We address the applicability of nonlinear model predictive control (NMPC) to rigid bodies with multi degrees of freedom. These systems have complicated nonlinear motion equations that cause large computational time for NMPC.We propose an asymptotically optimal NMPC core based on the uniform state sampling concept. We examined the optimality and the computational cost of the proposed core using double and triple inverted pendulum models. The result showed that the proposed core calculates sub-time-optimal motions with 100 and 1,000 times faster than the competing cores with maintaining the same optimality. We applied the proposed core to a sixth inverted pendulum model. The result showed that the proposed NMPC core is able to calculate a sub-time-optimal motion of the model.