We investigate motion-planning for a team of robotic vehicles assigned to a collaborative intelligent task in the form of global linear temporal logic (LTL) specifications. Specifically, we extend recent results from the literature to include nonholonomic kinematic constraints on the robotic vehicles. The problem formulation relies on workspace cell decompositions, where certain regions of interest in the robots' shared workspace are defined. The proposed algorithm involves two graphs: first, the topological graph arising from the workspace cell decomposition, and second, a graph arising from vertex aggregation on the previous graph. The main technical innovation is the application of the so-called method of lifted graphs to determine the feasibility of edge transitions in these graphs. We illustrate the proposed approach with numerical simulation examples.