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.