Active shock absorber control in humanoid robot falls with nonlinear optimization on a reduced dynamics model

We propose a reduced-model-based analytic approach to active shock absorption by a falling humanoid robot at impact. We model the segment between the contact point at impact and the impacting limb extremity attached to the torso or waist of the humanoid robot as a one degree-offreedom linear mass-spring-damper system. By mapping the joint angle limits and torque limits of the joints in the impacting limb to a corresponding position limit and force limit in the reduced model, we formulate a nonlinear optimization problem to find an admissible pair of parameters of the reduced model (stiffness, damping) that prevents the model from violating the constraints before reaching a steady state rest. The nonlinear constraints are analytically derived using symbolic computation tools and then numerically solved with off-the-shelf nonlinear optimization solver. The reduced model trajectories are then mapped back on the full body of the humanoid robot and illustrated on the HRP-4 robot in simulation.