According to some embodiments, a method includes: receiving an endpoint impedance matrix representing a desired stiffness or damping at the robot endpoint; reflecting the endpoint impedance matrix to an equivalent joint-space matrix associated with one or more of the robot joints, the equivalent joint-space matrix having a nullspace corresponding to near-zero-valued eigenvalues; generating a nullspace-filled impedance matrix from the equivalent joint-space matrix based in part on replacing the near-zero-valued eigenvalues with selected finite positive real values; generating a robot control law using the nullspace-filled impedance matrix; and using the robot control law to control the robot.