Geometric Path Planning and Synchronization for Multiple Vehicles

In known environments, vehicles plan paths to the target and take precautions to minimize risks. Due to limited dynamics, bounded turning radii, and unfavorable initial conditions, they may be momentarily exposed to threats. In this study, we propose multi-objective real-time optimization based on Dubins paths for multiple vehicles. They synchronize target arrival by reasonably changing speeds and selecting paths of similar lengths. The closer the threats are to the robots and the target, the more path options are available. Risk is reduced in path planning by minimizing the duration of exposure to threats. Vehicles strike a balance between exposure to threats and travel time to targets. We use a probability-based approach to reduce the computation burden and select satisfactory paths such that vehicles synchronize target arrival reasonably far away from threats. The performances of the proposed methods are verified in several simulation examples.