Linear-Time Dynamics of Characters with Stiff Joints

Characters, like other articulated objects and structures, are typically simulated using articulated dynamics algorithms. There are efficient linear-time algorithms for the simulation of open-chain articulated bodies, but complexity grows notably under additional constraints such as joint limits, loops or contact, or if the bodies undergo stiff joint forces. This paper presents a linear-time algorithm for the simulation of open-chain articulated bodies with joint limits and stiff joint forces. This novel algorithm uses implicit integration to simulate stiff forces in a stable manner, and avoids drift by formulating joint constraints implicitly. One additional interesting feature of the algorithm is that its practical implementation entails only small modifications to a popular algorithm.