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  • 1.
    Ho, Du
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Some results on closed-loop identification of quadcopters2018Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In recent years, the quadcopter has become a popular platform both in research activities and in industrial development. Its success is due to its increased performance and capabilities, where modeling and control synthesis play essential roles. These techniques have been used for stabilizing the quadcopter in different flight conditions such as hovering and climbing. The performance of the control system depends on parameters of the quadcopter which are often unknown and need to be estimated. The common approach to determine such parameters is to rely on accurate measurements from external sources, i.e., a motion capture system. In this work, only measurements from low-cost onboard sensors are used. This approach and the fact that the measurements are collected in closed-loop present additional challenges.

    First, a general overview of the quadcopter is given and a detailed dynamic model is presented, taking into account intricate aerodynamic phenomena. By projecting this model onto the vertical axis, a nonlinear vertical submodel of the quadcopter is obtained. The Instrumental Variable (IV) method is used to estimate the parameters of the submodel using real data. The result shows that adding an extra term in the thrust equation is essential.

    In a second contribution, a sensor-to-sensor estimation problem is studied, where only measurements from an onboard Inertial Measurement Unit (IMU) are used. The roll submodel is derived by linearizing the general model of the quadcopter along its main frame. A comparison is carried out based on simulated and experimental data. It shows that the IV method provides accurate estimates of the parameters of the roll submodel whereas some other common approaches are not able to do this.

    In a sensor-to-sensor modeling approach, it is sometimes not obvious which signals to select as input and output. In this case, several common methods give different results when estimating the forward and inverse models. However, it is shown that the IV method will give identical results when estimating the forward and inverse models of a single-input single-output (SISO) system using finite data. Furthermore, this result is illustrated experimentally when the goal is to determine the center of gravity of a quadcopter.

  • 2.
    Ho, Du
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    On the equivalence of inverse and forward IV estimators with application to quadcopter modeling2018In: 18th IFAC Symposium on System Identification (SYSID), Proceedings, Elsevier, 2018, Vol. 51, no 15, p. 951-956Conference paper (Refereed)
    Abstract [en]

    This paper concerns the estimation of a dynamic model from two measured signals when it is not clear which signal should be used as input to the model. In this case, both a forward and an inverse model can be estimated. Here, a basic instrumental variable approach is used and it is shown that the forward and inverse model estimators give identical parameter estimates provided that corresponding model structures have been used. Furthermore, it is shown that this scenario occurs when properties of a quadcopter are estimated from accelerometer and gyro signals and, hence, that it does not matter which signal is used as input.

  • 3.
    Ho, Du
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Linder, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Mass estimation of a quadcopter using IMU data2017In: 2017 International Conference on Unmanned Aircraft Systems (ICUAS), June 13-16, 2017, Miami, FL, USA, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1260-1266Conference paper (Refereed)
    Abstract [en]

    In this paper, an approach to estimate the mass of a quadcopter using only inertial measurements and pilot commands is presented. For this purpose, a lateral dynamic model describing the relation between the roll rate and the lateral acceleration is formulated. Due to the quadcopter’s inherent instability, a controller is used to stabilize the system and the data is collected in closed loop. Under the effect of feedback and disturbances, the inertial measurements used as input and output are correlated with the disturbances, which complicates the parameter estimation. The parameters of the model are estimated using several methods. The simulation and experimental results show that the instrumental-variable method has the best potential to estimate the mass of the quadcopter in this setup.

  • 4.
    Ho, Du
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Linder, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Vertical modeling of a quadcopter for mass estimation and diagnosis purposes2017In: Proceedings of the Workshop on Research, Education and Development on Unmanned Aerial Systems, RED-UAS, Linköping, Sweden, 3-5 October, 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017Conference paper (Refereed)
    Abstract [en]

    In this work, we estimate a model of the vertical dynamics of a quadcopter and explain how this model can be used for mass estimation and diagnosis of system changes. First, a standard thrust model describing the relation between the calculated control signals of the rotors and the thrust that is commonly used in literature is estimated. The estimation results are compared to those using a refined thrust model and it turns out that the refined model gives a significant improvement. The combination of a nonlinear model and closed-loop data poses some challenges and it is shown that an instrumental variables approach can be used to obtain accurate estimates. Furthermore, we show that the refined model opens up for fault detection of the quadcopter. More specifically, this model can be used for mass estimation and also for diagnosis of other parameters that might vary between and during missions.

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