Attitude Kinematics, Dynamics and Control

Kinematics

The AVS Lab continues to perform and publish research in the area of spacecraft kinematics, dynamics and control. Even after over a 100 years of research into the kinematic description of a rigid body, new kinematic descriptions continue to be developed. Recently, our group has been studying various aspects of creating new 3-parameter sets using generalized projections of the Euler Parameter (quaternion) unit constraint surface onto a three-dimensional hyperplane. This has led to interesting new classes of attitude coordinates which either generalized earlier available minimal attitude parameter sets such as the Modified Rodrigues Parameters (MRPs) or the Classical Rodrigues Parameters (CRPs).

The Hypersurface Stereographic Orientation Parameters (HSOPs), illustrated in the figure above, allow the stereographic projection point to be on a general location on the quaternion constraint surface. This allows the prior MRPs and Asymmetric Stereographic Orientation Parameters (ASOPs) to be united into one family. Similarly, the Symmetric Stereographic Orientation Parameters (SSOPs) allow for the projection point to be moved along the scalar quaternion axis. In all these cases interesting minimal attitude parameter sets can be created with custom singular behavior. For example, it is possible to create attitude coordinates which will go singular (values grow infinitly large) if a partiuclar rotation angle is achieved with respect to a reference orientation, regardless about which axis this specific rotation is achieved. Or, coordinates can be create that go singular only if a particular rotation about a specific axis is performed.

Dynamics and Control

The dynamics and control of spacecraft continues to be of interest. In particular, spacecraft equiped with the proposed Variable Speed CMG (VSCMG) devices continue to be researched. Such devices combine features of both the reaction wheel, and the CMG, and provide compact non-singular attitude control mechanisms. A cluster of such VSCMG will provide a large nullspace of the control actuation modes, which enables auxililary control objectives to be such such as power retrieval, wheel speed balancing, wheel speed reduction, etc. While the CMG device can provide a significant torque amplification in contrasts to the reaction wheel devices, the CMG cluster suffer from singularies such as the gimbal locks. Allowing the wheel speed to be variable, rather than fixed, provide complex but interesting means to shift the internal momentum, and avoid such singularities. Further, the null-space of the VSCMG clusters can also be used to avoid the classical CMG configurations. This research has yielded very promising results, as the required null motion reaction wheel torques tend to be very small, and appear to be feasible with the existing CMG reaction wheel motors.

Some recent efforts have also expanded this work to consider employing a variable speed mechanism on dual-gimbal CMGs (DGVSCMG). In principle, a single DGVSCMG devices would provide 3 degrees of actuation, and thus could provide complete three-axis attitude control. However, some of the torque amplification benefits of the single-gimbal CMG devices can be lost in such a setup. The space station is currenlty using dual-gimbal CMG devices because they allow for more angular momentum to be absorbed before a momentum dumping maneuver is required.


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