OCULUS - A unified visual solver for Optimal Control Problems via indirect methods

Indirect Methods (IMs) for solving Optimal Control Problems (OCPs) are computationally efficient but often require human intervention to initiate the optimization process. One of the primary challenges in using IMs, regardless of the problem being solved, is selecting appropriate initial costates. Indeed, the advantage of a highly efficient computational tool comes at the cost of these methods being extremely sensitive to initial guesses. OCULUS (Optimal Control with User-friendly Layout Unified Solver) addresses this issue by quasi-automating the initialization process and providing an interactive interface that streamlines the solution of single-and multiple-point boundary value problems. OCULUS is a versatile visualizer and solver capable of handling any indirect optimal control problem where the dynamical model features either autonomous bang-bang control (where control switches based on the sign of the switching function) or predefined switching decision arcs. A major drawback of traditional IM implementations is the trade-off between computational efficiency and user-friendliness. Codes relying on compiled languages like Fortran or C++ offer high performance but lack intuitive visualization, while Python and MATLAB provide better visualization but suffer from slow computational speed. OCULUS bridges this gap by allowing users to integrate compiled dynamic files while maintaining real-time visualization capabilities within a dynamically updated GUI that adapts to user-defined setups. Users can adjust costates between integration steps, apply differential corrections incrementally, and refine parameters manually before resuming optimization. OCULUS has already demonstrated its effectiveness in academia. Students using the solver for their thesis research have reduced problem setup time from several months to just a few weeks, eliminating the need for repeated manual iterations in the early stages of learning the subject. Moreover, OCULUS features an automatically populated database that stores previously converged solutions, enabling interpolation-based or neighboring initial guesses for new boundary conditions once at least one previous solution has been found. Users can select different integration methods based on precision, speed, and robustness requirements and fine-tune the finite-difference method with user-defined sensitivity thresholds. By automating critical aspects of IMs and providing an interactive, adaptable environment, OCULUS makes solving complex optimal control problems more accessible. It allows researchers and engineers to focus on problem formulation and analysis rather than struggling with initialization and convergence challenges (however instructive those challenges may be). The presented work includes an Earth-Moon n-body transfer case study, illustrating the solver's capabilities.