Minimum base reaction control for multi-link systems in a field with obstacles

An iterative linear programming based technique is proposed for the determination of control profiles which minimize the base reaction force of multi-link systems in a field with obstacles. The center of mass transformation is exploited to permit posing the dynamics of the multi-link system as a point mass, reducing complex manipulator dynamics to a set of linear dynamic equations. The problem of minimizing the base reaction force is reduced to minimizing the 2 norm of the control vector. A recursive approach for approximating the spherical control constraint with multiple planes permits posing the problem as a linear programming problem. The technique developed requires no initial guess and guarantees the globally optimal solution. The proposed technique is illustrated on a 3 degrees of freedom two-link manipulator.