Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach

Abstract

Summary This paper proposes a robust algorithm for time‐optimal rigid spacecraft reorientation trajectory generation. Based on the Pontryagin's maximum principle, the first‐order necessary optimality conditions are derived. These optimality conditions are numerically satisfied by adopting a pseudospectral method integrated homotopic approach to solve the associated shooting functions. First, the energy‐optimal reorientation solution is obtained using the Radau pseudospectral method, which has a spectral convergence speed and can give a precise estimation of the initial costates used to start the homotopic approach. Then, a modified homotopy scheme is given to deform the associated energy‐optimal solution to the desired time‐optimal solution continuously. Finally, for the inertially symmetric spacecraft reorientation problem, the newly found time‐optimal solutions are presented. The performance of the algorithm is illustrated by simulating a general asymmetric rigid spacecraft time‐optimal reorientation problem. Copyright © 2014 John Wiley & Sons, Ltd.

Analysis of the inertially symmetric rigid spacecraft time‐optimal three‐axis reorientation

“…In this paper, the kinematic equations are modeled using the modified Rodrigues parameter (MRP) vector, which is parameterized as where e 1 , e 2 , and e 3 are the components of the Euler vector (eigenaxis) and ϕ is the rotation angle. Reasons for choosing MRP vector for the kinematic description are given in . The time evolution of the MPR vector derived from yields Denoting , the matrix B in satisfies …”

“…This paper tries to give a detailed analysis of the rest‐to‐rest time‐optimal three‐axis reorientation for the inertially symmetric (cubical or spherical) rigid spacecraft, which is particularly motivated by the results obtained in . Bilimoria and Wie found five‐switch and seven‐switch time‐optimal solutions for rotation angles on the intervals [73,180] deg and [1,72] deg, respectively.…”

“…Numerical results shown that, for the same rotation angle, reorientation time of the six‐switch time‐optimal solution is relatively shorter than the seven‐switch time‐optimal solution. Li and Xi proposed a Radau pseudospectral method (RPM) integrated homotopic approach to obtain the time‐optimal solutions. Numerical results indicated the existence of six‐switch time‐optimal solutions for rotation angles on the interval [73,164] deg.…”

“…Numerical results indicated the existence of six‐switch time‐optimal solutions for rotation angles on the interval [73,164] deg. More importantly, it has been observed in that the switching times and control torques for the five‐switch and six‐switch time‐optimal solutions assuming certain symmetric property. In this paper, by re‐optimizing the seven‐switch time‐optimal solutions given in , it would be shown that switching times and control torques of the seven‐switch time‐optimal solutions are also symmetric.…”

Particle Swarm Optimization for Time-Optimal Spacecraft Reorientation with Keep-Out Cones

“…The minimum time reorientation maneuver of a rigid spacecraft is a well-known problem; the first related work regarding a numerical approach dates back to the 1990s [1][2][3][4]. These papers have been used as a reference providing some test cases for successive works as in [5][6][7]; the research still focuses on this problem with several approaches, for example, through homotopic approach algorithms [8], pseudospectral optimization analysis [9,10], or with hybrid numerical techniques [11].…”