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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> subsystems, the state variables of the subsequent ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-th subsystem become virtual control inputs for the preceding <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> 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.