Nonlinear control of multiple spacecraft formation flying using the constraint forces in Lagrangian systems

Abstract

Getting inspiration from the constraint forces in the classical mechanics, we presented the nonlinear control method of multiple spacecraft formation flying to accurately keep the desired formation arrays. Considering nonlinearity and perturbation, we changed the question of the formation array control to the Lagrange equations with the holonomic constraints and the differential algebraic equations (DAE), and developed the nonlinear control for design of the follower spacecraft tracking control laws by solving the DAE. Because of using the idea of the constraint forces, this approach can adequately utilize the characteristic of the dynamic equations, i.e., the space natural forces, and accurately keep the arbitrary formation array. Simulation results of the circular formation keeping with the linear and nonlinear dynamical equations were included to illuminate the control performance.satellite formation flying, array keeping, nonlinear control, Lagrangian systems, constraint forces

An analytical method for out-of-plane relative equilibrium formation using inter-spacecraft forces

“…Refs. [16,17] considered the spacecraft in a formation as linked by virtual joint, then the control force needed to precisely maintain an equilibrium configuration is turned into the constraint forces of each joint. Larsen et al [18] investigated the modeling of satellites coupled tightly using tethers, and used a topology description to automate the formulation of the general equations for the motion of each satellite in a formation.…”

Robust nonlinear control of spacecraft formation flying using constraint forces

“…In ref. [9], the constraint forces control method (CFCM) was presented to accurately keep the formation arrays. CFCM offers the potential for reducing the propellant cost because it makes full use of the characteristic of the formation dynamic equations and the array constraints.…”