Motion-planning with linear temporal logic specifications for a nonholonomic vehicle kinematic model

We present a new technique for the control of a nonholonomic vehicle kinematic model subject to linear temporal logic (LTL) specifications. The proposed technique is based on partitioning of the vehicle's planar workspace into cells. The main result of this paper is the precise characterization of acceptable sequences of cells, which can be traversed by admissible state trajectory of the vehicle model while satisfying the given LTL specifications. The proposed approach does not require complete controllability of the vehicle model in the presence of workspace constraints, and no linearization of the model is involved. The key technical innovation is the so-called lifted graph. Edge transitions in the lifted graph are associated with certain forward- and backward reachable sets of the vehicle model. We illustrate the proposed technique with numerical simulation examples.