Pareto Optimal Control for Natural and Supernatural Motions

Optimization is a natural tool for designing natural motion control strategies. However, optimal motions can be expensive to compute. Furthermore, we are often interested in knowing an entire family of optimal motions rather than single motion. For a motion such as a jump, the solution family of interest is described by the pareto-optimal front that defines the trade-off between effort and jump height. In this paper we explore algorithms for computing a set of controllers that span the pareto-optimal front for jumping motions. Once computed, these controllers can then drive physics-based simulations in real time. We also develop supernatural jump controllers through the optimized introduction of external forces. We show that the pareto-optimal front can naturally span both natural and supernatural regimes. This allows for controllers that can naturally transition from physics-based motions to motions assisted by external forces as the task demands increase.