PLATFORM: the GMV's Test-bench for Formation Flying, RvD and Robotic Validation

This chapter studies the spacecraft rendezvous problem and the spacecraft formation flying problem by using the TPF approaches. For the spacecraft rendezvous problem, the target spacecraft can be in arbitrary eccentric orbits, and for the spacecraft formation flying problem, the reference spacecraft is assumed to be in a circular orbit. By clarifying that the T-H equation and C-W equation are both ANCBC and NCE, the TPF approach for stabilization and consensus of linear systems with input and output delays built in the previous chapters are extended to solve the considered problems. Some simulations are carried out to validate the effectiveness of the proposed approaches.

Spacecraft relative navigation with an omnidirectional vision sensor

In this paper, a recently proposed SE(3)-constrained extended Kalman filter (EKF) is extended to formulate a strategy for relative orbit estimation in a space-based sensor network. The resulting consensus SE(3)-constrained EKF utilizes space-based sensor fusion and is applied to the problem of spacecraft proximity operations and formation flying. The proposed filter allows for the state (i.e., pose and velocities) estimation of the deputy satellite while accounting for measurement error statistics using the rotation matrix to represent attitude. Via a comparison with a conventional filter in the literature, it is shown that the use of the proposed consensus SE(3)-constrained EKF can improve the convergence performance of the existing filter for satellite formation flying. Moreover, the benefits of faster convergence and consensus speed by using communication networks with more connections are illustrated to show the significance of the proposed sensor fusion strategy in spacecraft proximity operations.

This paper presents a hardware-in-the-loop (HITL) simulation approach for multiple spacecraft formation flying. Considering a leader-follower formation flying configuration, a Fuzzy Logic controller is developed first to maintain the desired formation shape under external perturbations and the initial position offsets. Cold-gas on/off thrusters are developed to be introduced to the simulation loop, and the HITL simulations are conducted to validate the effectiveness of the proposed simulation configuration and Fuzzy Logic control.

Spacecraft formation flying has received an enor- mous amount of attention over the past few years as a promising alternative to monolithic- and often large- space structures. Balanced optimal energy control of such distributed space systems guarantees maximum lifetime for these missions and hence is of great importance in mission feasibility studies. In this paper, an optimal control strategy for two and three spacecraft distributed space systems that are commanded to attain new relative coordinates, is proposed, guaranteeing balanced energy consumption among the spacecraft. We will delineate on the relevant mission scenarios both in deep space as well as in close proximity to a gravitational force field as in Earth's orbit. Index Terms— Formation flying, balanced energy reconfig- urations, optimal control

Performance Testing of Lithion 8-Cell, 25 AHr Lithium-Ion Batteries for Future Aerospace Applications

The prescribed performance robust control method for the leader/follower (L/F) formation is proposed in this paper to solve the problem of spacecraft formation flying (SFF) full-process control (FPC). The objective of FPC is to establish an ultra-close formation with the constraint of collision avoidance between two spacecraft, and then to maintain the formation configuration with high-precision accuracy in a period of time. The main contribution of this paper lies in the following three aspects. Firstly, the six-degree-of-freedom (DOF) error dynamics model of SFF is developed to describe the synchronization motion of the L/F system. Secondly, the prescribed performance bound that comprehensively considers transience and transient performance is designed, which is key for the realization of collision avoidance and high-precision accuracy requirements. Finally, combing prescribed performance control and robust control theories, based on the backstepping method, the predefined performance robust controller is designed, and the tracking errors are proven to converge to the predefined performance bounds in the presence of external disturbances by using the predefined performance robust controller. Illustrative simulations are performed to verify the proposed theoretical results.

Precise relative GPS navigation is essential technology for rendezvous and formation flying of spacecraft in Low Earth Orbit. Key design issues of precise relative GPS navigation software are studied and a novel formulation is proposed for the mission which requires high accuracy when the separation distance is up to several km. The navigation filter estimates float navigation solutions by extended Kalman filter with elaborate dynamics models, and resolves ambiguities of integer carrier phase biases to achieve high accuracy fix navigation solutions. A relative navigation software with the proposed formulation is implemented and evaluated in two different ways. One is a test using spacebourne GPS receivers and a GPS signal simulator to evaluate the performance and sensitivity of the software against variation of parameters. The other is a test using actual telemetry data from Gravity Recovery and Climate Experiment (GRACE) to demonstrate the software performance. The design, implementation, and results of the evaluation are presented and discussed on this paper.

We present several results of the leader-following paradigm in the formation flying of multiple spacecraft in free space. In this direction, ideas from elementary graph theory and linear matrix inequalities are combined with logic-based switching to shed light on the various control designs which are feasible using the leader-following mechanism for various formation flying scenarios.

In early 2004, JPL successfully landed two Rovers, named Spirit and Opportunity, on the surface of Mars after traveling > 300 million miles over a 6-7 month period. In order to operate for extended duration on the surface of Mars, both Rovers are equipped with rechargeable Lithium-ion batteries, which were designed to aid in the launch, correct anomalies during cruise, and support surface operations in conjunction with a triple-junction deployable solar arrays. The requirements of the Lithium-ion battery include the ability to provide power at least 90 sols on the surface of Mars, operate over a wide temperature range (-20(super 0)C to +40(super 0)C), withstand long storage periods (e.g., including pre-launch and cruise period), operate in an inverted position, and support high currents (e.g., firing pyro events). In order to determine the inability of meeting these requirements, ground testing was performed on a Rover Battery Assembly Unit RBAU), consisting of two 8-cell 8 Ah lithium-ion batteries connected in parallel. The RBAU upon which the performance testing was performed is nearly identical to the batteries incorporated into the two Rovers currently on Mars. The primary focus of this paper is to communicate the latest results regarding Mars surface operation mission simulation testing, as well as, the corresponding performance capacity loss and impedance characteristics as a function of temperature and life. As will be discussed, the lithium-ion batteries (fabricated by Yardney Technical Products, Inc.) have been demonstrated to far exceed the requirements defined by the mission, being able to support the operation of the rovers for over three years, and are projected to support an even further extended mission.

In early 2004, JPL successfully landed two Rovers, named Spirit and Opportunity, on the surface of Mars after traveling > 300 million miles over a 6-7 month period. In order to operate for extended duration on the surface of Mars, both Rovers are equipped with rechargeable Lithium-ion batteries, which were designed to aid in the launch, correct anomalies during cruise, and support surface operations in conjunction with a triple-junction deployable solar arrays. The requirements of the Lithium-ion battery include the ability to provide power at least 90 sols on the surface of Mars, operate over a wide temperature range (-20(deg)C to +4O(deg)C), withstand long storage periods (e.g., cruise period), operate in an inverted position, and support high currents (e.g., firing pyro events). In order to determine the viability of meeting these requirements, ground testing was performed on a Rover Battery Assembly Unit (RBAU), consisting of two 8-cell 8 Ah lithium-ion batteries connected in parallel. The RBAU upon which the performance testing was performed is nearly identical to the batteries incorporated into the two Rovers currently on Mars. The testing performed includes, (a) performing initial characterization tests (discharge capacity at different temperatures), (b) simulating the launch conditions, (c) simulating the cruise phase conditions (including trajectory corrections), (d) simulating the entry, decent, and landing pulse load profile (if required to support the pyros) (e) simulating the Mars surface operation mission simulation conditions, as well as, (f) assessing performance capacity loss and impedance characteristics as a function of temperature and life. As will be discussed, the lithium-ion batteries (fabricated by LithiodYardney, Inc.) were demonstrated to far exceed the requirements defined by the mission, and are projected to support an extended mission (> 2 years) with margin to spare.

Spacecraft formation flying is a fast improving technology for space missions, showcasing reduced cost, increased flexibility and efficiency and design redundancy over similar single satellite missions. Furthermore, it provides a viable solution for missions requiring high spacial and temporal resolutions. While a lot of work has been conducted on spacecraft formation flying control, very few of these algorithms have been validated on flight hardware or through hardware experiments. The L 1 adaptive control algorithm is a promising algorithm that can deal with various model uncertainties in real time. It's capability has been demonstrated through numerous aerospace simulations and also through real world experience on board NASA's AirSTAR aircraft. As such, this work focuses on the design, simulation, implementation and validation of the L 1 adaptive controller for spacecraft formation flying. More specifically, this thesis first introduces the L 1 adaptive control architecture using examples for simple linear systems, to gain an understanding of the controller implementation and behaviour. The desired controller design decisions are discussed I would like to begin by thanking my thesis supervisor, Steve Ulrich, for his support, guidance and motivation. His enthusiasm and mentorship always motivated me to put my best foot forward and I cannot imagine doing this with a better supervisor and mentor.

Background: In the field of biomechanical analysis of pedaling motion, researchers studied the relationship between cost energy and cycling technique for optimal use of the force applied to the pedals, to improve cycling velocity for minimal energy cost or to compute the joint powers according to the resistive load. For that, numerous measuring devices have been developed and investigated to evaluate resultant torque and/or power output. Recently, new pedal sensors I-Crankset (ICS) are sold to measure the forces applied to the pedals and to calculate the torque and/or power output produced during cycling. These pedals’ sensors were calibrated and certificated, but it was essential to check if these devices still measured accurately after their integration on an ergometer. Purpose: The aim of this study was to compare dynamically this new device for measuring crankset’s resultant torque, mechanical power and work outputs.  Methods: A subject (Male, 75 kg, 1.82 m, trained rider) took part to this study conducted ethically according to international standards. The rider adjusted the cycle ergometer according to its personal settings. Figure 1 described the test bench. It was composed of: a chainring (A) was used to connect the ergocycle to the bench through a chain and a flywheel (D) associated with a mechanical braking device (E) composed of a tray with additional masses. The evaluation protocol was implemented to achieve three pedaling conditions and so to cover the usual torque and power ranges (Table 1). For each condition, the subject produced a pedaling torque to overcome that resistive load during one trial of 90 seconds. Feedback of cadence was displayed on the Control SRM bicycle computer. The torque reference sensor (model 1641/1648, Lebow) named RTSL (C) was installed on the axis (B). The scientific version SRM sensor was mounted on the crankset of the ergocycle. The ICS sensors were fixed at each pedal. The relative pedal to crank and the crank to ergometer angles were measured using encoders.  Analyzed parameters: As all the signals are acquired at 200 Hz and synchronized, for each cycle and for each acquisition system, we had the same number of acquisitions samples. According to the sample rate and protocol used, more than 12 000 instantaneous measures will be available for the comparison of several devices. Three power outputs were computed through these equations: (1)  with , k is the reduction coefficient between SRM and bench chainrings, ratio of the two diameters. (2) SRM:,  is the average angular velocity of the crankset over the cycle. (3) ICS: ,  is instantaneous angular velocity of the crankset computed from encoders measures. The mechanical work outputs  were given by integration over the time of the power outputs. By design, the SRM only measures an average angular velocity, so we computed mechanical work firstly considering this constant angular velocity () and secondly considering instantaneous angular velocity provided by ICS encoders (). Statistical analysis: For each condition, the same analysis was performed on torque, power and work outputs obtained from the different sensors. These instantaneous parameters, once pedaling cycles normalized, were compared using a coefficient of multiple correlation inter-protocol (CMC ip ) to appreciate the similarity of the instantaneous measures waveforms given by various sensors in a single acquisition of the same parameter. For each condition (n=30 cycles) and for all conditions (n=90 cycles), the averaged torque and power output were computed over each cycle and then these values were compared pairwise of sensors (A Bland-Altman analysis). A global normalized averaged torque evolution over cycles was also computed for condition 1 and for each sensor using.  Results: Mechanical power output comparisons: Table 2 reports all the data for the comparison of the averaged power output measured by the three sensors, for the each condition and all conditions. Especially for condition 3, we note an increase for the power output of the mean bias and error range between SRM and RTSL against those computed for the torque [mean bias: -4.4 ±2.3% for the power vs -1.20 ±0.53% for the torque; error range: 29 W (9.2%) for the power and 0.79 Nm (1.9%) for the torque]. This is not the case for ICS. The figure 3 confirms these results with a 95% limits of agreement larger for the SRM than ICS [respectively -1.81; 7.37 W and -20.70; 9.48 W for ICS and SRM]. Mechanical work output comparisons: Table 3 shows the difference of cumulative output work over thirty cycles between ICS and RTSL then SRM and RTSL for each condition. The differences are also expressed as the percentage of the total cumulated work. To analyze the influence of the angular velocity, we integrated power output over time to compute the work output in using i) the torque and angular velocity measured by SRM (W SRM ) and ii) the SRM torque multiplied by ICS angular velocity (W SRM* ). These results are presented at the last lines of table 4. The relative error is under 2% whatever the conditions, excepted for condition 3 between SRM and RTSL (5.26%). This error can be reduced by using I‰ ICS provided by ICS to compute the W SRM* (1.44 %).  Discussion: Power output discussion. For the power output, we note high values of  between ICS and RTSL (Table 3). For the steady state condition (C1: 210 W), ICS power mean relative error (0.1 ±0.5%) is better than [1] when comparing Velotron cycle ergometer (-0.8% for constant 250 W trial) with a test bench. For condition 2 (150 – 250 W, 80 rpm), ICS results (1.8 ±0.5%, Table 2) are closed to power mean relative error reported by [4] when comparing Powertap (-1.5 ±0.6% for 50-1000 W at 100 rpm trial) with a test bench. As SRM is considered as a gold standard [5], we will try to position ICS against SRM. Before that, we check that SRM results are consistent with literature. The mean relative errors reported by [1] (0.18%) and [4] (0.1 ±1.1%) are lower than errors of the present study (respectively 0.8 ±1.2% for condition 1 and -0.8 ±2.1% for condition 2). These differences can be related to the possibility of the test bench used by [6] to maintain a constant pace along all the cycle unlike the protocol of this study (mean cadence: 8.3 ±0.2 rad/s for conditions 1 and 2). Indeed, it’s difficult for a rider to produce a constant crankset angular velocity like the motorised test bench used by [1] and [3]. [1] shows that a rapidly increasing angular velocity results in a more inaccurate power measurement (mean relative error: -3.3 %; CI = -8.1 to 1.5 %). This is closer to the results for condition 3 (-4.4 %; CI = -9 to 0.2 %). This condition accentuates the inability of the SRM to record, by design, instantaneous crankset angular velocity. For a similar pedaling cadence and power output, the relative mean error (1.2 %) between Powertap ergometer and SRM reported by [2] is comparable with the relative error between ICS and SRM computed for condition 1 (0.9%, Table 3). However, ICS seems to be more accurate than SRM when looking at the individual results obtained for SRM (-2.4%) and ICS (1.2%) against RTSL for all conditions. Consequently, as for the torque, ICS can be considered sufficiently accurate. Work output discussion: Table 3 show the requirement to precisely measure the instantaneous values of crankset angular velocity to calculate the work as part of an energy study of the pedaling motion. Thus, when pedaling with constant angular velocity, the power output computed by SRM () is enough accurate to calculate the work output (). For the conditions 1 and 2, the error respectively equal to 0.98% and 1.16% is acceptable. But when the angular velocity is variable, the error becomes equal to 5.26% for the SRM while it is still under 2% for ICS. This result confirms those obtained by [1] which indicates that a rapidly increasing angular velocity causes an inaccuracy in calculating the SRM power. This error is reduced to 1.44% when the torque measured by SRM () is multiplied by the instantaneous angular velocity measured by ICS (). So, ICS should be preferred for power and work outputs investigations.  Conclusions: The study showed that ICS sensor was an accurate powermeter comparable to a standard reference sensor and to SRM regardless the pedaling cadence (56 to 90 rpm) and the resistive load (18 to 42 Nm). However, ICS was more efficient than SRM for evaluating the work particularly when the pedaling angular velocity various significantly. This study showed that it was therefore essential to measure both instantaneous torque and angular velocity in order to conduct an energy analysis of the pedaling motion.

Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing precision dual spacecraft formation flying to enable a “virtual” telescope (VT). Using precision alignment of two spacecraft very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Furthermore, orders of magnitude improvement in science imaging over conventional single spacecraft instruments is possible with advances in precision formation flying. Precise astrometric alignment control is required for accurate inertial pointing of the VT. This work presents orbit design and control approaches for VT formation flying, with specific application to the recently proposed Virtual Telescope Demonstration Mission (VTDM) using cubesats. The characteristics of the mission orbit are derived from solutions to Hill’s equations for the relevant mission orbit. A relative orbit control technique pertaining to the astrometric alignment problem is developed by utilizing the Constrained Model Predictive Control (CMPC) approach. This method enables design of formation flying control laws for a thruster assembly with limited magnitude. Precision formation flying is achieved by use of separate control laws for formation maintenance and precision astrometric alignment. The proposed control scheme compensates for inertial astrometric alignment errors as well as differences in orbital perturbations between the VTDM satellites. Numerical simulations are shown to validate the performance of the proposed relative orbit and alignment control laws for the VTDM. The results satisfy mission requirements and indicate the general applicability of the control algorithm to the VT formation flying architecture. Consequently, the proposed methods of orbit design and control can be applied to inertial astrometric alignment and formation keeping for the many proposed dual spacecraft precision formation flying missions.

In order to ensure the success of the Mars exploration mission, it is necessary to accurately simulate the unique environment on the surface of Mars in a ground test and verify the effectiveness of the thermal control measures of the Mars rover. This paper proposes a thermal balance test method that can simultaneously simulate environmental factors such as Martian surface gas atmosphere, wind speed, pressure, solar radiation, and atmospheric temperature. This proposed test method meets the thermal design verification requirements of component-level products. Compared with similar large-scale facilities, the test cost is low, and the implementation efficiency is high. Furthermore, the influence of the Martian wind field on the surface temperature distribution of the product under both the Martian day and night environment was investigated using the proposed test method. The research results show that although the atmospheric pressure on the surface of Mars is much lower than the surface of the Earth, the Martian wind will still form forced convection heat transfer on the surface of the probe and its auxiliary products, which will affect the heat distribution of the products. In the thermal control design of the products, it is necessary to consider the impact of all the above environmental factors and carry out corresponding comprehensive environmental test verification.