A Simplified Contact Model for Treating the Balance of Biped Virtual Characters

In this work, we present a physically-based model for maintaining the equilibrium of biped characters. We use Proportional-Derivative (PD) Controllers to mimic the characteristics of angular joints, and deal with the equilibrium through a method that uses the transpose of the Jacobian matrix that relates the angular and linear momentum at the Center of Mass (COM) of the character's body to the corresponding quantities at all its links, which are treated as end effectors. Also, we propose a contact model for treating the interaction between the feet and the ground that confers great stability to the character and makes it easier for the controller and for the starting of the simulation. It also makes it convenient for the animator to adjust the model so as to consider a trade-off between more physical realism and more stability. The system does not use optimization and is simple to implement. The robustness of the controller is demonstrated through a series of tests.