Spacecraft Formation Optimization with a Multi-Impulse Design

Optimal formation and control of cooperative wheeled mobile robots

“…Therefore, r (i) e in Eq. (15) can be written as r (2) . Now, the desired trajectories of each robot x (i)…”

“…However, although the problem of formation control has been well studied, finding the best arrangement of robotic members has been less studied [14,15]. As a result, in this paper, this important issue is first addressed.…”

Optimal configuration of tetrahedral spacecraft formations

“…Since we are assuming a spherical Earth gravity model, during a coast phase the only equinoctial element that changes with time is the true longitude, L. In particular, during a coast phase the differential equation for the true longitude can be written as (4) Observing that all quantities except L in equation (4) are constant, we can separate variables in equation (4) to give (5) Integrating both sides of equation (5), we obtain (6) where are the initial and terminal time, respectively, of the coast phase while are the initial and terminal true longitude. Since all other states are constant during a coast phase (again, because we have assumed…”

“…Much of the work in this area focuses on various ways to formulate and solve an optimal control problem that either initializes or reconfigures the tetrahedral formation. In reference [4], a hierarchical strategy is compared to a particle swarm approach to find optimal tetrahedral reconfiguration trajectories. In a similar application [5], a search space reduction technique is used to solve the formation optimal control problem.…”

Autonomous Guidance & Control of Earth-Orbiting Formation Flying Spacecraft

“…Such examples are linear programming [51,35], multi-agent optimization techniques [57], particle swarm optimization [24], genetic algorithms [2] or optimal control theory [9,55]. These techniques use highly powerful numerical optimization algorithms to solve for the best maneuver to perform to reach a desired formation.…”