An Analytical Solution to the Problem of Optimal Control of the Reorientation of a Rigid Body (Spacecraft) Using Quaternions

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

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Optimal Control of Fuzzy Systems with Application to Rigid Body Attitude Control

Aerospace Engineering ◽

10.5772/intechopen.82181 ◽

2019 ◽

Author(s):

Yonmook Park

Keyword(s):

Optimal Control ◽

Rigid Body ◽

Attitude Control ◽

Fuzzy Systems ◽

Body Attitude

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Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics

Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2007-34574 ◽

2007 ◽

Cited By ~ 10

Author(s):

Sigrid Leyendecker ◽

Sina Ober-Blo¨baum ◽

Jerrold E. Marsden ◽

Michael Ortiz

Keyword(s):

Optimal Control ◽

Rigid Body ◽

Null Space ◽

Numerical Dissipation ◽

Discrete Version ◽

Dynamical Equations ◽

Time Stepping ◽

Minimal Dimension ◽

Energy And Momentum ◽

External Forces

This paper formulates the dynamical equations of mechanics subject to holonomic constraints in terms of the states and controls using a constrained version of the Lagrange-d’Alembert principle. Based on a discrete version of this principle, a structure preserving time-stepping scheme is derived. It is shown that this respect for the mechanical structure (such as a reliable computation of the energy and momentum budget, without numerical dissipation) is retained when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced time-stepping equations serve as nonlinear equality constraints for the minimisation of a given cost functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. The resulting discrete optimal control algorithm is shown to have excellent energy and momentum properties, which are illustrated by two specific examples, namely reorientation and repositioning of a rigid body subject to external forces and the reorientation of a rigid body with internal momentum wheels.

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