Completeness of Randomized Kinodynamic Planners with State-based Steering

Abstract — The panorama of probabilistic completeness re-sults for kinodynamic planners is still confusing. Most exist-ing completeness proofs require strong assumptions that are difficult, if not impossible, to verify in practice. To make completeness results more useful, it is thus sensible to establish a classification of the various types of constraints and planning methods, and then attack each class with specific proofs and hypotheses that can be verified in practice. We propose such a classification, and provide a proof of probabilistic completeness for an important class of planners, namely those whose steering method is based on the interpolation of system trajectories in the state space. We also provide design guidelines for the interpolation function and discuss two criteria arising from our analysis: local boundedness and acceleration compliance. I