Algorithms for modeling, dynamics simulation and optimal control that respect and exploit the geometric structure of the state space. The goal is to design more physically realistic, numerically stable and efficient algorithms. The core idea is to employ a unifying variational principle over set of discrete paths for 1) deriving the dynamics and 2) computing the optimal path. The resulting algorithms preserve momentum, state space structure, and exhibit stable energy behavior. This allows coarser discretization without singularities and thus improved computational efficiency for integration and optimization purposes.

Examples: real-time optimization of single and multi-body systems:

Example: real-time receding horizon fast quadrotor flight through urban terrain: