Spatio-temporal decomposition: a knowledge-based initialization strategy for parallel parking motion optimization

Motion planning methodologies for parallel parking have been well developed in the last decade. In contrast to the prevailing and emerging parking motion planners, this work provides a precise and objective description of the parking scenario and vehicle kinematics/dynamics. This is achieved by formulating a unified optimal control problem that is free of subjective knowledge (e.g., human experiences). The concerned optimal control problem, when parameterized into a large-scale nonlinear programming (NLP) problem, is extremely difficult to solve. This bottleneck has hindered many research efforts previously. Although the feasible regions of NLP problems are clearly defined, the majority of NLP-solving processes still require high-quality initial guesses, which accelerate the convergence process. In this work, we propose a spatio-temporal decomposition based initialization strategy to generate reliable initial guesses, so as to facilitate the NLP-solving process. In contrast to the typical facilitation strategies in robotic motion/path planning, our spatio-temporal decomposition strategy considers only objective kowledge, further breaking the limitation of subjective knowledge and making full use of a vehicle's maneuver potential. A series of comparative simulations verifies that the proposed initialization strategy is advantageous over its prevailing competitors, and that the proposed motion planner is promising for on-line planning missions. Theoretical analysis that supports our initialization strategy is given as well.