Initial Three-Dimensional Trajectory Design for Solar Sails Using Bezier Shaping Approach

Abstract

An approach for the fast generation of a minimum-time, three-dimensional trajectory for a spacecraft propelled by a solar sail with reflection control devices (RCDs) is presented using the authors' previously proposed Bezier curve-based shaping approach. In this approach, the time variation of the position components of the spacecraft are assumed in advance to follow Bezier curve functions. By optimizing a finite set of unknown coefficients defining the shape of the Bezier curves used to approximate the generic state variables, the boundary constraints and equations of motion are satisfied simultaneously under a timeoptimized performance index. Unlike the thrust vector of a conventional electric thruster, that of an RCDequipped solar sail is constrained. To consider the thrust characteristics of such solar sails, the propulsive acceleration inequality constraints were numerically investigated for an asteroid rendezvous. The simulation results demonstrate that the presented approach is able to design the transfer trajectory of a spacecraft propelled by an RCD-equipped solar sail in about 1% of the time required by the conventional Gauss pseudospectral method with comparable accuracy by considering the actual characteristics of the thrust vector. This allows for quick feasibility assessments of different solar sail spacecraft mission profiles during the preliminary mission design stage.INDEX TERMS Solar sail, reflection control devices, Bezier curve, shape-based method.

Shape-based approach for solar sail trajectory optimization

“…Very accurate solutions can instead be obtained using the procedure described in Ref. [16] or [17]. However, these methods are characterized by a high number of unknown variables that prevent the genetic algorithm from converging toward feasible solutions.…”

“…Indeed, the techniques of Ref. [16,17] make use of a nonlinear programming solver, and, as such, they require good starting points to find a local minimum solution. Moreover, the user is required to choose a suitable number of discretization points and Fourier series coefficients when dealing with the method of Ref.…”

“…[16], or the order of the Bezier curve function for the approach of Ref. [17], which may depend on the particular mission scenario. This implies a higher usercomputer interaction with respect to the proposed method.…”

“…Suitable constraints may be also enforced on the propulsive acceleration to get feasible trajectories. Other authors have also proposed to use finite Fourier series [15,16] or Bézier curves [17,18] to shape the spacecraft trajectory, or to use deep neural networks to estimate the transfer time [6]. The shape-based method has also been proved to be effective in producing good initial guesses to more complex and refined optimization techniques [19].…”

Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

“…Straight lines, constant slopes, and arcs are commonly seen components of a flight trajectory, representing different kinds of steady flight conditions. Between those segments are transition phases, where an appropriate smooth design is crucial for accurate trajectory following [1]- [3]. This paper addresses the sub-optimal, constrained, efficient, and smooth trajectory generation problem for these transition maneuvers.…”