目标位置,作为输入数据;The
所述路径规划输出模块200,配置为基于所述输入数据,双臂机器人通过预构建的动态运动基元模型得到对应的规划路径,并沿该规划路径移动至所述目标位置;The path planning
其中,所述动态运动基元模型,其构建方法为:Wherein, the construction method of the dynamic motion primitive model is:
步骤A10,基于双臂机器人的D-H参数表,构建双臂机器人模型并通过蒙特卡洛算法求解双臂机器人的工作空间;Step A10, based on the D-H parameter table of the dual-arm robot, construct a dual-arm robot model and solve the workspace of the dual-arm robot through a Monte Carlo algorithm;
步骤A20,在所述工作空间中设置起始位置、目标位置及对应的示范路径,并实时采集双臂机器人沿所述示范路径移动时的轨迹运动数据,作为第一数据;所述轨迹运动数据包括位移、速度、加速度;Step A20, set the starting position, the target position and the corresponding demonstration path in the workspace, and collect the trajectory motion data when the dual-arm robot moves along the demonstration path in real time, as the first data; the trajectory motion data Including displacement, velocity, acceleration;
步骤A30,基于所述第一数据,通过预构建的第一模型,得到示范路径对应的非线性强迫项,作为第一强迫项;所述第一模型为不包含强迫项的离散运动的动态运动基元模型;Step A30, based on the first data, obtain a nonlinear forcing term corresponding to the demonstration path through a pre-built first model, as the first forcing term; the first model is a dynamic motion of discrete motion that does not include the forcing term primitive model;
步骤A40,基于所述第一强迫项,结合设定的学习路径的起始位置、目标位置,通过局部加权法获取每个基函数的最佳权重值,并构建所述学习路径对应的非线性强迫项,作为第二强迫项;Step A40, based on the first forcing term, combined with the starting position and target position of the set learning path, obtain the optimal weight value of each basis function through a local weighting method, and construct a nonlinear corresponding to the learning path. compulsion, as a second compulsion;
步骤A50,在所述第一模型中加入所述第二强迫项、预构建的加速度排斥项,构建带有避障功能的动态运动基元模型,作为最终构建的动态运动基元模型;所述加速度排斥项基于人工势场的负梯度构建。Step A50, adding the second forced term and the pre-built acceleration exclusion term to the first model, and constructing a dynamic motion primitive model with an obstacle avoidance function as the final dynamic motion primitive model; the The acceleration repulsion term is constructed based on the negative gradient of the artificial potential field.
所述技术领域的技术人员可以清楚的了解到,为描述的方便和简洁,上述描述的系统的具体的工作过程及有关说明,可以参考前述方法实施例中的对应过程,在此不再赘述。Those skilled in the technical field can clearly understand that, for the convenience and brevity of description, for the specific working process and related description of the system described above, reference may be made to the corresponding process in the foregoing method embodiments, which will not be repeated here.
需要说明的是,上述实施例提供的基于动态运动基元和人工势场的双臂机器人轨迹规划系统,仅以上述各功能模块的划分进行举例说明,在实际应用中,可以根据需要而将上述功能分配由不同的功能模块来完成,即将本发明实施例中的模块或者步骤再分解或者组合,例如,上述实施例的模块可以合并为一个模块,也可以进一步拆分成多个子模块,以完成以上描述的全部或者部分功能。对于本发明实施例中涉及的模块、步骤的名称,仅仅是为了区分各个模块或者步骤,不视为对本发明的不当限定。It should be noted that the trajectory planning system for a dual-arm robot based on dynamic motion primitives and artificial potential fields provided by the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above can be used as required. The function allocation is completed by different function modules, that is, the modules or steps in the embodiments of the present invention are decomposed or combined. For example, the modules in the above-mentioned embodiments can be combined into one module, or can be further split into multiple sub-modules to complete All or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing each module or step, and should not be regarded as an improper limitation of the present invention.
本发明第三实施例的一种存储装置,其中存储有多条程序,所述程序适用于由处理器加载并实现上述的基于动态运动基元和人工势场的双臂机器人轨迹规划方法。A storage device according to the third embodiment of the present invention stores a plurality of programs, which are suitable for being loaded by a processor and implementing the above-mentioned dual-arm robot trajectory planning method based on dynamic motion primitives and artificial potential fields.
本发明第四实施例的一种处理装置,包括处理器、存储装置;处理器,适用于执行各条程序;存储装置,适于存储多条程序;所述程序适于由处理器加载并执行以实现上述的基于动态运动基元和人工势场的双臂机器人轨迹规划方法。A processing device according to a fourth embodiment of the present invention includes a processor and a storage device; the processor is adapted to execute various programs; the storage device is adapted to store multiple programs; the programs are adapted to be loaded and executed by the processor In order to realize the above-mentioned dual-arm robot trajectory planning method based on dynamic motion primitives and artificial potential field.
所述技术领域的技术人员可以清楚的了解到,未描述的方便和简洁,上述描述的存储装置、处理装置的具体工作过程及有关说明,可以参考前述方法实例中的对应过程,在此不再赘述。Those skilled in the technical field can clearly understand that the undescribed convenience and brevity are not described. Repeat.
本领域技术人员应该能够意识到,结合本文中所公开的实施例描述的各示例的模块、方法步骤,能够以电子硬件、计算机软件或者二者的结合来实现,软件模块、方法步骤对应的程序可以置于随机存储器(RAM)、内存、只读存储器(ROM)、电可编程ROM、电可擦除可编程ROM、寄存器、硬盘、可移动磁盘、CD-ROM、或技术领域内所公知的任意其它形式的存储介质中。为了清楚地说明电子硬件和软件的可互换性,在上述说明中已经按照功能一般性地描述了各示例的组成及步骤。这些功能究竟以电子硬件还是软件方式来执行,取决于技术方案的特定应用和设计约束条件。本领域技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能,但是这种实现不应认为超出本发明的范围。Those skilled in the art should be aware that the modules and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software or a combination of the two, and the programs corresponding to the software modules and method steps Can be placed in random access memory (RAM), internal memory, read only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or as known in the art in any other form of storage medium. In order to clearly illustrate the interchangeability of electronic hardware and software, the components and steps of each example have been described generally in terms of functionality in the foregoing description. Whether these functions are performed in electronic hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may use different methods of implementing the described functionality for each particular application, but such implementations should not be considered beyond the scope of the present invention.
术语“第一”、“第二”等是用于区别类似的对象,而不是用于描述或表示特定的顺序或先后次序。The terms "first," "second," etc. are used to distinguish between similar objects, and are not used to describe or indicate a particular order or sequence.
术语“包括”或者任何其它类似用语旨在涵盖非排他性的包含,从而使得包括一系列要素的过程、方法、物品或者设备/装置不仅包括那些要素,而且还包括没有明确列出的其它要素,或者还包括这些过程、方法、物品或者设备/装置所固有的要素。The term "comprising" or any other similar term is intended to encompass a non-exclusive inclusion such that a process, method, article or device/means comprising a list of elements includes not only those elements but also other elements not expressly listed, or Also included are elements inherent to these processes, methods, articles or devices/devices.
至此,已经结合附图所示的优选实施方式描述了本发明的技术方案,但是,本领域技术人员容易理解的是,本发明的保护范围显然不局限于这些具体实施方式。在不偏离本发明的原理的前提下,本领域技术人员可以对相关技术特征作出等同的更改或替换,这些更改或替换之后的技术方案都将落入本发明的保护范围之内。So far, the technical solutions of the present invention have been described with reference to the preferred embodiments shown in the accompanying drawings, however, those skilled in the art can easily understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.
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