Singularities in robotics lead to a reduction in the number of degrees of freedom. When it comes to spacecraft employing control moment gyros (CMGs), singularities may occur due to the internal alignment of the gimbals, which inhibit the creation of torque in at least one direction. This translates into a loss of control authority that has a direct impact on the spacecraft’s pointing performance. In this work, a convex optimization-based allocation framework for singularity avoidance is put forward. The presented solution aims to provide a singularity-robust allocation scheme that can be used as an add-on to a conventional attitude controller. To this end, the proposed algorithm employs a novel, computationally efficient, and numerically robust singularity metric to assess the proximity to the singularities of a cluster of CMGs. With this information, a model predictive controller determines control actions that guide the system towards singularity-free configurations. A particularity about this allocation algorithm is that its formulation boils down to a simple set of convex equalities and inequalities, given that the new singularity metric can be written in a linear form, unlike most of the literature solutions, such as the condition number, which are highly complex and nonlinear. Lastly, the proposed approach is applied to a two-dimensional CMG cluster in a realistic simulation environment. The results confirm that the system effectively avoids all the internal singularities of the cluster at a relatively low computational expense.

中文翻译：

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从奇点分析到奇点避免：控制力矩陀螺仪航天器姿态控制的新颖度量和凸分配


机器人技术的奇点导致自由度的减少。当涉及采用控制力矩陀螺仪 (CMG) 的航天器时，由于万向节的内部对准可能会出现奇点，这会抑制至少一个方向上扭矩的产生。这意味着失去控制权，直接影响航天器的指向性能。在这项工作中，提出了一种用于避免奇点的基于凸优化的分配框架。所提出的解决方案旨在提供一种奇点鲁棒分配方案，该方案可以用作传统姿态控制器的附加组件。为此，所提出的算法采用一种新颖的、计算效率高且数值鲁棒的奇点度量来评估 CMG 簇奇点的接近度。利用这些信息，模型预测控制器可以确定引导系统实现无奇点配置的控制动作。这种分配算法的一个特殊性在于，它的公式可以归结为一组简单的凸等式和不等式，因为新的奇点度量可以以线性形式编写，这与大多数文献解决方案（例如条件数）不同。是高度复杂和非线性的。最后，所提出的方法应用于现实模拟环境中的二维 CMG 集群。结果证实该系统以相对较低的计算成本有效地避免了集群的所有内部奇点。