Time-optimal rendezvous for elliptic orbits

Time optimal rendezvous trajectories for variable thrust intercepting and orbiting space vehicle

Analysis of the partially filled viscous ring damper

A ring partially filled with a viscous fluid has been analyzed as a nutation damper for a spinning satellite. The fluid has been modelled as a rigid slug of finite length moving in a tube and resisted by a linear viscous force. It is shown that there are two distinct modes of motion, called the spin synchronous mode and the nutation synchronous mode. Time constants for each mode are obtained for both the symmetric and asymmetric satellite. The effects of a stop in the tube and an offset of the ring from the spin axis are also investigated. An analysis of test results is also given including a determination of the effect of gravity on the time constants in the two modes

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented

Orbit Determination of LEO Satellites for a Single Pass through a Radar: Comparison of Methods

The problem of determining the orbit of a space object from measurements based on one pass through the field of view of a radar is not a new one. Extensive research in this area has been carried out in the USA and Russia since the late 50s when these countries started the development of ballistic missile defense (BMD) and Early Warning systems. In Russia these investigations got additional stimulation in the early 60s after the decision to create a Space Surveillance System, whose primary task would be the maintenance of the satellite catalog. These problems were the focus of research interest until the middle 70s when the appropriate techniques and software were implemented for all radars. Then for more than 20 years no new research papers appeared on this subject. This produced an impression that all the problems of track determination based on one pass had been solved and there was no need for further research. In the late 90s interest in this problem arose again in relation to the following. It was estimated that there would be greater than 100,000 objects with size greater than 1-2 cm and collision of an operational spacecraft with any of these objects could have catastrophic results. Thus, for prevention of hazardous approaches and collisions with valuable spacecraft the existing satellite catalog should be extended by at least an order of magnitude This is a very difficult scientific and engineering task. One of the issues is the development of data fusion procedures and the software capable of maintaining such a huge catalog in near real time. The number of daily processed measurements (of all types, radar and optical) for such a system may constitute millions, thus increasing the number of measurements by at least an order of magnitude. Since we will have ten times more satellites and measurements the computer effort required for the correlation of measurements will be two orders of magnitude greater. This could create significant problems for processing data close to real time even for modern computers. Preliminary "compression" of data for one pass through the field of view of a sensor can significantly reduce the requirements to computers and data communication. This compression will occur when all the single measurements of the sensor are replaced by the orbit determined on their basis. The single measurement here means the radar parameters (range, azimuth, elevation, and in some cases range rate) measured by a single pulse

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions Based on a Bank of Norm-Inequality-Constrained Epoch-State Filters

Sequential probability ratio tests explicitly allow decision makers to incorporate false alarm and missed detection risks, and are potentially less sensitive to modeling errors than a procedure that relies solely on a probability of collision threshold. Recent work on constrained Kalman filtering has suggested an approach to formulating such a test for collision avoidance maneuver decisions: a filter bank with two norm-inequality-constrained epoch-state extended Kalman filters. One filter models 1he null hypothesis 1ha1 the miss distance is inside the combined hard body radius at the predicted time of closest approach, and one filter models the alternative hypothesis. The epoch-state filter developed for this method explicitly accounts for any process noise present in the system. The method appears to work well using a realistic example based on an upcoming highly-elliptical orbit formation flying mission

Spacecraft Formation Dynamics and Design

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76961/1/AIAA-13002-440.pd

Mitigation of the Impact of Sensing Noise on the Precise Formation Flying Control Problem

The specific objectives of this proposed research were: 1. Further investigation into the impact of CDGPS sensing errors for high Earth orbit missions. 2. Identify augmentation approaches of the CDGPS that will improve the relative state for low and high Earth orbit missions. 3. Integration of the navigation and control concepts into the GSFC Formation Flying Testbed. In addition this was a cooperative effort with Dr. Jonathan How at MIT. Dr. Alfriend was to spend two weeks working with Dr. How and his students. The travel for these two weeks was paid by the Texas Engineering Experiment Station (TEES) as cost sharing