**Spacecraft Attitude Control Using Control Moment**

Gyro Reconfiguration

Gyro Reconfiguration

**Kanthalakshmi SRINIVASAN ^{1}, Deepana GANDHI^{1}, Manikandan VENUGOPAL^{2}**

^{1 }Department of Instrumentation and Control Systems Engineering,

PSG College of Technology,

Coimbatore – 641004, India,

klakshmiramesh@yahoo.co.in, deepana.gandhi@gmail.com

^{2 }Department of Electrical and Electronics Engineering,

Coimbatore Institute of Technology

Coimbatore – 641004, India,

manikantan-cit@gmail.com

**Abstract**: The orientation of a satellite in space described relative to some other object or system is known as the attitude of the satellite. The attitude may be changing with time. To be able to control the attitude of the satellite, it must be equipped with actuators that can produce the required torque. Control Moment Gyroscope is a space craft control actuator which acts as torque amplifier. It is suitable for three axis slew manoeuvring by providing the necessary torques via gimbaling a spinning flywheel. Control Moment Gyroscope is considered to be more efficient in terms of power consumption and slew rate. A major drawback encountered with the use of the Control Moment Gyroscope is the possibility of singularities for certain combinations of gimbal angles. The objective of this work is to detect these singularities so that robust steering laws can be developed.

**Keywords**: Control Moment Gyroscope, Gimbal angles, Singularities, Attitude Control, Steering laws.

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**CITE THIS PAPER AS**:

Kanthalakshmi SRINIVASAN, Deepana GANDHI, Manikandan VENUGOPAL, **Spacecraft Attitude Control Using Control Moment Gyro Reconfiguration**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 23 (3), pp. 285-296, 2014. https://doi.org/10.24846/v23i3y201407

**1. Introduction**

With the development of space technologies, different classes of satellites are constructed and utilized for various space missions. From the moment that a satellite is launched into its initial orbit, commonly called a transfer orbit, multiple attitude and orbital changes must be performed to obtain the desired final orbit. The motion of a spacecraft can be divided into two types: translational motion and rotational motion. Translational motion describes the motion of a spacecraft in an orbit, whereas the rotational motion describes the orientation (attitude) of the spacecraft in space with respect to a particular reference like the earth and sun. The Attitude control is the process of orienting the spacecraft in a specified predetermined direction. It is an important subsystem in a spacecraft and is responsible for pointing and slewing of the spacecraft. The spacecraft is considered to be a rigid body whose attitude can be described by Euler`s equations of rotational motion which govern the rotational dynamics of rigid bodies.

Their solution gives the angular velocity vector due to applied torque and kinematic differential equations, which relate the time derivatives of the orientation angles to the angular velocity vector. Attitude representation can be done using three or four parameters. The three-parameter attitude representation techniques are Euler angles, Gibbs vector, Cayley Rodrigues vector and Modified Rodrigues parameter. The four-parameter representation of attitude is given by the unit quaternion (Euler parameters).

Attitude is the three-dimensional orientation of a vehicle with respect to a specified reference frame. Attitude systems include the sensors, actuators, avionics, algorithms, software, and ground support equipment used to determine and control the attitude of a vehicle. Spacecraft attitude changes according to the fundamental equations of motion for rotational dynamics, the Euler equations.

*Attitude determination* is the process of combining available sensor inputs with knowledge of the spacecraft dynamics to provide an accurate and unique solution for the attitude state as a function of time, either onboard for immediate use, or after the fact (i.e. post-processing).

*Attitude control* is the combination of the prediction of and reaction to a vehicle`s rotational dynamics. Because spacecraft exist in an environment of small and often highly predictable disturbances, they may in certain cases be passively controlled. Alternately, a spacecraft may include actuators that can be used to actively control orientation. These two general types of attitude control are not mutually exclusive.

A general framework for the analysis of the attitude tracking control problem for a rigid body is presented in [1]. A survey of attitude representations in a single consistent notation and set of conventions is given in [2]. The relations between the various representations of the attitude and the kinematic equations are given completely. The transformations connecting different attitude covariance representations are presented by an infinitesimal rotation.

A case study on spacecraft attitude control is presented in [3]. The plant (spacecraft attitude model) is a second order, nonlinear, multi-input-multi-output system defined by Euler`s equations of rotational motion and the kinematic differential equations. The Modified Rodrigues parameter (MRP) is used for kinematic parameterization and is the only measurable variable at the plant output.

Control Moment Gyroscopes (CMGs) are proposed in [4] as torque actuators that can effectively answer the attitude control requirements of future spacecraft. The CMGs technology presented can greatly improve the torque and momentum capability of spacecrafts and consequently their agility.

The work on CMG based AOCS is of great interest for past few years. A top-down analysis strategy so as to define the right product future missions, starting from review of system needs in Earth observation and scientific missions to the preliminary mechanism design is presented in [5]. An innovative solutions, which simplify the system, the operations and the CMG mechanisms is presented.

A cluster of small-sized single-gimbal control moment gyros (SGCMGs) is proposed in [8] as an attitude control actuator for high-speed manoeuvre of small satellites.

Two objectives dominate consideration of control moment gyroscopes for spacecraft manoeuvres: high torque (equivalently momentum) and singularity-free operations.

A significant body of research toward these two goals using a minimal three-control-moment-gyroscope array to provide significant singularity-free momentum performance increase spherically (in all directions) by modification of control-moment-gyroscope skew angles is presented in [9], and compared with the ubiquitous pyramid geometry skewed at 54.73 deg.

The performance of a control moment gyroscope cluster for 3-axis attitude control for small satellites is presented in paper [10]. Experimental results on the performance of a Control Moment Gyroscope (CMG) cluster are presented in [12]. The experimental data are compared with simulation (theoretical) results and both are used to verify the principles, benefits and performance specifications of the CMG cluster.

The major problem encountered with the application of CMG is the occurrence of singularities for certain combination of gimbal angles. This paper describes the techniques used to detect the occurrence of singularity and the robust steering laws that can be used to overcome singularity.

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