Time optimal attitude control for a rigid body

Abstract

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.

Fast Slew Maneuvers for the High-Torque-Wheels BIROS Satellite

“…Next, consider the spacecraft equipped with the n reaction wheels just introduced. Rotation matrices R 2 SOð3Þ, representing a linear transformation of vectors in body-fixed or 'hub' frame into the inertial frame, are preferred as the attitude parameterization since they are both global and unique, 23) where the configuration space or manifold of rotation matrices 21) is given by the special orthogonal group SOð3Þ with the conditions…”

“…The objective of time-optimal slew maneuver problems 20,21) consists on finding optimal wheel-motor torque commands ( w;i ði ¼ 1; . .…”

“…Some of these results have been experimentally validated for imaging satellites in-orbit. 20) Time-optimal reorientation solutions for rigid bodies have also been found using a geometric mechanics approach 21,22) together with indirect optimization. However, most of the work reported in literature does not consider time-optimal control solutions of spacecraft equipped with reaction wheels driven by independently constrained piecewise-constant sampled-time control inputs.…”

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

“…The angle of exclusion is determined by the sensor baffle and the source (considering its angular dimension and its intensity), and it is typically between 15 and 45 deg, depending on the sensitive optical sensor [15][16][17]. Several numerical methods, such as the randomized motion planning [18], the logarithmic barrier potentials [19], or the Lie group variational integrator [20], have been used to obtain the optimal solution.…”

Time optimal attitude control of 3D pendulum

“…Time optimal attitude control of a free rigid body using geometrically exact computations on SO(3) subjected to constraints on control input is studied in [7]. We extend this work to the case of a 3D pendulum in presence of uniform gravity providing a computational approach to find the optimal control.…”