Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Abstract

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Computational guidance for planetary powered descent using collaborative optimization

“…To validate the effectiveness of the CO-based computational guidance for the planetary powered descent, the iSIGHT® and MATLAB® environments are adopted to implement the numerical simulations and analyses. All [13,19,[20][21][22] is generated through formulating the optimal guidance problem as a finite-dimensional second-order cone programming problem, and solving it in polynomial time via currently available direct numerical algorithms. A global optimum can be efficiently obtained with deterministic stopping criteria and prescribed level of accuracy [20,22].…”

“…However, the LQR gains must be designed offline. Pinson [13] applied the convex optimization method to design an optimal propellant powered descent trajectory that can be quickly computed onboard. This algorithm can run autonomously once the dynamical model coefficients are determined.…”

Small Body Precision Landing via Convex Model Predictive Control

“…Remark III.1. Problem 1 is a non-convex problem due to (9). Convexifying this constraint is a main focus of this work.…”

“…More recently, small body operations have received similar attention. [2][3][4][5][6][7][8][9][10] A small body may be a comet, asteroid or small planetoid that exhibits a highly non-uniform gravitational field as compared to larger, more uniform bodies.…”

Solar-sail deep space trajectory optimization using successive convex programming

“…Numerical methods for solving the optimization problem are basically divided into two major classes as indirect methods and direct methods (Rao 2009). The indirect method requires the use of the maximum principle to derive the first order necessary conditions of the optimal solution, which leads to a two-point boundary value problem and can be solved numerically, such as shooting method (Pontryagin 1987). As summarized by Bryson et al (Bryson and Ho 1975), the main difficulty of this method is to find a first and accurate estimate of the initial unknown costate values that produces a solution reasonably close to the boundary conditions and first-order constraints, because the extremal solutions are often very sensitive to small changes of the initial constate values.…”