目标导向的关节结构运动控制方法研究
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摘要
关节结构是在自然界及人造机械中普遍存在的结构。在计算机动画和数控机床的研究中均涉及到关节结构的建模和运动控制。正向运动学和逆向运动学是两种典型的运动控制方法。逆向运动学是一种目标导向的运动控制方法,通常的解法有牛顿迭代法、伪逆矩阵法、SR逆矩阵法、阻尼最小二乘法等基于非线性方程的方法,以及循环坐标下降法、时空约束、动力学约束等基于优化的方法。在此基础上还有各类利用冗余自由度来满足关节链约束或完成第二任务的逆向运动学方法。这些方法为关节结构进一步的运动学建模和求解建立了基础。
首先在传统的点逆向运动学基础上提出了关节结构的曲线逆向运动学算法,针对关节链的末端效应器沿曲线运动的情形,建立了高维的关节角度空间中关节链运动曲线与三维的末端效应器运动轨迹之间的直接联系,推导出了关节链运动曲线的递推公式,进一步给出了误差控制方法,提出了完整的算法流程,并实现了雅可比加权最小范数伪逆方法(Weighted Least-Norm, WLN)在曲线逆向运动学算法中的重用。
在传统的五轴机床运动学模型基础上,引入刀具运动链来描述刀具几何形状在加工中的运动偏移作用,用以替代传统的刀触点偏置算法,提出了机床-刀具运动链模型及相应的运动控制算法。刀具子运动链与机床运动链的表示形式一致,提供额外的两个被动自由度,使本章提出的五轴机床运动模型在描述刀触点时能够更充分地发挥五轴加工的灵活性。
提出了一种基于空间聚类的逆向运动学算法,采用基于数学的建模方法,将正向运动学看作关节角度空间中的点到末端效应器位置空间中点的映射,将逆向运动学看作末端效应器位置空间中的点到关节角度空间中点的映射,进而提出了一种基于聚类的逆向运动学算法。该方法采用双层继承结构模型(Hierarchical Inherit Model),对末端位置空间和关节角度空间中的点集分别进行聚类,并建立聚类之间的对应关系作为运动模型。
提出了一个基于运动捕捉数据和贝叶斯网络的运动合成系统,可以根据足迹来合成人体行走动画。该系统能够从运动捕捉数据中提取关键帧和步态参数,用于贝叶斯网络学习,学习后的贝叶斯网络能够根据足迹序列生成完整的虚拟人行走运动。这种方法结合了贝叶斯网络的非确定性推理能力和步态参数对肢体末端的控制。
Joint is a widespread kind of structure in natural world and artificial machines. The modeling and motion control of joint are researched in computer animation and CNC machine tools. Forward kinematics and inverse kinematics are two types of usually used motion control methods. Inverse kinematics is goal-oriented. The solutions to inverse kinematics are grouped into two categories, one is based on nonlinear equations such as Newton-like iterative method, pseudo-inverse matrix, SR-inverse matrix, damped leased squares method; the other is based on optimizations such as cyclic coordinate descent, time-space constraint, dynamic constraint. Furthermore, there are inverse kinematic methods that using redundant degrees of freedom to satisfy kinematic chain constraints or achieve secondary task. These methods established solid foundation for further modeling and solution.
Curve inverse kinematics for joint structure is proposed in this thesis in the case of end effector move along curve. Curve inverse kinematics establishes direct contact of kinematic chain motion curve in joint angle space and end effector trajectory in3-D space. The recursive equation of joint angle is derived, and two kind of error control mechanism are proposed to construct a complete algorithm. Weighted least norm method are used together with curve inverse kinematics to handle singularity.
The offset coursed by cutter shape are researched for CNC machine tool. Instead of traditional cutter contact offset, a machine-cutter kinematic chain model and corresponding motion control method are proposed. The machine-cutter kinematic chain has unified form, and introduces two more passive degrees of freedom to exert the most flexibility of CNC machine.
Another inverse kinematics algorithm based on spatial clustering is proposed. By using a mathematical modeling method, the forward kinematics can be seen as the mapping from the point in the space of joint angles to the position of the end effector in the3D space, while the inverse kinematics seen as the mapping from the end effector position in3D space to the points in the joint angle space. The method uses a double layer Hierarchical Inherit Model, one layer is the position of the end effector, denoted by P layer, and the other layer is the joint angle layer, referred to Q layer. The set of points in both P and Q layers are clustered successively, and the establishment of the correspondence relationship between the clusters could be extracted as motion model. The solution of the inverse kinematic is to find a suitable cluster in Q layer by given a cluster in P layer.
Motion synthesis system based on motion capture data and Bayesian network is proposed. The system can synthesize human walking animation according to given footprints sequence. The system extracts keyframes and gait parameters from motion capture data and for samples for Bayesian network learning. Footprint sequences are input to the trained Bayesian network, and a complete virtual human walking motion is generated automatically. This approach combines the control of extremities by gait parameters and non-deterministic reasoning ability of the Bayesian network. Experiments show that synthetic motion fully meet time and space constraints and maintain good realism.
首先在传统的点逆向运动学基础上提出了关节结构的曲线逆向运动学算法,针对关节链的末端效应器沿曲线运动的情形,建立了高维的关节角度空间中关节链运动曲线与三维的末端效应器运动轨迹之间的直接联系,推导出了关节链运动曲线的递推公式,进一步给出了误差控制方法,提出了完整的算法流程,并实现了雅可比加权最小范数伪逆方法(Weighted Least-Norm, WLN)在曲线逆向运动学算法中的重用。
在传统的五轴机床运动学模型基础上,引入刀具运动链来描述刀具几何形状在加工中的运动偏移作用,用以替代传统的刀触点偏置算法,提出了机床-刀具运动链模型及相应的运动控制算法。刀具子运动链与机床运动链的表示形式一致,提供额外的两个被动自由度,使本章提出的五轴机床运动模型在描述刀触点时能够更充分地发挥五轴加工的灵活性。
提出了一种基于空间聚类的逆向运动学算法,采用基于数学的建模方法,将正向运动学看作关节角度空间中的点到末端效应器位置空间中点的映射,将逆向运动学看作末端效应器位置空间中的点到关节角度空间中点的映射,进而提出了一种基于聚类的逆向运动学算法。该方法采用双层继承结构模型(Hierarchical Inherit Model),对末端位置空间和关节角度空间中的点集分别进行聚类,并建立聚类之间的对应关系作为运动模型。
提出了一个基于运动捕捉数据和贝叶斯网络的运动合成系统,可以根据足迹来合成人体行走动画。该系统能够从运动捕捉数据中提取关键帧和步态参数,用于贝叶斯网络学习,学习后的贝叶斯网络能够根据足迹序列生成完整的虚拟人行走运动。这种方法结合了贝叶斯网络的非确定性推理能力和步态参数对肢体末端的控制。
Joint is a widespread kind of structure in natural world and artificial machines. The modeling and motion control of joint are researched in computer animation and CNC machine tools. Forward kinematics and inverse kinematics are two types of usually used motion control methods. Inverse kinematics is goal-oriented. The solutions to inverse kinematics are grouped into two categories, one is based on nonlinear equations such as Newton-like iterative method, pseudo-inverse matrix, SR-inverse matrix, damped leased squares method; the other is based on optimizations such as cyclic coordinate descent, time-space constraint, dynamic constraint. Furthermore, there are inverse kinematic methods that using redundant degrees of freedom to satisfy kinematic chain constraints or achieve secondary task. These methods established solid foundation for further modeling and solution.
Curve inverse kinematics for joint structure is proposed in this thesis in the case of end effector move along curve. Curve inverse kinematics establishes direct contact of kinematic chain motion curve in joint angle space and end effector trajectory in3-D space. The recursive equation of joint angle is derived, and two kind of error control mechanism are proposed to construct a complete algorithm. Weighted least norm method are used together with curve inverse kinematics to handle singularity.
The offset coursed by cutter shape are researched for CNC machine tool. Instead of traditional cutter contact offset, a machine-cutter kinematic chain model and corresponding motion control method are proposed. The machine-cutter kinematic chain has unified form, and introduces two more passive degrees of freedom to exert the most flexibility of CNC machine.
Another inverse kinematics algorithm based on spatial clustering is proposed. By using a mathematical modeling method, the forward kinematics can be seen as the mapping from the point in the space of joint angles to the position of the end effector in the3D space, while the inverse kinematics seen as the mapping from the end effector position in3D space to the points in the joint angle space. The method uses a double layer Hierarchical Inherit Model, one layer is the position of the end effector, denoted by P layer, and the other layer is the joint angle layer, referred to Q layer. The set of points in both P and Q layers are clustered successively, and the establishment of the correspondence relationship between the clusters could be extracted as motion model. The solution of the inverse kinematic is to find a suitable cluster in Q layer by given a cluster in P layer.
Motion synthesis system based on motion capture data and Bayesian network is proposed. The system can synthesize human walking animation according to given footprints sequence. The system extracts keyframes and gait parameters from motion capture data and for samples for Bayesian network learning. Footprint sequences are input to the trained Bayesian network, and a complete virtual human walking motion is generated automatically. This approach combines the control of extremities by gait parameters and non-deterministic reasoning ability of the Bayesian network. Experiments show that synthetic motion fully meet time and space constraints and maintain good realism.
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