B-plane and Picard–Chebyshev integration method: Surfing complex orbital perturbations in interplanetary multi-flyby trajectories

GPU-based high-precision orbital propagation of large sets of initial conditions through Picard–Chebyshev augmentation

“…The test case follows what already computed in [12,13]. The first resonant phase with Venus of a Solar Orbiter-like mission was reproduced, designing a continuous trajectory even during flyby injections and exits.…”

“…designing flyby 𝑗 + 1 before flyby 𝑗, to preserve accuracy and continuity while also fulfilling mission requirements. The reader can find more insight on the design algorithm and technique in [12,13]. The Matlab ® * * implementation proposed in [12,13] was re-run on a single core of a local workstation equipped with an Intel ® Core TM i7-7700 CPU (3.60 GHz), running Windows ® 10 Pro.…”

“…The reader can find more insight on the design algorithm and technique in [12,13]. The Matlab ® * * implementation proposed in [12,13] was re-run on a single core of a local workstation equipped with an Intel ® Core TM i7-7700 CPU (3.60 GHz), running Windows ® 10 Pro. The algorithm converged running 13509 PC integrations in 506.3 seconds, to the residual Δr * and impulsive action Δv * for the required maneuver presented in Table 1.…”

“…Recent developments [10] nearly halved the required computational time by implementing the Kustaanheimo-Stiefel [11] formulation of the dynamical motion. This work takes inspiration from the results obtained in [12,13], whose aim was to optimize a multi-flyby trajectory arc while taking advantage of the natural dynamics of the N-body relativistic environment. Despite the conceptual complexity, the combined b-plane and Picard-Chebyshev (PC) approach led to an overall computationally feasible algorithm, for a Matlab ® sequential implementation converging to an optimal trajectory in a few minutes only.…”

“…Differently from the previous developments of the method, this work introduces an augmentation of the dynamical system being integrated to enable stable massive parallelism for the short-term propagation of large sets of initial conditions. The results obtained in [12,13], as all the simulated trajectories analyzed to find the optimal one, are re-run as a direct application of the proposed approach, discussing the parallelization options in deep detail. Within a single run, the common time nodes of all the trajectory arcs allow to rework the iterative refinement process of PC.…”