Towards Discrete Mechanics and Optimal Control for Complex Models

摘要

Methods for trajectory optimization originate from the need to solve spaceflight mechanics problems beginning in the 1950s and 1960s. The rise of digital compute power popularized so-called direct methods from the 1980s onwards. Since the 1990s, these methods have been used extensively in various fields like robotics and chemical reaction kinetics. Discrete Mechanics and Optimal Control (DMOC) is a relatively new but not very widespread method that offers nice mathematical properties. It has mostly been applied to small mechanical problems so far. We show that the method can offer competitive performance when being used on more complex models like a 2D human model. Furthermore, we point out that the method can take advantage of parallel compute architectures nicely. It relies on a variational principle and temporal discretization that lead to a sparse constraint Jacobian that scales well.