From singularity analysis to singularity avoidance: novel metric and convex allocation for spacecraft attitude control with control moment gyros.

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. • Detailed analysis of singularities across different systems of control moment gyros. • Novel singularity metric based on the distance to the closest singularity. • Derivation of a convex MPC-based allocation algorithm for singularity avoidance. • Proposed approach can circumvent internal singularities at a low computational cost. [ABSTRACT FROM AUTHOR]