ESA GNC Conference Papers Repository

Fast Sequential Convex Programming with Relaxed Convergence Criteria
Alexander Popov, Cristiano Contini, Mattia Zamaro
Presented at:
Sopot 2023
Full paper:

The growing interest in lunar exploration demands the development of spacecraft which can land autonomously on the MoonÂ’s surface. Typically, such missions define an ellipse around some selected landing point and any location within this ellipse is deemed acceptable for touchdown. To ensure a safe landing, a spacecraft can employ a hazard detection and avoidance (HDA) system, capable of identifying potential dangers at the target and triggering diversion to another point within the ellipse. The choice of landing site for a mission is a compromise between scientific priorities and landing safety. However, many scientific sites of interest may not be well-suited to landers as there may be hazards, such as craters or rocks, which greatly limit the size of a potential landing ellipse. To enable a broader range of missions, a lander should be capable of diverting to a new target at relatively low altitude and efficiently reaching the target with pinpoint accuracy. This would not only make it possible to reduce the minimum landing ellipse size for a given vehicle design, but it would also allow for a relaxation of the surface hazard requirements within the chosen ellipse. If this can be achieved, then a much more versatile set of lunar landing sites can be considered, prioritising scientific needs over engineering limitations. Fast and accurate retargeting demands a sophisticated guidance algorithm which can rapidly compute a trajectory to a new point. This paper presents progress on such an algorithm, which solves a trajectory optimisation problem to achieve fuel-optimal pinpoint landing. To enable late diversion, this algorithm must be able to run on board the spacecraft in real time, and so our research has focused on the use of fast, resource-efficient methods based on sequential convex programming. We recommend two related strategies which can enable fast termination of sequential convex programming algorithms: Hermite interpolation to extract a continuous-time state trajectory from the convex solver, and mesh refinement to enable efficient convergence towards an accurate solution. In combination, these techniques can ensure that the algorithm terminates after only a few iterations, using relatively relaxed stopping criteria, while still producing a feasible solution which can exactly satisfy terminal equality constraints. The benefits of this framework are demonstrated using the case study of guidance for an autonomous lunar lander with a complete model of the system dynamics in six degrees of freedom.