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A constrained robust switching MPC structure for tilt-rotor UAV trajectory tracking problem

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Abstract

In tilt-rotor UAVs, both the fuselage and tilting rotors contribute to the vehicle’s rotational motion. Consequently, the system’s dynamics rise to a highly-nonlinear system, making it challenging to find feasible and desired control solutions. The common control practices devise a logic-based controller to switch between different flight modes or map the control inputs to the conventional helicopter-type control inputs. However, they fail to provide energy-efficient fast trajectory tracking, especially in the presence of external disturbances. This paper proposes a general-model dynamic formulation and a two-layered constrained model predictive control (MPC) strategy to tackle the trajectory tracking problem for tilt-rotor UAVs. After splitting the vehicle’s dynamics into translational and rotational parts, a constrained linear MPC (LMPC) is designed for the translational dynamics to follow a reference trajectory. We formulate the LMPC as a quadratically-constrained quadratic problem that leads to a feasible set-point solution for the rotational control layer without violating the physical constraints. Also, an optimizer is designed to generate a thrust vector, which leverages the vehicle’s full potential via a continuous transition between the rotation in the fuselage and that in tilting rotors. In the second layer, the nonlinear rotational dynamics are approximated via piecewise affine subsystems. A constrained robust switching MPC with mode-dependent dwell time (MDT) is then designed to follow the first layer’s generated trajectories (Euler angles and thrust vectors). By providing admissible MDTs, the rotational dynamics feasibility, stability, and robustness are preserved in the presence of disturbances. Also, by employing an augmented dynamic model, this control design would allow for directly incorporating actuator constraints into the problem formulation. We demonstrate the controller’s performance and effectiveness via simulations.

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Data Availability Statement

The paper’s data are generated using simulation, and we provide all the information needed in the paper to replicate the simulation.

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Funding

We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) Collaborative Research and Development Grant to Drs Gupta and Mehrandezh, 536142-8 and NSERC Discovery Grant to Dr Gupta, RGPIN-2017-05818.

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Authors and Affiliations

  1. Faculty of Engineering Science, Simon Fraser University, 8888 University Dr, Burnaby, BC, Canada

    Abolfazl Eskandarpour, Kamal Gupta & Mohammad Soltanshah

  2. Faculty of Engineering, University of Regina, Regina, SK, Canada

    Mehran Mehrandezh

  3. School of Engineering Science, SFU, Burnaby, BC, Canada

    Mehran Mehrandezh

  4. 4Front Robotics Ltd, Calgary, AB, Canada

    Alejandro Ramirez-Serrano

Authors
  1. Abolfazl Eskandarpour
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  2. Mehran Mehrandezh
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  3. Kamal Gupta
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  4. Alejandro Ramirez-Serrano
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  5. Mohammad Soltanshah
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Contributions

The order of authors reflects the contribution to the research. The first draft of the manuscript was written by Mr. Eskandapour and Drs Gupta and Mehrandezh provided detailed critique, comments and modifications over several iterations that resulted in the final version.

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Correspondence to Abolfazl Eskandarpour.

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Conflict of interest

Mr Eskanadapour, Mr Soltanshah, Drs Gupta and Mehrandezh have no finicncial interests. Dr. Ramirez-Serrano is the Founder and CEO of 4Front Robotics Ltd.

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Eskandarpour, A., Mehrandezh, M., Gupta, K. et al. A constrained robust switching MPC structure for tilt-rotor UAV trajectory tracking problem. Nonlinear Dyn 111, 17247–17275 (2023). https://doi.org/10.1007/s11071-023-08787-y

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