SINGLE AXIS POINTING BY MEANS OF TWO REACTION WHEELS Alessandro Zavoli (1) , Fabrizio Giulietti (2) , Giulio Avanzini (3) , and Guido De Matteis (4) (1) ‘Sapienza’ Universit` a di Roma, Via Eudossiana 18, Rome, Italy 00184, (+39) 064458 5210 , alessandro.zavoli@uniroma1.it (2) Universit` a di Bologna, Via Fontanelle 40, Forl` ı, Italy 47121, (+39) 0543 374424, fabrizio.giulietti@unibo.it (3) Universit` a del Salento, Campus Ecotekne, Lecce, Italy 73100, (+39) 0832297798, giulio.avanzini@unisalento.it (4) ‘Sapienza’ Universit` a di Roma, Rome, Italy 00184, (+39) 064458 5210 , guido.dematteis@uniroma1.it Abstract: The paper deals with attitude dynamics of an underactuated spacecraft, proposing a technique for aiming a body-fixed axis (e.g. sensor, antenna, nozzle, etc.) arbitrarily close to a prescribed direction in space by means of two reaction wheels only, when the total angular momentum of the spacecraft is zero. The technique is based on a simple kinematic planning scheme, where an eigenaxis rotation is performed around an admissible rotation axis, that is, an axis that lies on the plane of the two active reaction wheels. Proof of almost global stability is provided, together with a detailed discussion of a few theoretical shortcomings. The latter can be circumvented in the numerical implementation of the control law, that remains simple and computationally efficient. Numerical simulations of single-axis pointing maneuvers for a reference spacecraft prove the practical viability and validity of the approach. The effect of non-ideal conditions, such as a small residual angular momentum, command torque saturation and off-diagonal terms in the inertia tensor, are also investigated. Keywords: Attitude control, Underactuated control, Reaction wheel failure. 1. Introduction The paper proposes a novel approach for single-axis pointing by using only two reaction wheels (RW), derived on the basis of a simple yet effective wheel rate command. This maneuver technique can be used for aiming the line-of-sight of a sensor, a nozzle or an antenna towards a target direction, or solar panels towards the Sun, after failure of one wheel for a non-redundant control system hardware or in the case of multiple failures for redundant systems. Examples of this kind of situation are the Far Ultraviolet Spectroscopic Explorer (FUSE) and Kepler space telescope, that both suffered from failures that left only two wheels available for maneuvers. Failure of mechanical actuators is also expected to potentially affect low-budget space missions based on small-size low-cost spacecraft (nano-, pico-, and cube-sat families). The control approach here proposed, derived from the kinematic planning scheme of Ref. [1], represents its practical, dynamic implementation, under the assumptions of zero overall angular momentum and a diagonal inertia tensor. The effects of a non-zero residual angular momentum and control axes not aligned with the principal axes of inertia will also be investigated at the end of the paper, highlighting limitations on pointing precision and convergence performance. The possibility of pointing a body-fixed axis towards and arbitrary direction represents a significant contribution, 1