Reliability-Based Soft Landing Trajectory Optimization near Asteroid with Uncertain Gravitational Field

Abstract

This paper investigates a reliability-based trajectory optimization method for the design of soft landing trajectory on an irregular shape asteroid with highly uncertain gravitational field. First, the gravitational field of the irregular asteroid is described by the finite particle model. Second, to avoid the singularity and reduce the sensitivity, the original finite particle model is modified to an "N-body/two-body" switching dynamic model. The trajectory optimization problem in the switching dynamic model is summarized as an optimal control problem and is then transformed into a two-point boundary value problem by Pontryagin's maximum principle. By solving the two-point boundary value problem with a homotopic continuation procedure, the nominal optimal trajectory is obtained. Third, the uncertainty caused by the nonuniform mass distribution of the asteroid is considered. With high uncertainty, the deterministic optimal control problem becomes a parameter optimization problem with reliability constraints. This problem is then solved by a sequential optimization and reliability assessment, and the parallel computation technique is adopted. Finally, two soft landing trajectories are optimized using the proposed method to demonstrate the effectiveness of the technique.Article in Advance / REN AND SHAN Downloaded by CARLETON UNIVERSITY LIBRARY on July 28, 2015 | http://arc.aiaa.org |

The significance and related technologies of asteroid detection

“…Lantoine et al [89] proposed a combination of direct and indirect methods to ensure the accuracy and reduce the solution time; Gao et al [90] improved the overall performance of the navigation control system by optimizing the landing trajectory to ensure the observability of the system state; Hu et al [91][92] proposed a small object attachment trajectory anti-difference optimization method to reduce the trajectory tracking error while optimizing the fuel consumption; Ren et al [93] improved the reliability of the optimization results by considering the uncertainty of the small object mass distribution in the attachment trajectory optimization problem based on the reliability theory. In terms of explicit feedback guidance, Hawkins et al [94] designed an autonomous asteroid attachment feedback guidance method based on zero-controlled displacement deviation/zero-controlled velocity deviation with reference to Earth re-entry guidance; Furfaro et al [95] proposed a multi-slip mode surface descent guidance method based on higher-order sliding mode control theory with good robustness to bounded unmodeled upturns.…”

Trajectory Optimization for Asteroid Landing Considering Gravitational Orbit-Attitude Coupling

“…The shooting methods are gradient-based algorithms [4], meaning it is extremely sensitive to the smoothness of the shooting function. However, according to (28) and (30), the optimal control law for u o is of a bang-bang control type, and the optimal control law for u a cannot guarantee the smoothness due to its ''ρ a = 0'' case, either.…”

Neural-network-based real-time trajectory replanning for Mars entry guidance

“…The density is estimated by where ρ 0 is the density on the surface of Mars, r 0 is the mean radius of Mars, h s is the constant scale height and κ , which lies in [−0.3, 0.3], is used to denote the uncertainty of the atmospheric density. 21…”