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Trajectory Tracking for Unmanned Aerial Vehicles in 3D Spaces under Motion Constraints

Saurabh Kumar, Shashi Ranjan Kumar, Abhinav Sinha

TL;DR

The paper addresses $3$D trajectory tracking for quadrotor UAVs under spatial constraints and partial inertia information. It introduces a nonlinear geometric control framework with a cascaded outer-position and inner-attitude loop, augmented by barrier Lyapunov functions and a disturbance observer to enforce constraints and cope with uncertainties. Theoretical results guarantee boundedness of position, velocity, orientation, and their rates, along with asymptotic convergence to the desired trajectories. Numerical simulations across orbital, helical, and bow-shaped paths demonstrate robust constraint satisfaction and accurate tracking under realistic actuator and inertia limits, highlighting practical viability.

Abstract

This article presents a three-dimensional nonlinear trajectory tracking control strategy for unmanned aerial vehicles (UAVs) in the presence of spatial constraints. As opposed to many existing control strategies, which do not consider spatial constraints, the proposed strategy considers spatial constraints on each degree of freedom movement of the UAV. Such consideration makes the design appealing for many practical applications, such as pipeline inspection, boundary tracking, etc. The proposed design accounts for the limited information about the inertia matrix, thereby affirming its inherent robustness against unmodeled dynamics and other imperfections. We rigorously show that the UAV will converge to its desired path by maintaining bounded position, orientation, and linear and angular speeds. Finally, we demonstrate the effectiveness of the proposed strategy through various numerical simulations.

Trajectory Tracking for Unmanned Aerial Vehicles in 3D Spaces under Motion Constraints

TL;DR

The paper addresses D trajectory tracking for quadrotor UAVs under spatial constraints and partial inertia information. It introduces a nonlinear geometric control framework with a cascaded outer-position and inner-attitude loop, augmented by barrier Lyapunov functions and a disturbance observer to enforce constraints and cope with uncertainties. Theoretical results guarantee boundedness of position, velocity, orientation, and their rates, along with asymptotic convergence to the desired trajectories. Numerical simulations across orbital, helical, and bow-shaped paths demonstrate robust constraint satisfaction and accurate tracking under realistic actuator and inertia limits, highlighting practical viability.

Abstract

This article presents a three-dimensional nonlinear trajectory tracking control strategy for unmanned aerial vehicles (UAVs) in the presence of spatial constraints. As opposed to many existing control strategies, which do not consider spatial constraints, the proposed strategy considers spatial constraints on each degree of freedom movement of the UAV. Such consideration makes the design appealing for many practical applications, such as pipeline inspection, boundary tracking, etc. The proposed design accounts for the limited information about the inertia matrix, thereby affirming its inherent robustness against unmodeled dynamics and other imperfections. We rigorously show that the UAV will converge to its desired path by maintaining bounded position, orientation, and linear and angular speeds. Finally, we demonstrate the effectiveness of the proposed strategy through various numerical simulations.
Paper Structure (9 sections, 8 theorems, 98 equations, 12 figures)

This paper contains 9 sections, 8 theorems, 98 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Background and Problem Statement
  3. Kinematics and Dynamics of Quadrotor
  4. Problem Statement
  5. Main Results
  6. Position Control
  7. Attitude Subsystem
  8. Simulations
  9. Concluding remarks

Key Result

Lemma 1

(doi:10.1016/j.automatica.2008.11.017) Consider the system where $\eta:=\left[w, z_{1}\right]^{\top} \in \mathcal{N}$, and $\varpi: \mathbb{R}_+\times \mathcal{N} \rightarrow \mathbb{R}^{l+1}$ is piecewise continuous in $t$ and locally Lipschitz in $z$, uniform in $t$, on $\mathbb{R}_{+} \times \mathcal{N}$. For any positive constants $k_{a_{1}}, k_{b_{1}}$ where $\mathcal{X}_{1}$ and $\mathcal{X

Figures (12)

  • Figure 1: Schematic representation of a quadrotor.
  • Figure 2: Geometrical representation of coordinate frames.
  • Figure 3: Sample illustration of the problem: UAV inspecting a tunnel.
  • Figure 4: The proposed control architecture for the quadrotor UAV.
  • Figure 5: Illustration of the outer loop design.
  • ...and 7 more figures

Theorems & Definitions (21)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Definition 1
  • Lemma 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • ...and 11 more