  This paper derives a closed-form method for computing hybrid force-velocity
control. The key idea is to maximize the kinematic conditioning of the
mechanical system, which includes a robot, free objects, a rigid environment
and contact constraints. The method is complete, in that it always produces an
optimal/near optimal solution when a solution exists. It is efficient, since it
is in closed form, avoiding the iterative search of previous work. We test the
method on 78,000 randomly generated test cases. The method outperforms our
previous search-based technique by being from 7 to 40 times faster, while
consistently producing better solutions in the sense of robustness to kinematic
singularity. We also test the method in several representative manipulation
experiments.
