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Feedback Linearization of the Rotational Dynamics of a Flock of Target Tracking Visual Sensor Array using Tait-Bryan Parameterization

机译:使用Tait-Bryan参数化的目标跟踪视觉传感器阵列群的旋转动力学的反馈线性化

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Using Tait-Bryan (TB) Parameterization, we revisit the visual sensor pointing control problem as a constrained dynamics on SO(3) from the point of view of a nonlinear multi input multi output (MIMO) system. The attitude of every sensor is assumed to satisfy a constraint, such as the ones proposed by Donders and Listing for the monocular and binocular eyes and the head rotation problems. While studying the problem of controlling the pointing direction of human head, the constraint, proposed by Donders, is that for every human head rotating away from its primary pointing direction, the rotational vectors are restricted to lie on a surface called the Donders’ surface. This paper assumes the existence of Donders’ surfaces for an array of visual sensors in a flock, tasked with the goal of tracking a point target in IR3. We assume that the Donders’ surfaces are described by a quadratic equation on the coordinates of the rotation vector. The inputs to the MIMO system are three external torque triplet, one for each visual sensor. The three output signals from each sensor are chosen as follows. Two of the signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders’ surface. Thus we have a square system and recent results have shown that this system is feedback linearizable on a suitable neighborhoodNof the state space. We estimate a lower bound on the size ofNby computing distance between the Donders’ and the associated Singularity surface. Our results are discussed for the monocular and the trinocular cases and a comparison is made from the point of view of the observed singularities. Analysis of the feedback linearizing control problem, from the point of view of ‘three eyed visual sensing’, is new.
机译:使用Tait-Bryan(TB)参数化,我们从非线性多输入多输出(MIMO)系统的角度重新审视了视觉传感器指向控制问题,将其作为对SO(3)的约束动力学。假定每个传感器的姿态都满足一个约束条件,例如Donders and Listing针对单眼和双眼的眼睛以及头部旋转问题提出的约束。在研究控制人头指向方向的问题时,Donders提出的约束条件是,对于每个旋转离开其主要指向方向的人头,旋转矢量都被限制在一个称为Donders表面的表面上。本文假设羊群中存在视觉传感器阵列的Donders表面,其任务是在IR3中跟踪点目标。我们假设Donders的表面由旋转矢量坐标上的二次方程式描述。 MIMO系统的输入是三个外部扭矩三重态,每个视觉传感器一个。每个传感器的三个输出信号选择如下。两个信号是正面指向方向的坐标。第三个信号测量状态向量与Donders表面之间的偏差。因此,我们有一个正方形系统,最近的结果表明,该系统可以在状态空间的适当邻域N上线性化反馈。通过计算Donders和相关奇点表面之间的距离,我们可以估计N大小的下界。我们讨论了单眼和三眼病例的结果,并从观察到的奇异性角度进行了比较。从“三眼视觉”的角度分析反馈线性化控制问题是新的。

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