用椭球走廊参数化轨迹，实现复杂环境下的高效避障规划
Trajectory Planning Using Safe Ellipsoidal Corridors as Projections of Orthogonal Trust Regions
- 将非凸避障走廊转化为球体的笛卡尔积，解耦问题规模与环境复杂度
- 在四旋翼基准测试中，轨迹更平滑且运行时间更低，尤其在复杂环境中优势明显
- 适合需要实时避障的无人机、机器人路径规划场景
在复杂环境中规划无碰撞轨迹仍是机器人领域的核心挑战。现有基于走廊的规划方法依赖自由空间的分解为无碰撞子集，随环境复杂度增加而性能下降，且需显式分配各段轨迹的时间窗口。本文提出一种新轨迹参数化方式，将非凸无碰撞走廊中的轨迹表示为球体的凸笛卡尔积，使问题规模与解的几何复杂度解耦。该表示自然避免显式时间分配，允许轨迹在椭球走廊内连续演化。基于此，我们构建了正交信任域问题（Orth-TRP），一个具有可分离块约束的专用凸优化问题，并设计了利用并行结构及每个子问题独特结构的高效求解器。在四旋翼轨迹规划基准测试中，本方法生成的轨迹更平滑，运行时间低于现有先进走廊规划算法，尤其在高度复杂的环境中表现更优。
原文摘要 · Abstract (English)
Planning collision free trajectories in complex environments remains a core challenge in robotics. Existing corridor based planners which rely on decomposition of the free space into collision free subsets scale poorly with environmental complexity and require explicit allocations of time windows to trajectory segments. We introduce a new trajectory parameterization that represents trajectories in a nonconvex collision free corridor as being in a convex cartesian product of balls. This parameterization allows us to decouple problem size from geometric complexity of the solution and naturally avoids explicit time allocation by allowing trajectories to evolve continuously inside ellipsoidal corridors. Building on this representation, we formulate the Orthogonal Trust Region Problem (Orth-TRP), a specialized convex program with separable block constraints, and develop a solver that exploits this parallel structure and the unique structure of each parallel subproblem for efficient optimization. Experiments on a quadrotor trajectory planning benchmark show that our approach produces smoother trajectories and lower runtimes than state-of-the-art corridor based planners, especially in highly complicated environments.
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