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首页> 外文期刊>Mechanics of solids >Biquaternion solution of the kinematic control problem for the motion of a rigid body and its application to the solution of inverse problems of robot-manipulator kinematics
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Biquaternion solution of the kinematic control problem for the motion of a rigid body and its application to the solution of inverse problems of robot-manipulator kinematics

机译：刚体运动的运动控制问题的双四元数解及其在机器人-机械手运动学反问题中的应用

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摘要

The problem of reducing the body-attached coordinate system to the reference (programmed) coordinate system moving relative to the fixed coordinate system with a given instantaneous velocity screw along a given trajectory is considered in the kinematic statement. The biquaternion kinematic equations of motion of a rigid body in normalized and unnormalized finite displacement biquaternions are used as the mathematical model of motion, and the dual orthogonal projections of the instantaneous velocity screw of the body motion onto the body coordinate axes are used as the control. Various types of correction (stabilization), which are biquaternion analogs of position and integral corrections, are proposed. It is shown that the linear (obtained without linearization) and stationary biquaternion error equations that are invariant under any chosen programmed motion of the reference coordinate system can be obtained for the proposed types of correction and the use of unnormalized finite displacement biquaternions and four-dimensional dual controls allows one to construct globally regular control laws. The general solution of the error equation is constructed, and conditions for asymptotic stability of the programmed motion are obtained. The constructed theory of kinematic control of motion is used to solve inverse problems of robot-manipulator kinematics. The control problem under study is a generalization of the kinematic problem [1, 2] of reducing the body-attached coordinate system to the reference coordinate system rotating at a given (programmed) absolute angular velocity, and the presentedmethod for solving inverse problems of robotmanipulator kinematics is a development of the method proposed in [3-5].
机译：在运动学陈述中考虑了将附有身体的坐标系简化为相对于固定坐标系相对移动的参考（编程）坐标系的问题，该坐标系具有沿给定轨迹的给定瞬时速度螺钉。刚体和归一化有限位移双四元数中的刚体运动的双四元数运动学方程用作运动的数学模型，并且将瞬时运动速度螺线在体坐标轴上的双正交投影用作控制。 。提出了各种类型的校正（稳定化），它们是位置和积分校正的双四元数类似物。结果表明，对于拟议的校正类型和使用非归一化有限位移双四元数和四维数，可以得到在参考坐标系的任何选定编程运动下不变的线性（不进行线性化获得）和稳态双四元数误差方程。双重控制允许人们构建全球性的常规控制法律。构造了误差方程的一般解，并获得了程序运动渐近稳定的条件。构造的运动学运动控制理论用于解决机器人-机械手运动学的逆问题。研究中的控制问题是将附体坐标系简化为以给定（编程）绝对角速度旋转的参考坐标系的运动学问题[1，2]的推广，以及解决机器人操纵器反问题的方法运动学是[3-5]中提出的方法的发展。

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