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Trajectory Optimization with Global Yaw Parameterization for Field-of-View Constrained Autonomous Flight

Yuwei Wu, Yuezhan Tao, Igor Spasojevic, Vijay Kumar

TL;DR

A novel global yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm and significantly reduces the needed control effort, and improves optimization feasibility.

Abstract

Trajectory generation for quadrotors with limited field-of-view sensors has numerous applications such as aerial exploration, coverage, inspection, videography, and target tracking. Most previous works simplify the task of optimizing yaw trajectories by either aligning the heading of the robot with its velocity, or potentially restricting the feasible space of candidate trajectories by using a limited yaw domain to circumvent angular singularities. In this paper, we propose a novel \textit{global} yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm. This approach effectively bypasses inherent singularities by including supplementary quadratic constraints and transforming the final decision variables into the desired state representation. This method significantly reduces the needed control effort, and improves optimization feasibility. Furthermore, we apply the method to several examples of different applications that require jointly optimizing over both the yaw and position trajectories. Ultimately, we present a comprehensive numerical analysis and evaluation of our proposed method in both simulation and real-world experiments.

Trajectory Optimization with Global Yaw Parameterization for Field-of-View Constrained Autonomous Flight

TL;DR

A novel global yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm and significantly reduces the needed control effort, and improves optimization feasibility.

Abstract

Trajectory generation for quadrotors with limited field-of-view sensors has numerous applications such as aerial exploration, coverage, inspection, videography, and target tracking. Most previous works simplify the task of optimizing yaw trajectories by either aligning the heading of the robot with its velocity, or potentially restricting the feasible space of candidate trajectories by using a limited yaw domain to circumvent angular singularities. In this paper, we propose a novel \textit{global} yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm. This approach effectively bypasses inherent singularities by including supplementary quadratic constraints and transforming the final decision variables into the desired state representation. This method significantly reduces the needed control effort, and improves optimization feasibility. Furthermore, we apply the method to several examples of different applications that require jointly optimizing over both the yaw and position trajectories. Ultimately, we present a comprehensive numerical analysis and evaluation of our proposed method in both simulation and real-world experiments.
Paper Structure (21 sections, 20 equations, 4 figures, 1 table)

This paper contains 21 sections, 20 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Orientation Representations
  4. Yaw Trajectory Planning
  5. keyframe Traversal Optimization
  6. Notation
  7. Differential-flatness-based Trajectory Optimization
  8. Perception-based Trajectory Generation
  9. Methodology
  10. Parameterization with Direct Mapping
  11. Optimization with Virtual Variables
  12. Traversal Planning via Nonlinear Optimization
  13. FOV Cost Functional
  14. Velocity Cost Functional
  15. Dynamics Cost Functional
  16. ...and 6 more sections

Figures (4)

  • Figure 1: Snapshots of hardware experiment of traversal planning with yaw constraints. We use our SWaP-constrained Falcon250 quadrotor platform and Scarab ground robot platform as a tracking target (\ref{['subsec:Hardware-Experiments']}). The video is available at: https://youtu.be/QMbkoTyKe-k
  • Figure 2: The comparison of different parameterization methods. We evaluated the relative minimum control cost (${\rm rad^2/s^3 }$), accumulated yaw distance (rad), average speed (rad/s), and success rate.
  • Figure 3: (a) Trajectory of proposed parameterization trajectories. The purple arrows represent position and yaw sequence, and the green arrows represent a sequence of discretized optimal trajectory. (b) The plots of position, velocity, and accelerations of position, yaw, and r trajectories.
  • Figure 4: Target tracking experiment. The right top image illustrates a current camera view from the quadrotor and the right bottom one shows a third person view. The left image visualizes its online planning process. The blue arrows represent the executed trajectory of the drone and the axes represent the odometry of the target. The red pyramid shape represents the current field of view. The red arrows represent the current start and end yaw angle, and the intermediate green arrows represent the planned trajectory.

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3