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Generating 6-D Trajectories for Omnidirectional Multirotor Aerial Vehicles in Cluttered Environments

Peiyan Liu, Yuanzhe Shen, Yueqian Liu, Fengyu Quan, Can Wang, Haoyao Chen

Abstract

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.

Generating 6-D Trajectories for Omnidirectional Multirotor Aerial Vehicles in Cluttered Environments

Abstract

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 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 manifold, while the complete 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.
Paper Structure (15 sections, 26 equations, 10 figures, 2 tables)

This paper contains 15 sections, 26 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System modeling and control
  3. Definitions
  4. System Modeling of OMAVs
  5. Position and Attitude Control
  6. method
  7. Whole-body Safety Constraint
  8. 6-D Trajectory Optimization
  9. Rotation Parameterization
  10. Simulations and Experiments
  11. Implementation Details
  12. Parameter Settings
  13. Simulation Results
  14. Real-World Experiments
  15. Conclusion

Figures (10)

  • Figure 1: The proposed 3-stage 6-D trajectory generation framework involves initial path search, SFC generation, and 6-D trajectory optimization.
  • Figure 2: This figure shows the frame definitions, the rotor tilt angle, and the CAD model of OmniHex. $\mathcal{F}_W$ uses the east-north-up (ENU) coordinate system. The origin of $\mathcal{F}_b$ coincides with the vehicle's Center of Mass (CoM); the $x_b$ axis points forward, the $y_b$ axis points to the body's left, and the right-hand rule determines the $z_b$ axis.
  • Figure 3: The control pipeline of OmniHex. As the position control and attitude control of OmniHex is decoupled, the linear and angular acceleration setpoints are calculated separately by their respective cascade PID controllers.
  • Figure 4: The 2-D illustration of spatial constraints \ref{['equ:origin_problem_cons_3']}-\ref{['equ:origin_problem_cons_5']}. In this case $k_1 = 3, k_2 = 6$, and $k_{M_{\mathcal{P} - 1}} = M - 3$.
  • Figure 5: Illustrations of some experiment settings. (a) shows the cuboid used to approximate the vehicle's shape, of which the center coincides with the vehicle's CoM, and the three symmetry axes are parallel with axes of $\mathcal{F}_b$. (b) shows the real OmniHex we develop.
  • ...and 5 more figures