On the Design of Deformable Input-/State-Lattice Graphs

Abstract — In this paper we describe a novel and simple to implement yet effective lattice design algorithm, which simultaneously produces input and state-space sampled lattice graphs. The presented method is an extension to the ideas suggested by Bicchi et al. on input lattices and is applicable to systems which can be brought into (2,n) chained form, such as kinematic models of unicycles, bicycles, differential-drive robots and car-like vehicles (pulling several trailers). We further show that a transformation from chained form to path coordinates allows the resulting lattice to be bent along any C 1 continuous path. We exploit this fact by shaping it along the skeleton of arbitrary structured environments, such as the center of road lanes and corridors. In our experiments in both structured (i.e. on-road) and unstructured (i.e. parking lot) scenarios, we successfully demonstrate for the first time the applicability of lattice-based planning approaches to search queries in arbitrary environments. Index Terms — Non-holonomic motion planning, deformable input- / state-lattice