Edward V. Bergmann

Steering Law Design for Redundant Single-Gimbal Control Moment Gyroscopes

Two steering laws are presented for single-gimbal control moment gyroscopes. An approach using the Moore-Penrose pseudoinverse with a nondirectional null-motion algorithm is shown by example to avoid internal singularities for unidirectional torque commands, for which existing algorithms fail. Because this is still a tangent-based approach, however, singularity avoidance cannot be guaranteed. The singularity robust inverse is introduced as an alternative to the pseudoinverse for computing torque-producing gimbal rates near singular states. This approach, coupled with the nondirectional null algorithm, is shown by example to provide better steering law performance by allowing torque errors to be produced in the vicinity of singular states.

Redundant single gimbal control moment gyroscope singularity analysis

The robotic manipulator is proposed as the mechanical analog to single gimbal control moment gyroscope systems, and it is shown that both systems share similar difficulties with singular configurations. This analogy is used to group gimbal angles corresponding to any momentum state into different families. The singularity problem associated with these systems is examined in detail. In particular, a method is presented to test for the possibility of nontorque-producing gimbal motion at a singular configuration, as well as to determine the admissible motions in the case when this is possible. Sufficient conditions are derived for instances where the singular system can be reconfigured into a nonsingular state by these nontorque-producing motions.

Approach to control moment gyroscope steering using feedback linearization

This paper presents an approach to steering control moment gyroscopes. A technique based on feedback linearization theory is used to transform the original nonlinear problem to an equivalent linear form without approximating assumptions. Under this transformation, the spacecraft dynamics appear linearly, and are decoupled from redundancy in the system of gyroscopes. A general approach to distributing control effort among the available actuators is described that includes provisions for redistribution of rotors, explicit bounds on gimbal rates, and guaranteed operation at and near singular configurations. A particular algorithm is developed for systems of double-gimballed devices, and demonstrated in two examples for which many existing approaches fail to give adequate performance.

An Advanced Spacecraft Autopilot Concept

An autopilot is developed for rotation and translation control of a rigid spacecraft of arbitrary design, using reaction control jets as control effectors. The autopilot incorporates a six-dimensional phase space control law, and a linear programming algorithm for jet selection. The interaction of the control law and jet selection are investigated and a recommended configuration proposed. Simulations are performed to verify the performance of the new autopilot and comparisons are made with an existing spacecraft autopilot. The new autopilot is shown to require 35.4% fewer words of core memory, 20.5% less average CPU time, up to 65% fewer firings, and consume up to 25.7% less propellant for the cases tested. However, the cycle time required to perform the jet selection computations may render the new autopilot unsuitable for existing flight computer applications, without modifications. Finally, the new autopilot is shown to be capable of performing attitude control in the presence of a large number of jet failures.

Input selection for a second-order mass property estimator

A strategy is developed for selecting online the attitude control jet firings to be commanded during the mass property estimation phase of the operation of any asymmetrical rigid satellite. Using symbolic manipulation, an effort is made to develop a selection stratgegy that accelerates convergence by maximally decreasing the change in the covariance of the estimation error at each time step. These results, which are too complex for online implementation, motivate a suboptimal direct search stragegy. Examples of mass property identification are then demonstrated on a high-fidelity simulation of the Space Shuttle. The results indicate that the suboptimal strategies yield significant reductions in the time to convergence for the mass property estimates and in the cumulative fuel usage relative to a typical predetermined jet firing sequence.

Collision Detection for Spacecraft Proximity Operations

A new collision detection algorithm has been developed for use when two spacecraft are operating in the same vicinity. The two spacecraft are modeled as unions of convex polyhedra, where the resulting polyhedron may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such .that one vehicle is moving with constant linear and angular velocity with respect to the other. Contacts between the vertices, faces, and edges of the polyhedra representing the two spacecraft are shown to occur when the value of one or more of a set of functions is zero. The collision detection algorithm is then formulated as a search for the zeros (roots) of these functions. Special properties of the functions for the assumed relative trajectory are exploited to expedite the zero search. The new algorithm is the first algorithm that can solve the collision detection problem exactly for relative motion with constant angular velocity. This is a significant improvement over models of rotational motion used in previous collision detection algorithms.