Attitude control of a two-link system subject to momentum constraints

A solution to the attitude control problem for a two-link planar system subject to angular momentum constraints is presented. Reference trajectories for simulating the motion of the constrained dynamic system are found by specifying the internal variables of the system and solving for the corresponding external variables. It is shown that the angular momentum constraint has quasi-holonomic character because it can be employed to reduce the dimensionality of the system by eliminating half a degree of freedom. A controller is designed for the reduced dynamic system and tested by digital computer sinmlation. The same controller can be used for the unreduced systeln if the angular momentum constraint is a linear function of the system states. Such an approach, however, cannot be employed if the constraint is a nonlinear function of the system state, in which case a controller must be designed which stabilizes both the system and the constraint equation. Computer simulations of the diving motion of a human are presented to illustrate the control approach.