## 6 Optimization Technique (ipopt)  
The optimization of the trajectories constituted a core purpose of this paper and a major portion of this research. Self-organizing satellites (autonomous) are proposed to be self-optimizing in-orbit as well to make sure the travel path is selected adequately and as quickly as possible for the real-time application of disaster management globally. There are several optimizing techniques implemented for individual satellites and in constellations in recent times [14; 15]. However, the purpose of the constellation optimization in this paper was to confront the perturbations and abnormalities in severe space environment and several unknown objects (Debris) and smoothen the trajectories under extremely non-linear conditions to perform and analyze real-time scenarios. For this research, several scenarios and possibilities were considered, and a non-linear optimizer was proposed to analyze its effectiveness for small satellite constellation operating in a Low-Earth Orbit. The Interior Point Optimizer (ipopt) is an optimization technique used for various purposes in the past and has served optimization needs over years. However, for this particular constellation scenario, this optimizer is being tested and aligned to the major parameters of the orbital dynamics to precisely know the best objective and coverage function possible for the given set-up in Section 3 of this paper. With regard to the orbit elements, the semi-major axis and inclination (as discussed earlier) remain as major orbital parameters to define the objection function and deliver the best solution for a full coverage scenario through a coverage function defined. This provides the fastest travel period possible to reach the nearest ground station with the longest pass feasible, resulting in the most optimal solution for a satellite or a plane to change its elements autonomously and deliver data at the quickest possible rate. The configuration proposed is shown pictorially in the flow diagram as presented by Figure 14 and was researched and analyzed for its importance to orbit. Given the constraints associated with small satellites, there is an absolute necessity to align autonomy with a significant approach and well-defined technique. The continuous propagation checks and its related anomalies were given a priority, and it is important to make sure that the orbital parameters are being maintained as designed for their particular position in the proposed constellation. After this, utilizing the techniques mentioned in Section 5, the nearest available ground stations were tracked and data in a 'long and full pass' was delivered with an optimized orbit and this was made continuous until the end of the lifecycle of the given constellation. This achieved paced and seamless data tracking from each ground station. A thorough study was executed to understand and implement this optimizer effectively in all portions of constellation and its planes. The Interior Point Optimizer (ipopt) is a software suite for large-scale nonlinear that finds best solutions locally which may or may not be the global optimal solutions. The form of this optimizer can be simply given as:  
\[ \begin{split}&\min_{x\in R^{n}}(f(x))\\ & s.t.\big{\{}g^{L}\leq g(x)\leq g^{U},x^{L}\leq x\leq x^{U}\big{\}} \end{split}  \tag{17}\]  
where \(x\in R^{n}\) are the optimization variables with lower and upper bounds of negative and positive infinities with \(x^{L}\leq x^{U}\), \(f:R^{n}\to R,g:R^{n}\to R\) are the objective and general nonlinear constraints respectively. Similarly, the \(f(x)\) and \(g(x)\) were used as nonlinear and non-convex in nature for this problem of constellation optimization. The \(g(x)\) also has the lower and upper bounds to negative and positive infinity as well with \(g^{L}\leq g^{U}\) and the equality constraint of the form \(g_{i}(x)=\overline{g}_{i}\) by making arrangement with \(g^{L}_{i}=g^{U}_{i}=\overline{g}_{i}\), respectively.