Power efficient balancing control for humanoids based on approximate optimal ankle compliance regulation

The balance control of humanoid robots against external perturbations is a fundamental prerequisite for operating in unstructured environments where physical interaction may unexpectedly occur. These balancing actions can be very demanding in terms of power and torque requirements for ankle joints especially after strong and sudden impacts. In this work, an optimal control problem is formulated for the linearized inverted pendulum model to reduce the peak power requirements during ankle balancing strategy. This optimal control which reduces peak torque and power is computed numerically and approximated by a piecewise linear function of the states called the approximate optimal compliance regulator. The balancing ability of this compliance regulator is evaluated against other optimal compliance methods. The stability of the linearly switching approximated optimal compliance regulator is determined from practical perspective using quadratic stability and parameter dependent Lyapunov functions. The efficacy of the proposed stabilizer is validated for a compliant humanoid.