The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values.
