Analysis of a simple model for post-impact dynamics active compliance in humanoids falls with nonlinear optimization

We analyse a mass-spring-damper model as an active compliance steering controller to adaptively comply with post-impact dynamics in humanoid falls. We use it as a one degree of freedom virtual link that can be attached between a point at impact and a given limb point (e.g. torso or waist of the humanoid). By mapping position and torque limits of the robot joints into corresponding position and force limits in the virtual link, we formulate a nonlinear optimization problem to find its admissible stiffness and damping that prevents violating the constraints before reaching a steady state rest. The nonlinear constraints are analytically derived using symbolic computation and then numerically solved with off-the-shelf nonlinear optimization solver. The virtual model trajectories are then mapped back on the full body of the humanoid robot and illustrated on the HRP-4 robot in simulation.