GPU-based contact-aware trajectory optimization using a smooth force model

We present a new formulation of trajectory optimization for articulated bodies. Our approach uses a fully differentiable dynamic model of the articulated body, and a smooth force model that approximates all kinds of internal/external forces as a smooth function of the articulated body's kinematic state. Our formulation is contact-aware and its complexity is not dependent on the contact positions or the number of contacts. Furthermore, we exploit the block-tridiagonal structure of the Hessian matrix and present a highly parallel Newton-type trajectory optimizer that maps well to GPU architectures. Moreover, we use a Markovian regularization term to overcome the local minima problems in the optimization formulation. We highlight the performance of our approach using a set of locomotion tasks performed by characters with 15 -- 35 DOFs. In practice, our GPU-based algorithm running on a NVIDIA TITAN-X GPU provides more than 30x speedup over a multi-core CPU-based implementation running on Intel Xeon E5-1620 CPU. In addition, we demonstrate applications of our method on various applications such as contact-rich motion planning, receding-horizon control, and motion graph construction.