Flat-RRT*: A sampling-based optimal trajectory planner for differentially flat vehicles with constrained dynamics

This paper introduces the \algo\space algorithm, which is a variant of the optimal Rapidly exploring Random Tree RRT* planner, accounting for actuation constraints on the vehicle dynamics in the optimal trajectory design. The proposed algorithm is applicable to vehicles that can be modelled with differentially flat dynamics, like unicycle and bicycle kinematics. The main idea is to exploit the flatness property so as to finitely parametrize trajectories, and design a set of motion primitives that represent optimal constrained trajectories joining two configurations in a grid space. A procedure to determine constrained (though sub-optimal) trajectories joining arbitrary configurations based on the motion primitives is then proposed. This eases and accelerates the construction of the tree to the purpose of online trajectory (re)planning in an uncertain environment, where the obstacle map may be continuously updated as the vehicle moves around, or unexpected events may occur and alter the free configuration space.