Flatness-based control in successive loops for free-floating space robotic manipulators

Abstract

Free-floating space robotic manipulators are robotic arms mounted on space platforms, such as spacecrafts or satellites which are used for the repair of space vehicles or the removal of non-cooperating targets such as inactive material remaining in orbit. In this article the control problem for the nonlinear dynamics of free-floating space robots is solved with the use of a flatness-based control approach which is implemented in successive loops. The state-space model of these robotic systems is separated into a series of subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. In this chain of $i=1,2,\cdots ,N$ subsystems, the state variables of the subsequent ( $i+1$ )-th subsystem become virtual control inputs for the preceding $i$ -th subsystem, and so on. In turn, exogenous control inputs are applied to the last subsystem and are computed by tracing backwards the virtual control inputs of the preceding $N-1$ subsystems. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed multi-loop flatness-based control method avoids complicated state-space model transformations in the dynamic model of free-floating space robots, and has a simple procedure for selecting stabilizing feedback gains.