Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros

• A new concept of directional passability is introduced for a SGCMG system.
• The directional passability is investigated in detail for specific directions.
• A new steering logic for passing the singular surface is proposed.
• The algorithm is based on the quadratic constrained quadratic optimization problem.
• The proposed steering logic is demonstrated through numerical simulations.

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.