Nonlinear control of multibody systems in shape space

Nonlinear control of planar multibody systems motivated by the classical cat-fall problem and the more practical problem of reorientation of multibody satellites in space are studied. A multibody system model reduced by translational and rotational symmetries was assumed in a Hamiltonian setting. A further reduction by the first integral (the system angular momentum) results in a configuration space of relative joint angles. This is equivalent to reducing the system to the symplectic leaf of the previously assumed model. The system after reduction is still Hamiltonian, and a canonical representation can be obtained. Angular-momentum-preserving controls generated by joint motors were introduced. The application of this linearizing input results in a reduced-dimension model and was found to capture the dynamics of the system in the shape space. The state space was extended to track the change in phase shift of the absolute angles. An important reachability result is proved. An optimal control problem was formulated to accomplish reorientation