Minimum perturbation coordinates on SO(3)
Minimum perturbation coordinates on SO(3)
复制标题
SO(3) 上的最小扰动坐标
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
H. Choset
中科院分区：
文献类型：
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作者：
M. Travers;R. Hatton;H. Choset
使用内部形状变化来控制其在空间中的方向的系统引起了几何控制界的兴趣已有一段时间。例子包括猫掉落的经典问题和应用较多的卫星姿态控制。这些系统的动力学以角动量守恒为主导，这在形状和空间方向的变化之间引起了一组约束。这种关系可以与李支架理论相结合，以确定产生所需净旋转的形状变化。李氏支架方法的主要缺点是它只适用于相对较小振幅的运动；这些方法依赖于系统动力学的局部线性化，当考虑更大的运动时，这种线性化就失效了。最近对一个相关问题——平面运动——的研究表明，通过为系统确定一组最小摄动坐标，可以减轻这种分解；李支架理论在最小摄动坐标中的应用使得这些方法可以应用于更广泛和更有趣的形状变化类。在这项工作中，我们将最小摄动坐标的推导引入三维旋转空间。我们表明，作为结果，我们能够得出可视化工具，提供控制设计人员的直觉，以选择惯性系统在自由飞行的循环控制器。这些工具在取自文献的最小卫星模型上进行了演示。
Systems that use internal shape changes to control their orientation in space have interested the geometric controls community for some time. Examples include the classic problem of a falling cat and the more applied attitude control of satellites. The dynamics of these systems are dominated by conservation of angular momentum, which induces a set of constraints between changes in shape and spatial orientation. This relationship can be combined with Lie bracket theory to identify shape changes that produce desired net rotations. The major weakness of the Lie bracket approach is that it only works for relatively small-amplitude motions; these methods depend on a local linearization of the system dynamics, which breaks down as larger motions are considered. Recent work on a related problem, planar locomotion, has shown that this breakdown can be mitigated by identifying a set of minimum perturbation coordinates for the system; application of Lie bracket theory in the minimum perturbation coordinates allows these methods to be applied to a broader and more interesting class of shape changes. In this work, we bring the derivation of minimum perturbation coordinates to the space of three-dimensional rotations. We show that as a result, we are able to derive visual tools that provide the control designer intuition into selecting cyclic controllers for inertial systems in free flight. These tools are demonstrated on a minimal satellite model taken from the literature.