# ESA GNC Conference Papers Repository

**Title:**

##### Beyond l-inf reaction wheel commanding: increased on-board autonomy through enhanced wheel failure handling

**Authors:**

**Presented at:**

**Abstract:**

This paper is a continuation of the work presented at the ESA GNC 2014 [1]. In the meantime, the L-Inf commanding algorithm presented there has become standard for missions currently under development such as ESA Metop-SG. Even more, [1] triggered an enhancement of wheel management of high practical importance which will be presented in this paper. It is theoretically solid and not just an academic exercise - it is for immediate application on-board spacecraft. Motivation During nominal operation, reaction wheels need to be operated in a certain speed range in order to avoid wheel performance degradation (or even harm) and reduced spacecraft pointing performance due to low speeds, zero crossings or vibrations. This is typically done by controlling the wheels in the null space. The null space (vector) of a common 4-wheel configuration is typically a pre-stored parameter on board. Newly, large spacecraft and/or agility requirements have led to configurations of 5 or more wheels such as on Metop-SG (6 wheels hexagonal or 5 wheels pentagonal). Handling multiple wheel failures has become of particular importance because wheels can be used in Safe Mode (providing angular momentum bias) but also for handling intermittent wheel failures in general. Handling multiple wheel failures provides increased system robustness and prevents potential loss of the spacecraft. However, 6 wheels lead to 6 and 15 possibilities of single and two wheel failures, respectively. In order to avoid a huge amount of pre-stored parameters on-board, the orthogonal null space basis shall rather be robustly computed on board. Methods of null space computation for on-board application The proposed algorithm for finding a basis for the null space (or kernel) of the wheel alignment matrix is composed of two steps: (1) generation of vectors that span the complete null space, (2) orthogonalization of (1). Two deterministic methods for (1) are presented: (1.1) via virtual torque commands using L-Inf and L2 commanding algorithms, (1.2) via a null space projection matrix using a generalized inverse. Method (1.1) was indirectly already posed in [1]. Using virtual torque commands into 'the right' directions (details in paper), empirical evidence has shown that this method yields the desired vectors. It is an intuitive approach that proved the feasibility of deterministic on-board null space computation. Method (1.2) is an enhancement of (1.1) towards a mathematically proven solution. A projection matrix of the null space of the wheel alignment matrix may be computed using any of its generalized inverses, such as those used to compute the L-Inf or L2 torque commands. It is shown that, using the L2 pseudo-inverse, the unique orthogonal projection matrix of the null space can be computed, whereas using any of the L-Inf generalized inverses yields a (non-unique) skewed projection matrix of the null space. These projection matrices (always) span the complete null space (proof in paper). A comparison of methods (1.1) and (1.2) w.r.t. on-board application will be given in the paper. For step (2) a number of solutions are available (e.g. Gram-Schmidt, Householder, Givens). The paper will focus on the numerically stable solution used on board. Towards enhanced null space control Null space constrained wheel momentum management is required in conjunction with the L-Inf torque commanding algorithm in order to attain the wheel array momentum envelope [3]. Furthermore, a multi-envelope, cascading approach that respects predefined wheel momentum operating bands yet still achieves the full L-Inf envelope is currently under development. These functions are only realizable autonomously by either storing a large number of null space bases in onboard memory or by the use of an onboard null space basis computation algorithm such as those presented here. Summary and Conclusion A deterministic method of null space basis computation suitable for onboard computation is presented. The increased autonomy is a perquisite for onboard wheel failure handling as it enables the recomputation of the null space basis with a single algorithm for all wheel failure cases. The presented work is dedicated to the demand of high on-board autonomy driven by more and more private customers requiring 'just' a working spacecraft without many interventions by ground, by military customers that demand a robust autonomous spacecraft, by European/ESA projects where high observability or agility is important (e.g. Metop-SG) and by non-Earth bound scientific missions due to non-availability because of transmission delays. The work is further dedicated to the demand of Robustness, in order to cope with multiple wheel failures during nominal operation without going into Safe Mode immediately, to enable wheel-based Safe Modes (e.g. for momentum bias control using a B-Dot Safe Mode) and to prevent potential loss of spacecraft due to intermittent wheel failures. The presented solutions are implemented for high power satellite avionics system established by Airbus, called Astrobus 400, for current missions such as Metop-SG, Agile Radar Earth Observation Missions (private, military) and Tandem-L.