Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each subproblem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft, and mixed boundary conditions are handled. The presented method is a modified version of an algorithm known as "approximating sequence of Riccati equations." Sample problems in astrodynamics are treated to show the effectiveness of the method, whose limitations are also discussed

Comparative Assessment Of Different Constellation Geometries For Space-Based Application

As services from space are becoming an asset for life on Earth and the demand for data from space increases, the international interest in satellite constellations is increasingly growing. GPS (Global Positioning System) provides positioning and navigation. Iridium contains a relatively larger number of satellites for communication purpose. Molniya is a high elliptical orbits constellation providing high latitude coverage. Disaster Monitoring constellation consists of remote sensing satellites and brings responsiveness needed for emergencies. Recently, some companies, such as OneWeb, Samsung and Space-X, have made public their plan to deploy mega constellations of nanosatellites for global internet. Different constellation geometries have been proposed to meet various mission requirements, each one having specific advantages in terms of coverage, responsiveness, cost, etc. Thus, designing a constellation is a trade-off choice. The choice for a constellation is highly influenced by many factors, such as the system cost, the interaction with space environment (radiation and space debris), and the targeted terrestrial coverage. The design of a constellation requires selecting the parameters that best meet the mission requirements. To accomplish this, several studies on the comparison of satellite constellations proposed detailed analysis, e.g. the multi-criteria comparison for responsive constellations, the coverage assessment of elliptical constellations. However, most of them only focused on one or few performances, lacking of generalisation. A general study of constellation geometry can provide a basis for understanding the constellation design. This will allow the process of constellation design to be expedited by offering a proposal of an existing constellation style. This paper comparatively assesses different constellation geometries, including the classical proposed geometries and some less used configurations, and chooses the constellation geometry best suitable for a given mission (e.g. remote sensing, global internet). In this work, several parameters of constellation design will be considered to make a quantitative assessment: coverage (global or local), frequency of ground track repetition, responsiveness (i.e., how fast a satellite can be launched and the data return to Earth after launch), robustness to failure and speed of replenishment, end of life disposal, number of satellites and orbital altitude. The assessment will be conducted in a parametric approach. Each factor will be quantitatively evaluated by deriving a fitness function. Then, a series of weighting coefficients adapted to the given mission requirements will be chosen for the global fitness functions. Through multi objective optimisation, the constellation geometry best suitable for the given mission requirements will be derived

Collision avoidance maneuver design based on multi-objective optimization

The possibility of having collision between a satellite and a space debris or another satellite is becoming frequent. The amount of propellant is directly related to a satellite’s operational lifetime and revenue. Thus, collision avoidance maneuvers should be performed in the most efficient and effective manner possible. In this work the problem is formulated as a multi-objective optimization. The first objective is the Δv, whereas the second and third one are the collision probability and relative distance between the satellite and the threatening object in a given time window after the maneuver. This is to take into account that multiple conjunctions might occur in the short-term. This is particularly true for the GEO regime, where close conjunction between a pair of object can occur approximately every 12h for a few days. Thus, a CAM can in principle reduce the collision probability for one event, but significantly increase it for others. Another objective function is then added to manage mission constraint. To evaluate the objective function, the TLE are propagated with SGP4/SDP4 to the current time of the maneuver, then the Δv is applied. This allow to compute the corresponding “modified” TLE after the maneuver and identify (in a given time window after the CAM) all the relative minima of the squared distance between the spacecraft and the approaching object, by solving a global optimization problem rigorously by means of the verified global optimizer COSY-GO. Finally the collision probability for the sieved encounters can be computed. A Multi-Objective Particle Swarm Optimizer is used to compute the set of Pareto optimal solutions.The method has been applied to two test cases, one that considers a conjunction in GEO and another in LEO. Results show that, in particular for the GEO case, considering all the possible conjunctions after one week of the execution of a CAM can prevent the occurrence of new close encounters in the short-term