Experimental Implementation of Riemann–Stieltjes Optimal Control for Agile Imaging Satellites

Scaling and Balancing for High-Performance Computation of Optimal Controls

“…To validate the extremality of the feasible solution, we use (41) and (22) to descale the adjoint covectors and the evolution of the Hamiltonian respectively. The results are shown in Fig.…”

A simple approach for predicting time-optimal slew capability

“…The solution to the optimal control problem are the reaction wheel torque trajectories, τ j ðtÞ, that minimize the cost function subject to the dynamic constraints and boundary conditions of problem Bðx o ; x f Þ in (12). Solutions to the optimal control problem in (12) are called shortest time maneuvers (STMs) [9] and can be obtained using a Legendre pseudospectral method [11].…”

“…For each nominal axis, various maneuver lengths: 11 to 121 in three degree increments followed by 151 to 901 in five degree increments, were solved using (12). The variability in slew times for each maneuver size, θ are denoted by the error bars in Fig.…”

“…The optimal control equivalent sphere, therefore, is simply used to represent the volume of a sphere that is equal to the volume of the agility envelope. While the optimal control equivalent sphere can be used to predict the benefits of optimal control without solving an optimal control problem, it is necessary to solve problem (12) in order to design maneuvers for flight implementation.…”

“…The first time-optimal attitude maneuvers performed on orbit were implemented as part of a series of attitude control experiments conducted on the NASA Transition Region and Coronal Explorer (TRACE) in August 2010 [9,10]. Successful ground tests of the concept for agile spacecraft actuated by control moment gyroscopes have also been performed at Honeywell [11,12]. The sum of these results showed that reductions in slew times greater than 50 percent are possible as compared with conventional maneuvers.…”