A new controller for use in robots with kinematic loops as well as in most other types of robots (such as those with fully actuated kinematic trees). The controller includes an inverse kinematics (IK) module that implements a versatile IK formulation for retargeting of motions, including expressive motions, onto mechanical systems (i.e., robots with loops and/or without loops). Further, the controller is configured to support the precise control of the position and orientation of end effectors and the center of mass (CoM) (such as of walking robots). The formulation of the algorithms carried out by the IK module safeguards against a disassembly when IK targets are moved outside the workspace of the robot. A regularizer is included in the controller that smoothly circumvents kinematic singularities where velocities go to infinity.