This paper develops full-state parametric controllers for standing balance of humanoid robots in response to impulsive and constant pushes. We also explore a hypothesis that postural feedback gains in standing balance should change with perturbation size. From an engineering point of view this is known as gain scheduling. We use an optimization approach to see if feedback gains should scale with the perturbation for a simulated robot. We simulate models in the sagittal and lateral plane and in 3-dimensions, use a horizontal push of a given size, direction and location as a perturbation, and optimize parametric controllers for different push sizes, directions and locations. During a simulated perturbation experiment, the appropriate controller is continuously selected based on the current push. For an impulse, the simulated robot recovers back to the initial state; for a constant push, the robot moves to an equilibrium position which leans into the push and has zero joint torques. We show the performance of optimized parametric controllers in response to different external pushes.
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