As fully-actuated systems, omnidirectional multirotor aerial vehicles (OMAVs) have more flexible maneuverability and advantages in aggressive flight in cluttered environments than traditional underactuated MAVs. %Due to the high dimensionality of configuration space, making the designed trajectory generation algorithm efficient is challenging. This paper aims to achieve safe flight of OMAVs in cluttered environments. Considering existing static obstacles, an efficient optimization-based framework is proposed to generate 6-D $SE(3)$ trajectories for OMAVs. Given the kinodynamic constraints and the 3D collision-free region represented by a series of intersecting convex polyhedra, the proposed method finally generates a safe and dynamically feasible 6-D trajectory. First, we parameterize the vehicle's attitude into a free 3D vector using stereographic projection to eliminate the constraints inherent in the $SO(3)$ manifold, while the complete $SE(3)$ trajectory is represented as a 6-D polynomial in time without inherent constraints. The vehicle's shape is modeled as a cuboid attached to the body frame to achieve whole-body collision evaluation. Then, we formulate the origin trajectory generation problem as a constrained optimization problem. The original constrained problem is finally transformed into an unconstrained one that can be solved efficiently. To verify the proposed framework's performance, simulations and real-world experiments based on a tilt-rotor hexarotor aerial vehicle are carried out.

翻译：作为全驱动系统，全向多旋翼飞行器（OMAVs）相比传统欠驱动多旋翼飞行器（MAVs）具有更灵活的机动性，并在杂乱环境中进行激进飞行时具备优势。本文旨在实现OMAVs在杂乱环境中的安全飞行。考虑到现有静态障碍物，我们提出了一种基于优化的高效框架，用于为OMAVs生成六自由度$SE(3)$轨迹。在给定运动学动力学约束以及由一系列相交凸多面体表示的三维无碰撞区域的前提下，所提方法最终生成一条安全且动力学可行的六自由度轨迹。首先，我们利用球极投影将飞行器姿态参数化为一个自由的三维向量，以消除$SO(3)$流形固有的约束，同时完整的$SE(3)$轨迹被表示为无固有约束的六维时间多项式。飞行器形状被建模为附着于机体坐标系的长方体，以实现全身碰撞评估。接着，我们将原始轨迹生成问题表述为一个约束优化问题。该原始约束问题最终被转化为一个可高效求解的无约束问题。为验证所提框架的性能，我们基于一架倾转旋翼六旋翼飞行器进行了仿真和真实世界实验。