Christopher D'Souza

High-Accuracy Trajectory Optimization for a Trans-Earth Lunar Mission

The trajectory optimization of a spacecraft subject to the gravitational effects of the moon, Earth, and sun are considered. The problem is how to achieve Earth-interface conditions from a low lunar orbit. Practical constraints of maximum thrust, fuel budget, and flight time generates a constrained, nonautonomous, nonlinear optimal control problem. Severe constraints on the fuel budget combined with high-accuracy demands on the endpoint conditions necessitate a high-accuracy solution to the trajectory optimization problem. The problem is first solved using the standard Legendre pseudospectral method. The optimality of the solution is verified by an application of the covector mapping principle. It is shown that the thrust structure consists of three finite burns with nearly linear steering-angle time histories. A singular arc is detected and is interpreted as a singular plane change maneuver. The Bellman pseudospectral method is then employed for mesh refinement to improve the accuracy of the solution.

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASAs next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test flight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to show the efforts made to-date in tuning the filter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. Filter performance is affected by many factors: data rates, sensor measurement errors, tuning, and others. This paper focuses mainly on the error characterization and tuning portion. Traditional efforts at tuning a navigation filter have centered around the observation/measurement noise and Gaussian process noise of the Extended Kalman Filter. While the Orion MODE team must certainly address those factors, the team is also looking at residual edit thresholds and measurement underweighting as tuning tools. Tuning analysis is presented with open loop Monte-Carlo simulation results showing statistical errors bounded by the 3-sigma filter uncertainty covariance. The Orion filter design uses 24 Exponentially Correlated Random Variable (ECRV) parameters to estimate the accel/gyro misalignment and nonorthogonality. By design, the time constant and noise terms of these ECRV parameters were set to manufacturer specifications and not used as tuning parameters. They are included in the filter as a more analytically correct method of modeling uncertainties than ad-hoc tuning of the process noise. Tuning is explored for the powered-flight ascent phase, where measurements are scarce and unmodelled vehicle accelerations dominate. On orbit, there are important trade-off cases between process and measurement noise. On entry, there are considerations about trading performance accuracy for robustness. Process Noise is divided into powered flight and coasting ight and can be adjusted for each phase and mode of the Orion EFT-1 mission. Measurement noise is used for the integrated velocity measurements during pad alignment. It is also used for Global Positioning System (GPS) pseudorange and delta- range measurements during the rest of the flight. The robustness effort has been focused on maintaining filter convergence and performance in the presence of unmodeled error sources. These include unmodeled forces on the vehicle and uncorrected errors on the sensor measurements. Orion uses a single-frequency, non-keyed GPS receiver, so the effects due to signal distortion in Earths ionosphere and troposphere are present in the raw measurements. Results are presented showing the efforts to compensate for these errors as well as characterize the residual effect for measurement noise tuning. Another robustness tool in use is tuning the residual edit thresholds. The trade-off between noise tuning and edit thresholds is explored in the context of robustness to errors in dynamics models and sensor measurements. Measurement underweighting is also presented as a method of additional robustness when processing highly accurate measurements in the presence of large filter uncertainties.

Orion Absolute Navigation System Progress and Challenges

The absolute navigation design of NASA’s Orion vehicle is described. It has undergone several iterations and modications since its inception, and continues as a work-in-progress. This paper seeks to benchmark the current state of the design and some of the rationale and analysis behind it. There are specic challenges to address when preparing a timely and eective design for the Exploration Flight Test (EFT-1), while still looking ahead and providing software extensibility for future exploration missions. The primary onboard measurements in a Near-Earth or Mid-Earth environment consist of GPS pseudorange and deltarange, but for future explorations missions the use of star-tracker and optical navigation sources need to be considered. Discussions are presented for state size and composition, processing techniques, and consider states. A presentation is given for the processing technique using the computationally stable and robust UDU formulation with an Agee-Turner Rank-One update. This allows for computational savings when dealing with many parameters which are modeled as slowly varying Gauss-Markov processes. Preliminary analysis shows up to a 50% reduction in computation versus a more traditional formulation. Several state elements are discussed and evaluated, including position, velocity, attitude, clock bias/drift, and GPS measurement biases in addition to bias, scale factor, misalignment, and non-orthogonalities of the accelerometers and gyroscopes. Another consideration is the initialization of the EKF in various scenarios. Scenarios such as single-event upset, ground command, and cold start are discussed as are strategies for whole and partial state updates as well as covariance considerations. Strategies are given for dealing with latent measurements and high-rate propagation using multi-rate architecture. The details of the rate groups and the data ow between the elements is discussed and evaluated.

High-Accuracy Moon to Earth Escape Trajectory Optimization

The trajectory optimization of a spacecraft is considered in the gravitational effects of the Moon, Earth, and Sun in the paper. Imposing practical constraints of maximum thrust, fuel budget, and flight time generates a constrained, non-autonomous, nonlinear optimal control problem. Severe constraints on the fuel budget combined with high accuracy demands on the endpoint conditions necessitates a high-accuracy solution to the trajectory optimization problem. The problem is first solved using the standard Legendre pseudospectral method. The optimality of the solution is verified by an application of the Covector Mapping Principle. It is shown that the thrust structure consists of three finite burns with nearly linear steering-angle time histories. A singular arc is detected and is interpreted as a singular plane-change maneuver. The Bellman pseudospectral method is then employed to improve the accuracy of the solution.

Orion Optical Navigation Progress Toward Exploration: Mission 1

Optical navigation of human spacecraft was proposed on Gemini and implemented successfully on Apollo as a means of autonomously operating the vehicle in the event of lost communication with controllers on Earth. The Orion emergency return system utilizing optical navigation has matured in design over the last several years, and is currently undergoing the final implementation and test phase in preparation for Exploration Mission 1 (EM-1) in 2019. The software development is past its Critical Design Review, and is progressing through test and certification for human rating. The filter architecture uses a square-root-free UDU covariance factorization. Linear Covariance Analysis (LinCov) was used to analyze the measurement models and the measurement error models on a representative EM-1 trajectory. The Orion EM-1 flight camera was calibrated at the Johnson Space Center (JSC) electro-optics lab. To permanently stake the focal length of the camera a 500 mm focal length refractive collimator was used. Two Engineering Design Unit (EDU) cameras and an EDU star tracker were used for a live-sky test in Denver. In-space imagery with high-fidelity truth metadata is rare so these live-sky tests provide one of the closest real-world analogs to operational use. A hardware-in-the-loop test rig was developed in the Johnson Space Center Electro-Optics Lab to exercise the OpNav system prior to integrated testing on the Orion vehicle. The software is verified with synthetic images. Several hundred off-nominal images are also used to analyze robustness and fault detection in the software. These include effects such as stray light, excess radiation damage, and specular reflections, and are used to help verify the tuning parameters chosen for the algorithms such as earth atmosphere bias, minimum pixel intensity, and star detection thresholds.

Absolute Navigation Performance of the Orion Exploration Fight Test 1

Launched in December 2014 atop a Delta IV Heavy from the Kennedy Space Center, the Orion vehicle’s Exploration Flight Test 1 successfully completed the objective to stress the system by placing the uncrewed vehicle on a high-energy parabolic trajectory, replicating conditions similar to those that would be experienced when returning from an asteroid or a lunar mission. Unique challenges associated with designing the navigation system for Exploration Flight Test 1 are presented with an emphasis on how redundancy and robustness influenced the architecture. Two inertial measurement units, one GPS receiver, and three barometric altimeters comprise the navigation sensor suite. The sensor data are multiplexed, using conventional integration techniques, and the state estimate is refined by the GPS pseudo- and delta-range measurements in an extended Kalman filter that employs UDU factorization. The performance of the navigation system during flight is presented to substantiate the design.