Orbit Design for Ground Surveillance Using Genetic Algorithms

Abstract

T HE orbits of remote sensing systems usually dictate the ground resolution, area coverage, and frequency of coverage parameters. Lower altitude orbits enable a spacecraft to provide higher resolution measurements, but orbital perturbations are nonnegligible due to atmospheric drag [1]. Electric propulsion systems can be used to compensate for atmospheric drag [2]. However, low altitude orbits lack wide coverage. Strategies to overcome the lack of coverage, by maneuvering the spacecraft using electric propulsion, were proposed in the literature [3]. In this case, the thrusters are not only used to compensate the perturbations, but are also used to continuously maneuver the spacecraft to achieve given coverage requirements over a given set of sites in a given time frame. One example is to visit a set of 20 sites within a time frame tf of 50 days. However, this solution complicates the satellite system. The motivation then is to find a lower cost solution for this kind of mission. This note proposes a new solution in which the spacecraft is placed in a natural orbit such that it visits all the sites within the time frame without maneuvering. An advantage is the short time for visiting all sites. Performing continuous thrust transfers to maneuver the satellite from one site to another often takes more time. The disadvantage is that some sites may not be visited accurately. A tradeoff between the accuracy and the revisit time for all the sites is needed when planning a mission. To find this natural orbit, we use a genetic algorithm (GA) to perform a directed search among all possible orbits. Implementing a genetic algorithm does not guarantee an optimal orbit, however, it has been shown that in subsequent iterations, better solutions will be sampled at exponentially increasing rates [4]. This issue will be discussed in the section titled Genetic Algorithms. GAs have been adopted in the literature to solve several orbital mechanics problems. We chose to solve the ground surveillance problem using genetic algorithms because this problem is characterized by many local minima. Conventional optimization methods (e.g., gradient methods) are not suitable for this kind of problem. GAs use random choice as a tool to guide a highly exploitative search in the design space [5]. Enumerated methods scan the whole domain andfind the optimal solution. Enumeratedmethods can provide good solutions to the problem.However, the efficiency of these algorithms is very low compared with genetic algorithms [5]. TheGA solution is used as a starting point to find a local minimum solution through traditional optimization methodologies. The final solution will be a local minimum in the neighborhood of the GA solution. Two types of constraints are considered. Thefirstmission searches for maximum resolution for each site for a given imaging sensor. The second mission tries to maximize the observation time.