This paper assumes a requirement for an unmanned multiunit satellite to be assembled in orbit. The requirement to be met is to bring the satellites together so tha t they do not collide but actually rendezvous. The equations of motion of the rendezvous satellite in a relative coordinate system are derived and used to compute a final injection velocity which would effect collision after a time r. The velocity is corrected periodically by a command guidance system and just before impact retrothrust is applied. A terminal infrared homing sj^stem is required to actually accomplish physical contact and joining of the satellites. The first satellite placed in orbit is the "control satellite" and controls all the satellites to be assembled and contains the ccmputer, command guidance equipment, precision orientation equipment, and other features necessary to effect rendezvous. The succeeding satellites contain a propulsion system, a rough at t i tude control system, and a command receiver plus whatever scientific equipment they carry to perform their basic mission. This paper presents the following:

Terminal Guidance System for Satellite Rendezvous

Formation flying is defined as a set of more than one spacecraft whose states are coupled through a common control law. This paper provides a comprehensive survey of spacecraft formation flying control (FFC), which encompasses design techniques and stability results for these coupled-state control laws. We divide the FFC literature into five FFC architectures: (i) multiple-input multiple-output, in which the formation is treated as a single multiple-input, multiple-output plant, (ii) leader/follower, in which individual spacecraft controllers are connected hierarchically, (iii) virtual structure, in which spacecraft are treated as rigid bodies embedded in an overall virtual rigid body, (iv) cyclic, in which individual spacecraft controllers are connected non-hierarchically, and (v) behavioral, in which multiple controllers for achieving different (and possibly competing) objectives are combined. This survey significantly extends an overview of the FFC literature provided by Lawton, which discussed the L/F, virtual structure and behavioral architectures. We also include a brief history of the formation flying literature, and discuss connections between spacecraft FFC and other multi-vehicle control problems in the robotics and automated highway system literatures.

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A survey of spacecraft formation flying guidance and control. Part II: control

Space Vehicle Dynamics and Control, Second Edition

A review of pseudospectral optimal control: From theory to flight

In this paper we investigate a singularity problem inherent in a system of redundant single-gimbal control moment gyros (CMGs). In particular, we present a simple yet effective way of passing through, and also escaping from, any internal singularities. The proposed approach is based on the so-called "singularity robust inverse," but it utilizes a nondiagonal weighting matrix in the mixed, two-norm and weighted least-squares minimization problem. The proposed steering logic effectively generates "deterministic dither signals" when the CMG system becomes near singular. Because the proposed CMG steering logic is based on the simple minimum two-norm, pseudoinverse solution, it does not explicitly avoid singularity encounters but it rather approaches and rapidly transits unavoidable singularities whenever needed. However, the proposed steering logic is not intended for special missions in which prescribed attitude trajectories are to be "exactly" tracked in the presence of internal singularities.

Singularity Robust Steering Logic for Redundant Single-Gimbal Control Moment Gyros

Steering law design for redundant single-gimbal control moment gyroscopes. [for spacecraft attitude control]

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.

Steering law design for redundant single-gimbal control moment gyroscopes

This paper examines the feasibility of using differential drag between two spacecraft as the means for controlling their relative positions. The equations ofirelative motion between two satellites are derived and a coordinate transformation is made to reduce the formationkeeping problem to the simultaneous solution of a double integrator and a harmonic oscillator. A simple feedback control law is developed that simultaneously and dependently solves the double integrator and harmonic oscillator; the control law consists of two parts: the main control law and the eccentricity minimizing control scheme. Results are presented of four test cases which show that the control law can drive a satellite from an initial position to a target position and maintain the satellite at that location.

Orbital Formationkeeping with Differential Drag

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.

Redundant single gimbal control moment gyroscope singularity analysis

Real-time algorithms that estimate the mass-property parameters commonly used in spacecraft control laws are developed based upon a stochastic estimation viewpoint. The elements of the inverse inertia matrix and the center-of-mass location vector are estimated from noisy measurements of the angular velocity using a secondorder filter, while estimates of the mass reciprocal are generated from noisy linear velocity measurements using a Kalman filter. Simulation results show that the rate of convergence of each estimate depends strongly upon the particular maneuver being performed, but that the mass properties can be estimated to within 1% error.

Edward V. Bergmann

Papers

Steering law design for redundant single-gimbal control moment gyroscopes. [for spacecraft attitude control]

Steering law design for redundant single-gimbal control moment gyroscopes

Orbital Formationkeeping with Differential Drag

Redundant single gimbal control moment gyroscope singularity analysis

Mass property estimation for control of asymmetrical satellites