Stable Proportional-Derivative Controllers

In computer animation, the proportional-derivative (PD) controller is a common technique for tracking characters' motion. A new formulation of the PD controller-stable PD (SPD)-allows arbitrarily high gains, even at large time steps. The key is to determine joint forces and torques while taking into account the character's positions and velocities in the next time step. SPD is stable even when combined with a physics simulator that uses simple Euler integration. SPD controllers have a variety of uses, including motion tracking in a physics simulator, keyframe interpolation with secondary motion, and constraint satisfaction for simulation.