Dynamically Feasible Motion Planning through Partial Differential Flatness

Differential flatness is a property which substantially reduces the difficulty involved in generating dynamically feasible trajectories for underactuated robotic systems. However, there is a large class of robotic systems that are not differentially flat, and an efficient method for computing dynamically feasible trajectories does not exist. In this paper we introduce a weaker but more general form of differential flatness, termed partial differential flatness, which enables efficient planning of dynamic feasible motion plans for an entire new class of systems. We provide several examples of underactuated systems which are not differentially flat, but are partially differentially flat. We also extend the notion of partial differential flatness to hybrid systems. Finally, we consider the infamous cart-pole system and provide a concrete example of designing dynamically feasible trajectories in the presence of obstacles.