Geometric Approach to Spacecraft Attitude Control Using Magnetic and Mechanical Actuation

I T IS well known that spacecraft in low Earth orbit can generate control torques via the interaction of theEarth’s geomagneticfield and onboard magnetic dipole moments (created via current-carrying coils) [1,2]. As mentioned in [3], the major shortcoming of magnetic actuation (as the only onboard actuator) is that control torques can only be applied to the spacecraft in a plane orthogonal to the instantaneous direction of the Earth’s magnetic field, which in turn means that the spacecraft is instantaneously underactuated. Recently, in [4,5], inertial pointing of a spacecraft using solely magnetic actuation was considered. It was shown that stabilization can be obtained while employing a quaternion and angular velocity proportional derivative (PD) type of control law. Owing to the timevarying nature of the system, the control gains are shown to be limited, which in turn leads to closed-loop performance limitations. Stability (and proof thereof) relies on averaging theory [6], which physically translates to the system possessing certain dynamic properties on average. In particular, it is assumed that on average control torques can be applied to the spacecraft in any direction owing to the fact the magnetic field is changing direction as the spacecraft orbits the Earth. Modern spacecraft are usually endowed with magnetic torquers and some type of mechanical actuator, such as reaction wheels. The magnetic torquers are usually used for detumbling of the spacecraft upon egress from the launch vehicle, as well as momentum dumping of reaction wheels. Reactionwheels are used for fine attitude control. Seldom are both magnetic torquers and reaction wheels intended to work together harmoniously in concert. Having both actuation systems work simultaneously can lead to power savings (depending on, among other things, orbit inclination, control scheme and gains, etc. [7]), as well as reduce reaction wheel torque requirements. Additionally, although most spacecraft are equipped with redundant reaction ormomentumwheels, failure of both primary and secondary wheels in one axis is possible, as discussed in [8]. Upon the failure of primary and redundant pitch axis wheels, the attitude control system of RADARSAT-1was redesigned (and subsequently uploaded while on orbit) to use the remaining wheels and magnetic actuation together, thus saving themission.Attitude control of spacecraft using two actuation systems was also considered in [9,10]. Motivated by [4,5], in [9] the same magnetic control law was augmented with reaction wheels; sufficient conditions were given such that the gain limited nature of the magnetic control law was relaxed, leading to better closed-loop system performance. In [10] the attitude control of a spacecraft using both magnetic torquers and thrusters based on a linear time-periodic model was considered, leading to linear timeinvariant and linear time-periodic control designs. Actuator saturation was also considered. In this paper we consider the control of a spacecraft using both magnetic and mechanical actuation in tandem. We present a geometric scheme whereby the control vector is decomposed into orthogonal and parallel components with respect to the orientation of the instantaneous magnetic field vector. The spacecraft magnetic torquers apply the orthogonal control component, while the remaining parallel component is applied by mechanical actuators, specifically, reaction wheels. We show that our control decomposition is not limited to spacecraft equipped with three wheels, but those equipped with one, two, or three wheels. Additionally, saturation of the torque rods is considered. The effectiveness of our method is shown to work well in simulation while employing an adaptive tracking controller.

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