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During quiet standing, humans tend to sway with a distinctive pattern that has been difficult to capture with simple engineering models. We have developed a nonlinear optimal control model for posture regulation. The proposed model consists of two main components: body dynamics and performance measure. The body dynamics are those of a double inverted pendulum in the sagittal plane controlled by ankle and hip torques. The performance measure is nonlinear quartic in the center of pressure and quadratic in the controls. Realistic values for both sensory and motor delays are included in the dynamic model. This nonlinear quartic regulator problem is solved approximately by the model predictive control technique. The resulting feedback control replicates both the experimentally observed sway and the coordinated nonlinear response. It should also use less muscular energy than other comparable controls. The method can easily be extended to more complex models of posture regulation.