The paper develops a novel motion model, called Generalized Multi-Speed Dubins Motion Model (GMDM), which extends the Dubins model by considering multiple speeds. While the Dubins model produces time-optimal paths under a constant-speed constraint, these paths could be suboptimal if this constraint is relaxed to include multiple speeds. This is because a constant speed results in a large minimum turning radius, thus producing paths with longer maneuvers and larger travel times. In contrast, multi-speed relaxation allows for slower speed sharp turns, thus producing more direct paths with shorter maneuvers and smaller travel times. Furthermore, the inability of the Dubins model to reduce speed could result in fast maneuvers near obstacles, thus producing paths with high collision risks. In this regard, GMDM provides the motion planners the ability to jointly optimize time and risk by allowing the change of speed along the path. GMDM is built upon the six Dubins path types considering the change of speed on path segments. It is theoretically established that GMDM provides full reachability of the configuration space for any speed selections. Furthermore, it is shown that the Dubins model is a specific case of GMDM for constant speeds. The solutions of GMDM are analytical and suitable for real-time applications. The performance of GMDM in terms of solution quality (i.e., time/time-risk cost) and computation time is comparatively evaluated against the existing motion models in obstacle-free as well as obstacle-rich environments via extensive Monte Carlo simulations. The results show that in obstacle-free environments, GMDM produces near time-optimal paths with significantly lower travel times than the Dubins model while having similar computation times. In obstacle-rich environments, GMDM produces time-risk optimized paths with substantially lower collision risks.

翻译：本文提出了一种名为“广义多速度杜宾斯运动模型”（GMDM）的新型运动模型，该模型通过考虑多速度情形扩展了杜宾斯模型。杜宾斯模型在恒定速度约束下能生成时间最优路径，但若放松该约束引入多速度，这些路径可能并非最优。这是因为恒定速度会导致最小转弯半径过大，从而产生更长的机动路径和更大的行程时间；而多速度松弛则允许低速急转弯，从而生成更直接的路径，缩短机动距离和行程时间。此外，杜宾斯模型无法降低速度可能导致近障碍物快速机动，从而增加碰撞风险。基于此，GMDM使运动规划器能够通过允许沿路径改变速度来联合优化时间与风险。GMDM基于六种杜宾斯路径类型构建，并考虑了路径段上的速度变化。理论上已证明，GMDM能实现任意速度选择下配置空间的完全可达性，同时证明了杜宾斯模型是GMDM在恒定速度下的特例。GMDM的解具有解析形式，适用于实时应用。通过大量蒙特卡洛仿真，在无障碍与密集障碍物环境下，本文对GMDM与现有运动模型就解质量（即时间/时间-风险成本）和计算时间进行了对比评估。结果表明：在无障碍环境中，GMDM生成接近时间最优的路径，其旅行时间显著低于杜宾斯模型，且计算时间相近；在密集障碍物环境中，GMDM生成时间-风险优化路径，碰撞风险大幅降低。