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Closed-Loop Model Identification and MPC-based Navigation of Quadcopters: A Case Study of Parrot Bebop 2

Mohsen Amiri, Mehdi Hosseinzadeh

TL;DR

This work tackles real-time quadcopter navigation under safety constraints and limited onboard compute by deriving a simple linear, decoupled model for quadrotor dynamics and implementing a steady-state-aware MPC (SSMPC). The model, based on $\ddot{p}_i+\alpha_i\dot{p}_i=\beta_i u_i$, enables low-complexity control, demonstrated through a discretization with $T_s=0.2$ s and experimental validation on the Parrot Bebop 2. The SSMPC optimizes over a steady-state characterizing vector $\theta$ and an input sequence to guarantee constraint satisfaction and convergence to the desired state, even with input limits. Experimental results show effective constant-reference tracking and 3D trajectory following with a per-step computation time of about $0.052$ s, confirming real-time feasibility on modest hardware. This work provides a practical, safe navigation framework for indoor or resource-constrained quadcopters.

Abstract

The growing potential of quadcopters in various domains, such as aerial photography, search and rescue, and infrastructure inspection, underscores the need for real-time control under strict safety and operational constraints. This challenge is compounded by the inherent nonlinear dynamics of quadcopters and the on-board computational limitations they face. This paper aims at addressing these challenges. First, this paper presents a comprehensive procedure for deriving a linear yet efficient model to describe the dynamics of quadrotors, thereby reducing complexity without compromising efficiency. Then, this paper develops a steady-state-aware Model Predictive Control (MPC) to effectively navigate quadcopters, while guaranteeing constraint satisfaction at all times. The main advantage of the steady-state-aware MPC is its low computational complexity, which makes it an appropriate choice for systems with limited computing capacity, like quadcopters. This paper considers Parrot Bebop 2 as the running example, and experimentally validates and evaluates the proposed algorithms.

Closed-Loop Model Identification and MPC-based Navigation of Quadcopters: A Case Study of Parrot Bebop 2

TL;DR

This work tackles real-time quadcopter navigation under safety constraints and limited onboard compute by deriving a simple linear, decoupled model for quadrotor dynamics and implementing a steady-state-aware MPC (SSMPC). The model, based on , enables low-complexity control, demonstrated through a discretization with s and experimental validation on the Parrot Bebop 2. The SSMPC optimizes over a steady-state characterizing vector and an input sequence to guarantee constraint satisfaction and convergence to the desired state, even with input limits. Experimental results show effective constant-reference tracking and 3D trajectory following with a per-step computation time of about s, confirming real-time feasibility on modest hardware. This work provides a practical, safe navigation framework for indoor or resource-constrained quadcopters.

Abstract

The growing potential of quadcopters in various domains, such as aerial photography, search and rescue, and infrastructure inspection, underscores the need for real-time control under strict safety and operational constraints. This challenge is compounded by the inherent nonlinear dynamics of quadcopters and the on-board computational limitations they face. This paper aims at addressing these challenges. First, this paper presents a comprehensive procedure for deriving a linear yet efficient model to describe the dynamics of quadrotors, thereby reducing complexity without compromising efficiency. Then, this paper develops a steady-state-aware Model Predictive Control (MPC) to effectively navigate quadcopters, while guaranteeing constraint satisfaction at all times. The main advantage of the steady-state-aware MPC is its low computational complexity, which makes it an appropriate choice for systems with limited computing capacity, like quadcopters. This paper considers Parrot Bebop 2 as the running example, and experimentally validates and evaluates the proposed algorithms.
Paper Structure (13 sections, 2 theorems, 17 equations, 4 figures)

This paper contains 13 sections, 2 theorems, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Closed-Loop Model Identification
  3. Model Structure
  4. Identification Procedure
  5. Experimental Validation: MPC-Based Navigation
  6. System Discretization
  7. Control Structure
  8. Determination of $Q_N$
  9. Determining the Terminal Constraint Set $\Omega$
  10. Theoretical Properties
  11. Experimental Setting
  12. Experimental Results
  13. Conclusion

Key Result

Theorem 3.1

Consider system eq:DiscreteMatrices, which is subject to the above-mentioned constraints on the control inputs. Suppose that eq:OptimizationProblemMain is feasible at $k=0$. Then, it remains feasible for all $k>0$.

Figures (4)

  • Figure 1: Parrot Bebop 2 and considered reference and body frames; note that to make the measurements more relevant, the considered body frame is different than the one in the "Parrot Drone Support from MATLAB" package MATLAB.
  • Figure 5: Bode plot of the identified model for each direction (blue lines) and the magnitudes computed based on Fourier transforms (red asterisks).
  • Figure 6: Set points traveled by the quadrotor Bebop 2 in the navigation experiment.
  • Figure 7: Path followed by the quadrotor when tracking the lemniscate of Bernoulli trajectory.

Theorems & Definitions (2)

  • Theorem 3.1: Recursive Feasibility
  • Theorem 3.2: Closed-Loop Stability