This paper addresses the problem of autonomous scheduling of space objects' observations from a network of tracking stations to enhance the knowledge of their orbit while respecting allocated resources. This task requires the coupling of a state estimation routine and an optimisation algorithm. As for the former, a sequential filtering approach to estimate the satellite state distribution conditional on received indirect measurements has been employed. To generate candidates, i.e. observation campaigns, a Structured-Chromosome Genetic Algorithm optimiser has been developed, which is able to address the issue of handling mixed-discrete global optimisation problems with variable-size design space. The search algorithm bases its strategy on revised genetic operators that have been reformulated for handling hierarchical search spaces. The presented approach aims at supporting the space sector by tracking both operational satellites and non-collaborative space debris in response to the challenge of a constantly increasing population size in the near Earth environment. The potential of the presented methodology is shown by solving the optimisation of a tracking window schedule for a very low Earth satellite operating in a highly perturbed dynamical environment.
This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets.The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.
This paper presents a novel optimisation approach, called Structured-Chromosome Genetic Algorithm (SCGA), that addresses the issue of handling variable-size design space optimisation problems. This is based on variants of standard genetic operators able to handle structured search spaces. The potential of the presented methodology is shown by solving the problem of defining observation campaigns for tracking space objects from a network of tracking stations. The presented approach aims at supporting the space sector in response to the constantly increasing population size in the around-Earth environment. The test case consists in finding the observation scheduling that minimises the uncertainty in the final state estimation of a very low Earth satellite operating in a highly perturbed dynamical environment. This is evaluated by coupling the optimiser with an estimation routine based on a sequential filtering approach that estimates the satellite state distribution conditional on received indirect measurements. The solutions found by employing SCGA are finally compared to the ones achieved using more traditional approaches. Namely, the problem has been reformulated to be faced using standard Genetic Algorithm and another variable-size optimiser, the "Hidden-genes" Genetic Algorithm variant.
This paper presents a belief-based formulation and a novel approach for the robust solution of optimal control problems under uncertainty. The introduced formulation, based on the Belief Markov Decision Process model, reformulates the control problem directly in terms of uncertainty distributions, called beliefs, rather than on realisations of the system state. Successively, an approach inspired by navigation analysis is developed to transcribe and solve such problem in the presence of observation windows, employing a polynomial expansion for the dynamical propagation. Finally, the developed method is applied to the robust optimisation of a flyby trajectory of Europa Clipper mission in a scenario characterised by knowledge, execution and observation errors.
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