NONLINEAR CONTROL OF PLANAR MULTIBODY SYSTEMS IN SHAPE SPACE

Modeling, reduction, and nonlinear control of planar multibody systems motivated by the classical cat-fall problem and the practical problem of reorientation of free-floating multibody satellites with rotational joints using angular-momentum-preserving controls is studied. The system model considered is reduced by the first integral (the system angular momentum) resulting in a Hamiltonian system with a configuration space of relative joint angles (shape space). Reconstruction of dynamics is applied to modify the shape-space model and track the phase shift of the absolute angles. An important reachability result is then proved in the unreduced configuration space. Control synthesis can then be found in a feedback form, solving the reorientation problem completely. Surprisingly, the reachability result breaks down in the case of the planar coupled two-body system with zero angular momentum, proving that the cat-fall phenomenon is definitely nonplanar.