1. A system for providing substantially stable control of a surgical instrument, comprising: a surgical manipulator for manipulating the surgical instrument; and at least one computer configured to: identify a first subset and a second subset of interaction geometric primitives associated with a virtual tool representing the surgical instrument; determine, based on the first subset, control forces in a first subspace; determine based on the second subset, control forces in a second subspace having at least one additional dimension to first subspace; wherein control forces in the additional dimension are only determined based on the second subset of interaction geometric primitives, which is different than the first subset of interaction geometric primitives; and determine a torque to constrain an orientation of the surgical instrument, wherein determining the torque comprises defining a virtual tool normal and a control plane normal and using the virtual tool normal and control plane normal to calculate the torque.