MPS: A New Method for Selecting the Stable Closed-Loop Equilibrium Attitude-Error Quaternion of a UAV During Flight

TL;DR

These results highlight the superior capabilities of the proposed MPS-based scheme when compared to a benchmark controller commonly used in aerial robotics, as the PFM used to quantify the cost of flight is reduced by 60.30 %, on average.

Abstract

We present model predictive selection (MPS), a new method for selecting the stable closed-loop (CL) equilibrium attitude-error quaternion (AEQ) of an uncrewed aerial vehicle (UAV) during the execution of high-speed yaw maneuvers. In this approach, we minimize the cost of yawing measured with a performance figure of merit (PFM) that takes into account both the aerodynamic-torque control input and attitude-error state of the UAV. Specifically, this method uses a control law with a term whose sign is dynamically switched in real time to select, between two options, the torque associated with the lesser cost of rotation as predicted by a dynamical model of the UAV derived from first principles. This problem is relevant because the selection of the stable CL equilibrium AEQ significantly impacts the performance of a UAV during high-speed rotational flight, from both the power and control-error perspectives. To test and demonstrate the functionality and performance of the proposed method, we present data collected during one hundred real-time high-speed yaw-tracking flight experiments. These results highlight the superior capabilities of the proposed MPS-based scheme when compared to a benchmark controller commonly used in aerial robotics, as the PFM used to quantify the cost of flight is reduced by 60.30 %, on average. To our best knowledge, these are the first flight-test results that thoroughly demonstrate, evaluate, and compare the performance of a real-time controller capable of selecting the stable CL equilibrium AEQ during operation.

Figures (6)

• Figure 1: Photograph of the UAV platform used in the flight tests, the Crazyflie 2.1, and depiction of the frames of reference used to describe its kinematics.$\boldsymbol{\mathcal{N}} = \{\boldsymbol{n}_1, \boldsymbol{n}_2, \boldsymbol{n}_3\}$ denotes the inertial frame of reference; $\boldsymbol{\mathcal{B}} = \{\boldsymbol{b}_1, \boldsymbol{b}_2, \boldsymbol{b}_3\}$ denotes the body-fixed frame of reference, whose origin coincides with the center of mass of the UAV.
• Figure 2: Block Diagram of the MPS-based Control Scheme. The MPS algorithm receives as inputs the attitude-reference quaternion, measured quaternion, angular-velocity reference, and measured angular velocity; then, it selects the value of $\sigma$ and sends it to the attitude controller, which computes the aerodynamic-torque control input, $\boldsymbol{\tau}_{\space\sigma}$. Last, the actuator mapping receives as input $\boldsymbol{\tau}_{\space\sigma}$ and maps it into the pulse width modulation (PWM) signals, $e_j$, for $j\in\{1,2,3,4\}$, that excite the DC motors of the flyer as described in Ying_ICRA_2016.
• Figure 3: Experimental setup used in the flight tests. Illustration of the flying arena and signals-and-systems diagram. The setup is equipped with a six-V5-camera Vicon motion-capture system, which is used to measure the position and attitude of the UAV during flight at a rate of $500\,\text{Hz}$. These data are then sent, via the Vicon PoE server, to the Vicon computer, which records and transmits the data to the main computer using the virtual-reality peripheral network (VRPN) interface. Last, the main computer transmits the position and attitude real-time data to the UAV, using the Python-Crazyflie-Client library, via radio at approximately $50$ Hz. The UAV transmits the signals generated by the online controller to the main computer using radio communication.
• Figure 4: Experimental signals corresponding to two different attitude references and two different controllers.(a) Real-time yaw reference and measured yaw signal for the parameter pair $\{2\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},170^\circ\}$ and benchmark controller. (b) Real-time yaw reference and measured yaw signal for the parameter pair $\{2\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},170^\circ\}$ and MPS-based controller. (c) Real-time $\Delta\Gamma$ and $\sigma$ signals corresponding to the case in (b), i.e., $\{2\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},170^\circ\}$. (d) Real-time yaw reference and measured yaw signal for the parameter pair $\{4\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},90^\circ\}$ and benchmark controller. (e) Real-time yaw reference and measured yaw signal for the parameter pair $\{4\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},90^\circ\}$ and MPS-based controller. (f) Real-time $\Delta\Gamma$ and $\sigma$ signals corresponding to the case in (e), i.e., $\{4\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},90^\circ\}$.
• Figure 5: Two flight tests performed using the MPS-based controller and benchmark scheme.(a) Photographic sequence from video footage of a flight test performed using the benchmark controller and the attitude reference defined by the parameter pair $\{2\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},170^\circ\}$. The third frame corresponds to the instant when the yaw reference is set to $0^\circ$; in this case, the benchmark controller selects $\sigma=+1$, which produces a reverse rotation and performance degradation. (b) Photographic sequence from video footage of a flight test performed using the proposed MPS-based controller and the attitude reference defined by the parameter pair $\{2\cdot\boldsymbol{b}_3\,\text{rad}\cdot\text{s}^{-1},170^\circ\}$. The third frame corresponds to the instant when the yaw reference is set to $0^\circ$; in this case, the MPS-based method selects $\sigma=-1$, which maintains the current direction of rotation and, thus, leads to high flight performance. These two experiments can be viewed in the accompanying supplementary movie.