RESUMO
Repointing maneuvers of a spacecraft in staring mode are investigated where the optical axis is required to align with the target orientation. Different from traditional three-axis reorientation maneuvers, the rotation about the optical axis is free of constraints for repointing maneuvers. Both static target observation and moving target detection constraints are considered. The problem is then formulated as a finite-time horizon optimal control problem with nonlinear terminal constraints. A simple and efficient state-dependent Riccati equation(SDRE) based dynamic programming approach is applied to tackle this nonlinear optimal control problem. The convergence of the attitude from initial conditions to the desired terminal constraint is rigorously proved for the first time. Considering the inability of the SDRE method to deal with the problem of large angle maneuvers, an improved SDRE approach combined with a waypoint is proposed to enhance control performance. Finally, numerical investigations are conducted and compared with the real optimal solutions obtained by using the optimization software.
RESUMO
In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function, which can be set to induce a stationary swarm, a rotating swarm with uniform translation, and a rotating swarm with a stationary center of mass. An analysis of the mean field equations shows that without a spring potential the motion of the center of mass is determined explicitly by a multivalued function. For a nonzero spring potential the swarm converges to a vortex formation about a stationary center of mass, except at discrete bifurcation points where the center of mass will periodically trace an ellipse. The analytical results defining the behavior of the center of mass are shown to correspond with the numerical swarm simulations.
