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Attitude Control for the Lumio Cubesat in Deep Space 70th International Astronautical Congress, Washington D.C., United States, 21-25 October 2019. Copyright 2019 by the authors. Published by the IAF, with permission and released to the IAF to publish in all forms. IAC-19,C1,6,4,x50894 ATTITUDE CONTROL FOR THE LUMIO CUBESAT IN DEEP SPACE A.´ Romero-Calvo,1 J. D. Biggs, 1 F. Topputo1 The Lunar Meteoroid Impact Observer(LUMIO) is a 12U CubeSat designed to observe, quantify, and characterize the impact of meteoroids on the lunar surface. The combination of a highly demanding Concept of Operations(ConOps) and the characteristics of the deep-space environment determine the configuration of the spacecraft. This paper presents the preliminary Attitude Determination and Control System(ADCS) design of LUMIO, the reaction wheels desaturation strategy and Moon tracking control laws. The proposed solution is shown to (a) prevent the saturation of the reaction wheels, (b) minimize propellant consumption, (c) minimize the parasitic ∆V , (d) keep the pointing angle below a certain limit, and e) maximize power generation. Although no attempt is made to optimize the control parameters, the most efficient alternative in terms of propellant consumption is identified. The proposed LUMIO design could lay the foundations for a standardized minimum mass and volume ADCS system for CubeSats operating in deep-space. Nomenclature ~ns Unit vector normal to surface A Actual DCM matrix Ω Aperture angle of a regular tetrahedron Hadamard’s product Ad Desired DCM matrix P Solar constant Ae Error DCM matrix R Reaction wheels matrix Ai Area of surface i R Moon radius Cj Jacobi constant M ~cpi Surface i position vector ρd Diffusely reflected radiation c Speed of light ρs Specularly reflected radiation ˆ d~ Disturbance estimation r Distance to the Sun S~ Unit vector from Sun to surface F~i Solar pressure force in panel i ∗ γ Thrusters tilting angle Pseudo-inverse operator ~ d s Values after saturation hr Desired angular momentum ∆t Minimum Impulse Bit ~hr Angular momentum of the reaction wheels MIB ∧ Inverse hat map T Torque matrix horbit Altitude of the spacecraft θ Positive real number ~ I Solar irradiance TSRP Solar radiation pressure torque ~ I~tot Total impulse vector t Thrust vector J Generic inertia matrix T Transpose operator · Jdepl Inertia matrix for LUMIO’s deployed configuration Time derivative Jmin Minimization function ~uRW Control momentum applied by the reaction wheels Jpack Inertia matrix for LUMIO’s packed configuration ~uc Control input ki Control parameters ~udes Desired thrust torque l Distance between nozzles and Y -Z plane ~ulim Thrust threshold m Number of thrusters ∆V Spacecraft velocity increment V mSC Mass of the spacecraft Skew-symmetric matrix or hat map N Matrix of thrust directions ~ω Actual angular velocity 1 Department of Aerospace Science and Technology, Politecnico di ~ωd Desired angular velocity Milano, Via Giuseppe La Masa, 34, 20156, Milan, Italy; [email protected] ~ωe Angular velocity error IAC-19,C1,6,4,x50894 Page 1 of 13 70th International Astronautical Congress, Washington D.C., United States, 21-25 October 2019. Copyright 2019 by the authors. Published by the IAF, with permission and released to the IAF to publish in all forms. X Body frame axis nearside, thus synthesizing a global information on the lunar meteoroid environment. LUMIO envisages a 12U CubeSat ~xM Normalized Moon pointing vector (J2000) form-factor placed in a halo orbit at Earth-Moon L2 to char- ~xS Normalized Sun pointing vector (J2000) acterize the lunar meteoroid flux by detecting the impact flashes produced on the far-side of the Moon. The mission x Distance between nozzles and X axis employs the LUMIO-Cam, an optical instrument capable of xi DCM unitary axis detecting light flashes in the visible spectrum [6]. LUMIO is one of the two winners of ESA’s LUnar CubeSat for Explo- Y Body frame axis ration(LUCE) SysNova competition, and as such it is being Y 0 Tilted body frame axis considered by ESA for implementation in the near future. One of the major challenges of the mission is the strict Z Body frame axis pointing budget, which imposes high-precision tracking of Z0 Tilted body frame axis a specific attitude that maximizes power generation. This is particularly relevant for the Attitude Determination and Control System(ADCS) due to the limited capacity of the reaction wheels. In addition, the de-tumbling and Acronyms de-saturation maneuvers are undertaken using only four thrusters, which adds to the complexity of the control de- ADCS Attitude Determination and Control System. sign. CDR Concurrent Design Review. This paper describes the attitude control strategy for the CMG Control Moment Gyroscope. LUMIO mission focusing on the configuration design of the CoM Center of Mass. reaction wheels and thruster-based de-saturation. Due to ConOps Concept of Operations. the tight constraint on the maximum momentum storage, DCM Direction Cosine Matrix. the placement of the reaction wheels significantly affects the ESA European Space Agency. desaturation strategy and requires optimization. Different LUCE LUnar CubeSat for Exploration. desaturation strategies are presented which require an un- LUMIO Lunar Meteoroid Impact Observer. conventional approach to their design due to the employment MIB Minimum Impulse Bit. of only four thrusters. RW Reaction Wheel. The work is organized as follows: Sec.2 summarizes the SRP Solar Radiation Pressure. mission and its most relevant characteristics for the ADCS TLO Top-Level Objectives. subsystem, whose configuration is discussed in Sec.3 and control laws in Sec.4. The performance of different reaction wheel configurations and desaturation strategies is analyzed 1 Introduction in Sec.5. Finally, the conclusions and potential future de- velopments are presented in Sec.6. The last decade has witnessed a paradigm shift in the space sector due to the popularization of nanosatellites. Their appearance has democratized access to space, boosted the 2 Mission Overview development of miniaturized technologies and extended the possibilities of distributed spacecraft architectures [1]. These 2.1 Top-Level Objectives(TLO) new capabilities, mainly tested in low-Earth orbits, have also The LUMIO mission aims to characterize the flux, magni- laid the foundations for the development of interplanetary tude, luminous energy, and size of the meteoroids impacting nanosatellite missions such as Mars Cube One [2]. the lunar farside. This would help advance the understanding CubeSats are a standardized class of nanosatellites ini- of how meteoroids evolve in the cislunar space and comple- tially conceived as educational tools or technology demon- ment the existing observations of the lunar nearside. From strators [3]. Their low cost, versatility and fast develop- the technological perspective, the mission wants to demon- ment time have led to their employment for actual scien- strate the deployment and autonomous operation of a Cube- tific projects. Interplanetary missions may benefit from their Sat in the lunar environment [7]. Those goals are summarized scalability, modularity and distributed architecture to obtain in the TLO listed in Tab.2. redundant and more detailed scientific information [4]. Some examples of recently proposed interplanetary CubeSats are 2.2 Concept of Operations(ConOps) the University of Colorado’s Earth Escape Explorer (CU- E3), the Cornell University Cislunar Explorers or the Fluid In the Circular Restricted Three-Body Problem, the libration & Reason-LLC Team Miles [5]. points are at rest with respect to a frame co-rotating with The Lunar Meteoroid Impact Observer(LUMIO) is a the smaller and larger primaries. Consequently, a halo orbit- 12U CubeSat mission to observe, quantify, and characterize ing the Earth–Moon L2 always faces the lunar farside. On the meteoroid impacts on the surface of the Moon by detect- top of this, for a wide range of Jacobi energies, Earth–Moon ing their flashes on the lunar far-side. This complements the L2 halos are almost locked into a 2:1 resonance, that is 2 knowledge gathered by Earth-based observations of the lunar orbital revolutions in 1 synodic period Tsyn = 29.4873 days. IAC-19,C1,6,4,x50894 Page 2 of 13 70th International Astronautical Congress, Washington D.C., United States, 21-25 October 2019. Copyright 2019 by the authors. Published by the IAF, with permission and released to the IAF to publish in all forms. Tab. 2: Top-Level Objectives of LUMIO[7]. Tab. 3: LUMIO ADCS high-level requirements [7]. ID Objective ID Name Requirement 01 To perform remote sensing of the lunar surface and measurement of astronomical observations not 01 De-Tumbling After the separation from the Lu- achievable by past, current, or planned lunar mis- nar Orbiter, the ADCS is required sions to de-tumble the spacecraft from 02 To demonstrate deployment and autonomous op- tip-off rates of, up to, 30 deg/s in eration of CubeSats in lunar environment, includ- each axis. ing localization and navigation aspects 02 Initialization Maneuver the solar panels to a 03 To demonstrate miniaturization of optical instru- power safe mode within a time mentation and associate technology in lunar envi- compatible with the electrical en- ronment ergy capability. 04 To perform inter-satellite link to a larger Lunar 03 Moon Point- The ADCS is required to point Communications Orbiter for relay of data and for ing with an accuracy of less than 0.1 TT&C deg during the science and naviga- 05 To demonstrate CubeSat trajectory control capa- tion phases. bilities into lunar environment 04 Power Maxi- The attitude is required to max- 06 To gain European flight heritage in emplacing and mization imize the power generation capa- operating assets at Earth-Moon Lagrange points bility of the solar panels given the Moon pointing (halo and part of the transfer) constraint and The quasi resonance locking, which is also preserved in the the Earth pointing (parking) con- full ephemeris quasi-halos, enables LUMIO operations to be straint.
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