Control aspects for safe-falling of humanoid robots

Kurzfassung

The aim of the project is to design an active controller for the safe falling of a humanoid robot. The problem can be split in two sub-sections: direction-changing and damage minimization. While the first aims to the protection of the working environment, the second focuses on the safeguard of the humanoid itself, minimizing the damages coming from the impact with the ground. This project is mainly focused on the damage minimization. Later, a preliminary work is done aimed to demonstrate the possibility to change the falling direction of a humanoid without any external force applied. An inverted pendulum has been used to model the dynamic behavior of the tipping robot whose mass is all concentrated in its center of mass. First, a relationship between the impact force and the impact velocity has been found. Then, an optimization problem was solved in order to find the best trajectory for the center of mass that minimizes the impact velocity. In the end, the minimized impact force has been distributed among the highest possible number of contact points in order to locally decrease the magnitude of the impact. The optimization problem has been solved thanks to the linearity between the Hamiltonian function and the control function, which is also bounded between a maximum and minimum value. Thus, the optimal control law is a bang-bang control whose number and time-position of the switches has been calculated numerically. For the direction-changing controller, again ad inverted pendulum model was used with a reaction wheel fixed on the free extremity that can rotate around the axis of the pendulum itself. In particular, the wheel models the behavior of the upper body of the humanoid that rotates around its torso. With this model, in the simplified case in which the inertia of the wheel and the length of the pendulum are considered constant in time, it is possible to accomplish the task generating an angular momentum with the rotation of the wheel itself.