Misconceptions of PD Control in Animation

Abstract

In this paper, we address certain misconceptions that have been perpetuated in the animation practice and research for quite some time related to the proportional-derivative (PD) control of physics-based systems. Because in animation we often think in terms of targeting keyframes, we tend to forget that PD control, in its simple form, has a very specific asymptotic behavior that approaches zero (or an offset) with zero velocity as time approaches infinity. We pay particular attention to the issue of introducing a ''desired'' or ''end'' velocity term in the equation of a proportional-derivative controller, and discuss how this term should be interpreted and how it relates to feedforward control rather than an end derivative problem.