Singular Control in Minimum Time Spacecraft Reorientation

Seywald, Hans; Kumar, Renjith R.

doi:10.2514/3.56607

Cited by 42 publications

(28 citation statements)

References 6 publications

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“…The proposed necessary conditions for optimality can be directly applied, without modification, to the case where the absolute value of each component of the control moment is bounded. In this case, the expressions for optimal singular control can be developed, for example, by following the approach given in [4], using the compact multiplier equations presented here.…”

Section: Discussionmentioning

confidence: 99%

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Time optimal attitude control for a rigid body

Lee¹,

Leok

McClamroch

2008

2008 American Control Conference

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Abstract-A time optimal control problem is studied for the attitude dynamics of a rigid body. The objective is to minimize the maneuver time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control input. Necessary conditions for optimality are developed directly on the special orthogonal group using rotation matrices. They completely avoid singularities associated with local parameterizations such as Euler angles, and they are expressed as compact vector equations. In addition, a discretetime control method based on a geometric numerical integrator, referred to as a Lie group variational integrator, is proposed to compute the optimal control input that respects the underlying geometric properties of the rigid body. The proposed method is demonstrated by a large-angle time optimal maneuver for an elliptic cylinder rigid body.

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Section: Discussionmentioning

confidence: 99%

“…It is known that the eigen-axis rotation is not generally time optimal [3], [4]. The attitude dynamics is often simplified in an optimality analysis, e.g., by assuming an inertially symmetric rigid body model [3], [4], [5], linearization [6] and constant magnitude angular velocity [5].…”

Section: Introductionmentioning

confidence: 99%

Time optimal attitude control for a rigid body

Lee¹,

Leok

McClamroch

2008

2008 American Control Conference

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“…References [5] and [6] considered the problem of time-optimal rest-to-rest This work has been supported in part by the ISRO-IITB Space Technology Cell, Indian Institute of Technology Bombay.…”

Section: Introductionmentioning

confidence: 99%

“…Both references showed that, contrary to expectation, an eigenaxis rotation in which the rigid body rotates about a bodyfixed axis, is not time optimal. While [5] used numerical techniques to arrive at this conclusion, [6] used the necessary conditions of optimal control to analyze the optimality of singular arcs of various finite and infinite orders. Other time-optimal reorientation problems considered in the literature include time-optimal maneuvers for spin stabilized symmetric spacecraft using magnetic actuation [7], and minimum-time reorientation of axisymmetric spacecraft using two independent bounded control torques perpendicular to the symmetry axis [8].…”

Section: Introductionmentioning

confidence: 99%

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Time-Optimal Attitude Reorientation at Constant Angular Velocity Magnitude with Bounded Angular Acceleration

Modgalya¹,

Bhat

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-This paper considers the problem of steering the orientation of an inertially symmetric rigid body of unit moment of inertia from an initial attitude and nonzero angular velocity to a specified terminal attitude in minimum time under an upper limit on the magnitude of angular acceleration with the magnitude of the angular velocity constrained to remain constant. Optimal control theory is used to show that singular optimal arcs are uniform eigenaxis rotations in which the body rotates at a uniform rate about a body-fixed axis, while nonsingular arcs are coning motions in which the body angular velocity vector rotates at a uniform rate about a body-fixed axis. Symmetries of the problem are exploited to further show that every optimal trajectory consists of at most one coning motion followed either by one uniform eigenaxis rotation or several coning motions of equal duration.

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

2014

Optim. Control Appl. Meth.

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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.

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Singular Control in Minimum Time Spacecraft Reorientation

Cited by 42 publications

References 6 publications

Time optimal attitude control for a rigid body

Time optimal attitude control for a rigid body

Time-Optimal Attitude Reorientation at Constant Angular Velocity Magnitude with Bounded Angular Acceleration

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

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