| A solution technique which converges on the globally optimal solution for a 2-norm minimization problem is developed. In this thesis, the class of minimum base reaction forces are considered. This solution technique achieves the globally optimal solution while offering the advantages of not requiring an initial guess and being easily extended to more complicated fields. Minimum base reaction control is best applied for manipulators which do not have an anchored base, such as those mounted on spacecraft or ships. Utilizing minimum base reaction for these type of manipulators will decrease the disturbances to the system attitude. Minimum base reaction can also be used for manipulators which perform repetitive maneuvers, decreasing the repeated stresses at the base and allowing for decreased requirements on the actuation strength. This thesis illustrates the method of converting constraints into a form to be used by the globally optimal solution method, including a planar approximation to a convex quadratic constraint, initial and final conditions and obstacle avoidance. The proposed technique is illustrated on two examples: a gantry crane and a two-link manipulator, both with 3 degrees of freedom. The results of the proposed technique are shown to be better than those presented in the literature. |
