Design and Control of a Nano-Control Moment Gyro

Design and Control of a Nano-Control Moment Gyro Cluster for Experiments in a Parabolic Flight Campaign ? H´ el` ene Evain ∗ Thomas Solatges ∗∗ Antoine Brunet ∗ Adrien Dias Ribeiro ∗∗∗ Lylia Sipile ∗ Mathieu Rognant ∗∗∗∗ Daniel Alazard † Jean Mignot ‡ ∗

Ph.D student, ONERA, Toulouse, France (e-mail: [email protected]). ∗∗ Ph.D student, ONERA and SITIA ∗∗∗ MSc student, ONERA and EI CESI, Toulouse, France ∗∗∗∗ Research Scientist, ONERA, Toulouse, France † Professor, ISAE SUPAERO, Toulouse, France ‡ AOCS Senior Expert, CNES, Toulouse, France Abstract: In this paper, a new system dedicated to the control of the attitude (orientation) of nanosatellites for future space missions is described. It is composed of a cluster of six Control Moment Gyros (CMGs) that presents advantages over current CMG clusters, and controlled by a new steering law. This law should be able to handle failures of Control Moment Gyros in the cluster, singularities and should be simple enough to be computed in real-time onboard satellites. In addition, the size of the cluster will remain small to be compatible with nanosatellite size constraints. This project was proposed by the Flying Squirrels team and selected for the 2017 Fly Your Thesis! programme by the ESA Education Office. Therefore, an in-house cluster of six Control Moment Gyros along with an innovative control law will be tested in a parabolic flight campaign in 2017. This paper outlines the main aspects of this project, from the scientific expected outcomes to the design of the experiment. Keywords: Guidance navigation and control, Actuators, Experiment Design 1. INTRODUCTION The aim of this project is to test an innovative and promising technological system aimed at controlling the attitude (i.e. controlling of the orientation) of nanosatellites (small satellites). This system is composed of a cluster of six mechanical actuators (single-gimbal control moment gyros), an inertial measurement unit and is controlled by a new steering law for these actuators described in Evain et al. (2016). Control moment gyros (CMGs) are actuators used in space systems. They can create large instantaneous torques while consuming little energy compared to reaction wheels (Busseuil et al. (1998)). However, steering a cluster of control moment gyros commonly requires an internal singularity avoidance strategy, to avoid configurations where torques cannot be created along an axis while the cluster has not reached its maximum capabilities, thus increasing the complexity of controlling these systems. Their use for nanosatellites is not common because of their mechanical complexity, the difficulty of steering them, and few offthe-shelf systems are commonly available in the market. Nevertheless, as noted in Votel and Sinclair (2012), there is an increasing demand for agile microsatellites, and CMG technologies are potential solutions to achieve the ? This work is supported by ISAE SUPAERO, ONERA and CNES.

missions. Indeed, there are more and more missions that require maneuvers or tracking capabilities (Ishimary and als. (2014)). In addition, the size of the nanosatellites is growing fast and a new attitude control system able to deal with the increasing weights may be required. Therefore, the CMG technology is promising since it presents these advantages. Some nanosatellites are indeed already testing nano-CMGs like SwampSat (Allgeier et al. (2010)) for instance. The nanosatellite Violet has also integrated nano-CMGs to test steering laws (Gersh and Peck (2009)). The main objective of our project is therefore to propose a new attitude control system based on a cluster of six control moment gyros spatially distributed in an isotropic pyramidal configuration, and a new steering law. Having six CMGs instead of four like usually proposed in CMG clusters enable greater resilience of the spacecraft to actuator failures, does not decrease the efficiency of the system and provides a cluster easier to control. Indeed, internal singularities are then located near the momentum saturation envelope (Kurokawa (1998)). The steering law should be able to handle actuators failures easily, saturations and singularities. This steering law is presented in Evain et al. (2016) and can be computed in real-time in satellites. An experimental setup testing this system will be constructed and the experiment will be carried out in parabolic flights through the ESA Education Office programme, Fly Your Thesis!.

The main challenges that our project has to face is to miniaturize the CMG cluster so as to fit in a nanosatellite, using off-the-shelf components. Also, experiments in parabolic flights have to meet stringent safety constraints due to the specific environment. In this paper, the choice of the cluster and of the tested steering law are explained, then the main experiment procedures are outlined followed by the preliminary design of the experiment. 2. TEST OF A NEW CMG CLUSTER SYSTEM Each CMG is composed of a flywheel (red wheel in Fig. 1) that spins at a constant rate around an axis X. A rotation speed (also called gimbal rate) around the Z-axis is calculated by the steering law and produces a torque around the last axis Y due to the gyroscopic effect. This torque is transmitted to the satellite by reaction, changing its attitude. Indeed, this device transfers angular momentum to the satellite, therefore limiting the capability of the cluster to control the attitude of the satellite to its intrinsic capabilities (also called momentum envelope).

Fig. 1. Control Moment Gyro (CMG) Having six CMGs instead of four in a pyramidal cluster offers a precious redundancy and therefore an increased reliability of the system, especially if using off-the-shelf components (not tested in spatial environment) like it is often the case in nanosatellites. With six CMGs instead of four, an individual failure will have less impact on the system performance. Calculations show that for an isotropic pyramidal cluster of four CMGs, the maximal possible angular momentum of the cluster is around 3.2ht (with ht the angular momentum of the flywheel, assumed equal for all CMGs), giving an efficiency of 80% (compared to the sum of the maximal capability of each CMG). In Fig. 2, the repartition of the cluster capacities along all 3-D directions in angular momentum is shown. For six CMGs, the maximal angular momentum is of 4.8ht , thus also 80% of the cluster capacities. This shows that sixCMG clusters are as efficient (for using its capabilities) as four-CMG clusters (see Fig. 2). Finally, six-CMG clusters present the great advantage of having most of the singularities located near the momentum envelope (see Kurokawa (1998)), which allows for a better usage of the available momentum without reaching singular configurations. Also, we can distinguish between

the singularities that can be passed by using null-motion (reconfiguration), called escapable, and the ones called inescapable (or elliptic) where the only way to pass the singularities is to come back in the trajectory or to create errors (see Kojima (2014)). The values of angular momentum where internal inescapable singularities can occur for four and six-CMG pyramidal isotropic clusters are given in Fig. 3 and 4. They are located nearer to the momentum envelope for six-CMG clusters than for four-CMG clusters. The calculation of these singular surfaces has been carried out following the work of Wie (2004). After meshing in the 3-D angular momentum directions, the singular gimbal positions corresponding to the meshed directions have been computed. Then, the criteria developed by Wie (2004) has discriminated between escapable and inescapable singularities. For visual purposes, the inescapable singularities are shown in the angular momentum space. However, it should be noted that because of the redundancy, one value of the cluster angular momentum matches various values in the gimbal angle space, therefore, even if a singularity is located at a particular angular momentum value, the system may or may not be in a singularity (it depends on its gimbal angles). The subfigures 3 and 4 show singular surfaces (continuous) corresponding to different singularity signatures. The coarseness of the mesh has been tested and the surfaces remain consistent even when more points are represented. Usually, the maneuvers begin with an initial null angular momentum, hence the singularities are encountered later for the six-CMG cluster in the space of angular momentum and the probability of falling into these singularities is smaller with six CMGs given the large space of gimbal angles. Therefore, having six CMGs greatly simplifies the steering laws since it makes the system encounter far fewer singularities. The control of CMG clusters is usually challenging because of the singularities and other constraints such as realtime implementation. The proposed control loop of the system is presented in Fig. 5. The inputs of the control law are the desired and measured attitudes (θd , θm ) and satellite angular rates (ωd , ωm ). The feedforward terms are used to compensate the nonlinear couplings between the satellite and the cluster. The steering law has to ˙ by convert the computed torque td into gimbal rates x, inverting eq. (1) under constraints. Then, a saturation may be applied to ensure that a feasible control x˙ d is sent to the motor controllers. td = ht J(x)x˙ (1) with td the torque to be created by the cluster, x˙ the gimbal rates vector and J(x) the jacobian matrix from the kinematic equations of the cluster. With more than three CMGs in the cluster, the J matrix is rectangular and can be rank-deficient (preventing the use of the Moore-Penrose inversion) when a singularity is encountered. Many steering laws have been proposed in the past. Some based on the Singular Robust Inverse add a term to ensure the J matrix is always invertible (Wie (2005), Bedrossian (1987)). Other methods search in the null-space of J to maximize a given function, they are called gradientbased methods (Asghar et al. (2006)). Restrictions of the workspace where no singularities are present are also studied (Kurokawa (1998)) as well as algorithms adding constraints in the J matrix to make it square and invertible

Fig. 2. Maximal angular momentum envelope for isotropic pyramidal 4-CMG (left) and 6-CMG clusters (right) (normalized angular momentum of the flywheels) θd , ωd

Attitude controller θm , ωm

+ +

td

Steering law

x˙

Saturation

x˙ d

Feedforward

xm , x˙ m

Fig. 5. Block diagram of the control-loop proposed

Fig. 3. Surfaces of internal inescapable singularities for an isotropic cluster of four CMGs (normalized angular momentum of the flywheels)

Fig. 4. Surfaces of internal inescapable singularities for an isotropic cluster of six CMGs (normalized angular momentum of the flywheels) as long as the constraints are compatible (Jones et al. (2012)). The steering law described in the paper by Evain et al. (2016) will be tested in our project. It can be computed in real-time in space applications. It uses the formalism of the Extended Kalman Filter (EKF) and contains a new formulation of the kinematic equations that helps escaping or avoiding singularities. Constraints can be

taken into account in a flexible way by adding equations in the EKF which will perform an optimisation between the different constraints, and prioritizing through the values of the covariance matrices. In particular, the actuator saturations (in gimbal speed) has to be considered. As long as the required torque is feasible by the system, the only risk of saturating the system is through the singularities, when the cluster will try to pass them by creating large velocities. If avoidance is correct, the system should not saturate. A specific constraint will be inserted in the EKF. Nevertheless, as no theoretical proof shows that the actuator will not saturate, a saturation block will be inserted. Indeed, the constraints imposed inside the EKF are taken into account, but are not guaranteed. Some methods as model predictive control (Clarke et al. (1987)) or quadratic optimization (Fossen and Johansen (2006)) would ensure that the constraints are verified but the calculations available into the space computers are not suitable for the attitude control issues. The performance of the steering law during typical maneuvers or spacecraft motions will be tested in terms of pointing accuracy, tracking performance (including avoidance of singularities), as well as its capacity to handle CMG failures in the cluster. For the experiment, the communication delays between the computer and the motors can be dealt with if needed in the steering law, while the delays between the measurements and the actual commands carried out will be taken into account in the attitude controller design. Typically, this controller will be composed of a proportional-derivative function, and will have to ensure enough phase margins to integrate the delays and be robust to inertia uncertainties

for instance. This controller will impose the dynamics of the closed-loop and these uncertainties in particular. The dynamics of the steering law will also be taken into account. The design of this control law is detailed in the paper by Evain et al. (2017).

3. EXPERIMENT PROCEDURE The parabolic campaign carried out by Novespace includes three flights of thirty parabolas each. One parabola gives about 20 seconds of microgravity during which our autonomous device will be free-floating and performing typical maneuvers. The different phases of the flight are given in Fig. 6. It is composed of : • Hypergravity phases : during this phase, the experimenters cannot perform the experiment which has to remain attached to the airplane for safety reasons. • Microgravity phases : during these phases, the experiment will be carried out. A control station fixed to the plane will send orders for each parabola that the nanosatellite will have to follow thanks to the onboard control laws and the CMG cluster. The remote control orders may be whether to: · Keep the nanosatellite pointed in a given attitude, by rejecting the outside perturbations. This will test the accuracy of the cluster at low gimbal rates. · Achieve rapid reorientations of the satellite to target precisely an attitude and come back to an initial position : the goal is to test the steering law accuracy, the rapidity of the maneuvers, the singularities avoidance and the saturation constraints. Also, these maneuvers will be tested with simulated failures of actuators : one or two Control Moment Gyros will be stopped and the automatic reconfiguration of the steering law will be tested. · Follow a target object : a simulated mission where a nanosatellite has to keep its camera fixed relatively to a moving object (modelling for instance a debris inspection or approach). To do so, a camera will be placed inside the nanosatellite, and an image processing algorithm will create a guidance law for the attitude controller in order to follow (in attitude) a target. That will test the reactivity and the accuracy of our steering law for unpredicted movements with dynamics relatively slow. Any type of operation can be carried out during one parabola. The whole system will be released at the beginning of the microgravity phases and then fly freely in an allocated area protected by a containment net inside the A310 ZERO-G plane. A control station fixed to the plane handles the communication, data logging, monitoring and remote control of the satellite. Fig. 7 shows the experiment integration with two experimenters, a control station (Green), the netted area (Purple) and the satellite (Orange).

Before the flight campaign, a test bench will be used in order to test the nanosatellite, check the performances, reliability and compliance with the safety constraints. 4. EXPERIMENT DESIGN The experimental device is a small (20cm diameter and 10 cm high) satellite including all the subsystems of a nanosatellite. It is composed of six CMGs and their control electronics, batteries, integrated processing system and sensors. Previous work by Steyn (2015), Patankar et al. (2014) and Sheerin (2015) have been studied to define the required performances of the attitude control system and deduce the characteristics of the cluster. In our case, the cluster will be able to create a maximal total angular momentum that, when transferred to the nanosat, will make it spin up to 40◦ /s. With two CMG failures, the maximal angular speed achieved by the nanosat will be 15◦ /s. These capacities have been chosen to ensure robustness to initial release errors and potential additional total angular momentum obtained from rebounds on the nets. The flywheels are actuated by small sensorless brushless motors regulated at a constant speed thanks to back EMF 1 . The gimbal motor rotates the flywheel around the z axis shown in Fig. 1. It performs a closed loop position and speed control based on an absolute rotary encoder. The preliminary design of the satellite is shown in Fig. 8. It shows the integration of the six CMGs, one Raspberry Pi 3 with a custom shield (for estimation, control and communication), two batteries and an inertial measurement unit. 5. CONCLUSION We propose to test a cluster of six Control Moment Gyros that presents the advantages of being reliable, has large momentum capabilities and has nearly no internal singularities. The new in-house steering law that can handle failures of Control Moment Gyros in the cluster, singularities, saturations and that can be calculated in real-time onboard satellites will be tested. In addition, we would like to show the possibility of integrating a miniaturized attitude control system in a nanosatellite, to extend their attitude control capabilities. Indeed, the simulation results of the steering law are promising (see Evain et al. (2016)) but actual implementation in an experiment will show its real performance and limitations. Increasing the Technological Readiness Level is expected through these experiments while reaching the safety and reliability level required to perform a parabolic flight. ACKNOWLEDGEMENTS The authors would like to thank the ESA Education Office for the opportunity offered. REFERENCES Allgeier, S., Nagabhushan, V., Leve, F., and Fitz-Coy, N. (2010). Swampsat - a technology demonstrator for operational responsive space. Astro 10, CASI Conference. 1

Electro-Motive-Force, generated by the rotation of a motor, allowing to measure its rotational speed

Fig. 6. Typical flight procedure for each parabola. Credits Novespace.

Fig. 7. Proposed integration of the experiment in the ZERO-G plane

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