Formulation of Torque-Optimal Guidance Trajectories for a CubeSat with Degraded Reaction Wheels Siddharth S. Kedare * and Steve Ulrich † Carleton University, Ottawa, Ontario K1S 5B6, Canada This paper presents the theory and design of a torque-optimal guidance algorithm for CubeSat applications. CubeSats and nano-satellites provide mission-flexible low-cost plat- forms for the academic and scientific communities to conduct cutting-edge research in the harsh environment of space. The mission life of nano-satellites may be limited by the at- titude actuators, and it is therefore beneficial to reduce torque and angular momentum usage during reorientation maneuvers. The algorithm focuses on being computationally lightweight and robust, while including the effects of gyroscopic moments, environmental torques, and degraded reaction wheels. Results indicate that this torque-optimal guidance algorithm demonstrates substantial improvements in performance and pointing accuracy over an Eigenaxis controller for similar maneuvers, with low to moderate computational overhead. In doing so, it presents a significant advancement towards the development of intelligent GN&C systems for small satellites. I. Introduction F or a space mission to be successful, a spacecraft must be capable of accurately pointing its payload at the required target. 1 The associated slewing maneuvers are typically executed by a series of motorized rotating masses such as reaction wheels, momentum wheels, or control moment gyroscopes (CMG), which provide maneuvering torque and angular momentum storage. 2 Over the duration of a mission, these devices accumulate angular momentum while countering persistent external disturbance torques from the space environment. This momentum accumulation necessitates the use of additional momentum control systems, such as magnetorquers or thrusters, to desaturate the wheels in a process known as momentum dumping. However, a full-size attitude control system (ACS) is too large and expensive to be installed on nano-satellites or CubeSats, 3 leading to the widespread use of pico-satellite reaction wheels 4 and passive control systems. 5, 6 Magnetorquers are often used alongside an active ACS for momentum dumping tasks, 7 due to their low cost, reliability, and simplicity. Though highly efficient, magnetorquers are not without their disadvantages. The Michigan Exploration Laboratory suspects that in October 2011, their M-Cubed CubeSat unintention- ally became magnetically conjoined to Explorer-1 Prime, a second CubeSat released simultaneously, via strong onboard magnets used for passive attitude control. 8 Such an occurrence highlights the necessity to explore alternate momentum dumping techniques as applicable to nano-satellites and CubeSat class pay- loads. Additionally, the magnetic field of the Earth is not well known, and is continuously being affected by solar weather. Near the geomagnetic equator, only roll and yaw momentum can be dumped, 9, 10 allowing for the saturation of pitch momentum. Furthermore, the use of magnetic dipoles generates an additional magnetic field on the spacecraft, which may disrupt the normal operation of sensors and spacecraft systems. Though microthruster attitude control systems are being developed for nanosatellite applications, 11 ex- isting systems are prone to leakage and require bulky pressure vessels for propellant storage. Valve actua- tion solenoids, though typically reliable, have the potential to be stuck open or closed, leading to mission- threatening scenarios, as was experienced during the Gemini 8 mission 12 in 1966. This paper focuses on the development and simulation of a near real-time low computational-cost guidance algorithm which exploits gyroscopic (internal) and space environment (external) disturbance torques to minimize the use of torque actuators during attitude maneuvers, hence minimizing the accumulation of * Research Affiliate, Department of Mechanical and Aerospace Engineering, 1125 Colonel By Drive. Member AIAA. † Assistant Professor, Department of Mechanical and Aerospace Engineering, 1125 Colonel By Drive. Senior Member AIAA. 1 of 25 American Institute of Aeronautics and Astronautics Downloaded by CARLETON UNIVERSITY on January 25, 2016 | http://arc.aiaa.org | DOI: 10.2514/6.2016-0088 AIAA Guidance, Navigation, and Control Conference 4-8 January 2016, San Diego, California, USA AIAA 2016-0088 Copyright © 2015 by Siddharth S. Kedare & Steve Ulrich. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. AIAA SciTech