Real-time Flight Control: Embedded Sensor Calibration and Data Acquisition

Aircraft must balance their forces and moments through aerodynamics and propulsion systems. As shown in Figure 1a, a fixed-wing aircraft balances four forces in steady flight: aerodynamic lift, aerodynamic drag, propulsion system thrust, and weight. Fixed-wing aircraft either pitch up or down, to climb or descend, and roll either to the left or to the right to turn to a new heading.

As shown in Figures 1b and 1c, a hovering multicopter must balance the upward thrust generated by the thruster units with its weight, while a multicopter flying at an appreciable speed rotates so that its thrust balances aerodynamic drag. To achieve stable flight, aircraft must also balance moments about all three axes. Rotations are defined with the following conventions for three-dimensional (3D) flight:

1. Roll (Φ) – rotation about the axis pointing toward the front of the vehicle (x), resulting in side to side motion
2. Pitch (θ) – rotation about the axis running from left to right (y), resulting in a forward and backward tilting motion
3. Yaw (Ψ) – rotation about the vertical axis (z), which results in a heading angle change

A flight control system issues motor and control surface commands that stabilize the aircraft roll, pitch, yaw attitude, and balance forces, as shown in Figure 1. Commands must be updated reliably and in real-time to assure the aircraft can correct for disturbances such as wind. To achieve and maintain a prescribed attitude, the control system must maintain an accurate estimate of the aircraft’s attitude (roll, pitch, yaw) as well as its changes in attitude over time (angular velocities). Because forces such as lift and drag critically depend on airflow, additional sensing is required to determine airspeed (V de Figure 1) and airflow direction with respect to the aircraft. To follow a prescribed trajectory, the aircraft must also sense its position through a sensor such as a GPS, Aircraft sensors enabling flight control are shown in Figure 2.

Once data is acquired from sensors, the signals are filtered to reduce the impact of noise and outliers on processed data quality. Then the data is aggregated into a full estimate of aircraft state, including 3D positions, linear velocities, orientation (attitude), and angular velocities. The aircraft state is sent to the flight controller, which then updates commands to the aircraft thrusters and/or control surfaces for fixed-wing configurations.

Aircraft Sensors

Aircraft, including fixed-wing and multicopter, rely on a sensor suite known as an inertial measurement unit (IMU) to determine 3D aircraft attitude and angular velocity. An IMU typically consists of three sensor types: accelerometers to measure linear acceleration; rate gyroscopes (gyros) to measure angular velocity; and magnetic field sensors to measure the direction and strength of the local magnetic field. A three-axis IMU, as illustrated in Figure 3, is configured with a three-axis reference coordinate system. A total of nine sensing elements, including three accelerometers, three rate gyros, and a three-axis magnetometer, provide independent measurements of linear acceleration (ax, ay, and az), angular velocity (ωx, ωy, ωz), and magnetic field (mx, my, and mz). An IMU is typically mounted near the aircraft’s center of gravity (CG), with the sensor axes aligned with the aircraft body axes, as shown in Figure 3.

Small IMU sensor packages are now available at a low cost. Each sensor emits an analog voltage, which can then be processed locally or sent directly to a flight computer, as described below. An integrated inertial navigation system (INS) combines an IMU with a GPS receiver. GPS units internally translate satellite signals to estimates of inertial position on the Earth, e.g., latitude, longitude, altitude, and 3D linear velocity of the aircraft represented in a local coordinate frame such as NED (North-East-Down). An IMU alone is capable of stabilizing aircraft attitude; however, with an INS, an aircraft can track a prescribed flight trajectory.

Because aerodynamic forces are strongly dependent on airspeed, V, fixed-wing aircraft require measurements of airflow for good flight controller performance. Flow measurements are collected using an air data system (ADS). In small-scale aircraft, often only airspeed is measured. In high-performance aircraft, measurements of flow direction and speed are required.

A basic pitot-static system [4], which is used to measure aircraft airspeed, V, is shown in Figure 4. The pitot tube itself has a central hole that faces directly into the oncoming flow. This hole is connected through a central tube to one port of a differential pressure sensor. Four holes equally spaced around the outside of the pitot tube are connected through a single peripheral tube to the other port of the differential sensor. The central tube measures stagnation or total pressure, P_T, which is the air pressure at a point where flow velocity is zero. The outer tube measures static air pressure, P_S, which is associated with the flow moving at freestream airspeed, V. Combined pressure from the four peripheral ports averages the four static pressure measurements to account for flow misalignment with the pitot tube as well as minor flow turbulence. The airspeed is computed from Bernoulli’s equation given atmospheric density ρ:

    (1)

Dynamic (differential) pressure measured by a pitot tube system is then given by:

    (2)

Airspeed, V, is then given by:

    (3)

A five-hole probe [5], shown in Figure 5, provides the ability to measure the freestream flow angle and speed. This probe, an extension of the baseline pitot-static system, also measures P_T from a central tube. Four other ports above and/or below and to either side of the central total pressure port typically connect to absolute pressure sensors. The angle of attack, α, matching the pitch angle θ during level flight, is computed from a function comparing the top and bottom pressure measurements:

    (4)

The calibration function, , is determined by placing the five-hole probe into a (small) wind tunnel, and then curve fitting the wind tunnel pressure data over a series of known angle of attack conditions between the minimum and maximum expected flight values for α. Similarly, side flow (sideslip) angle β, which is typically small, is computed from a function comparing the left and right pressure measurements:

    (5)

Similarly, the calibration function  is determined by curve fitting wind tunnel pressure data collected over a series of known sideslip angle conditions between minimum and maximum expected flight values for β.

The IMU and ADS enable an aircraft to sense its attitude, angular velocities, and airspeed (and potentially direction). A GPS unit, typically connected either through an off-the-shelf INS or a separate GPS-only interface to a flight computer, provides measurements of inertial position and velocity. A GPS unit [6] aggregates time-of-arrival data from multiple satellites to estimate the receiver position from triangulation. Baseline GPS has a position accuracy on the order of 1-3 meters in open areas; most UAVs host baseline GPS units. GPS can also receive Wide Area Augmentation System (WAAS) signals [7] from a signal source in a local region that reduce position estimation errors to under a meter. GPS positions are measured in Earth’s coordinate system, typically LLA (Latitude, Longitude, Altitude). GPS also provides a local measurement of an aircraft’s 3D velocity relative to the Earth in NED (North-East-Down) or ENU (East-North-Up) Earth-based coordinate systems. GPS units internally compute position and velocity information and communicates these values to an onboard flight computer.

GPS allows an aircraft to follow a flight plan described by waypoints in an Earth-fixed coordinate frame. Many missions, e.g., small UAV surveillance, require the UAV to navigate with respect to a local environment. For this purpose, the UAV may still carry a GPS receiver but will rely on onboard sensors such as cameras, radar, or Lidar, to navigate with respect to a local environment. Many researchers have studied UAV navigation with respect to a local environment using onboard sensors, such as in applications of search and rescue [8] and for small UAV localization in an urban canyon environment where GPS signal reception is unreliable [9].

Data Acquisition (DAQ) and Sensor Calibration

Each IMU and ADS sensor emits an analog voltage that passes through an Analog-to-Digital (A/D) converter then a digital processor or microprocessor. A/D conversion can be performed directly on the flight computer, or a dedicated microprocessor may perform A/D conversion and retransmit data. Because signal is lost over long signal wires, it is advantageous to perform A/D conversion close to the sensor signal source. Therefore, many modern IMUs embed a microprocessor and transmit digitized voltage readings through a (lossless) serial connection. For example, the MPU-9250 hosts the nine IMU sensors (3 accelerometers, 3 rate gyros, 3-axis magnetometer) and a microprocessor on a single printed circuit board. Collected data is then distributed to the flight computer over an I2C serial connection [10].

In this demonstration, we illustrate the use of an IMU with I2C connection and the direct collection of analog data on the flight computer using two embedded computing platforms: a Diamond Systems Athena II and a Beaglebone Blue. They were selected due to their diverse hardware interface capabilities. Both are lightweight and have a small form factor appropriate for installation on a small UAV. The Athena II is a well-established product; its strength is in high-resolution (16-bit A/D) data resolution, which with the lightweight QNX Neutrino real-time operating system, assures reliable data acquisition up to 3 kHz. The Beaglebone Blue, running a variant of Linux, has a lower resolution A/D converter, but it interfaces to a variety of serial devices, including I2C. The Beaglebone is low-cost, has a faster processor, and is compatible with numerous Linux-based applications. It is, therefore, a better general-purpose choice for low-cost experiments. The Athena II is used in this experiment to demonstrate its utility in directly capturing sensor data with application to research-based flight data acquisition, such as in a flexible wing experimental UAV platform [11].

Before deployment for flight control, IMU and ADS sensors must be properly calibrated. End-to-end calibration accounts for voltage scaling and bias as the physical sensor output passes through the A/D converter to the computer and then is translated to MKS (meter-kilogram-second) units:

    (6)

where the acquired signal,  in volts, is offset by bias voltage, b, and is then scaled by factor m to an MKS unit reading, . IMUs with a serial interface may provide options to collect readings in either volts or MKS units based on the manufacturer’s calibration. Directly acquired sensor data for IMU or ADS requires reading an integer value from each A/D channel (in counts), which is translated to a floating-point voltage reading based on the A/D converter’s resolution (e.g., 12 bits or 16 bits) and full-scale voltage range. To account for imprecisions in both default sensor calibrations and the A/D conversion process, it is typically advantageous to calibrate IMU and ADS once fully integrated into the DAQ pipeline.

For the IMU, accelerometer voltages are scaled to a reading relative to zero acceleration in meters per second squared, and rate gyro voltages are scaled to a reading relative to zero angular velocity in radians per second. Calibration of a magnetometer requires a more careful process that accounts for local disturbance sources [12]. In this experiment, we illustrate the use of a rate table to calibrate rate gyros and accelerometers. Note that in complex environments, a magnetometer may not be accurate despite best efforts at calibration; in these cases, heading is determined through alternate means, e.g., consideration of GPS velocity vector heading.

Signal Filtering

Sensor signals inevitably contain electrical noise as well as noise from physical sources, such as in-flight structural vibration. Such noise typically takes the form of single outliers in the data and high-frequency noise; both can be attenuated with low-level signal filtering. Two commonly applied sensor signal filters [13] are applied in our experiments: a moving average filter to attenuate high-frequency noise and a median filter to reject signal outliers from single-channel sequential signals, or “salt and pepper,” from images. The simple moving average estimates the current signal as the mean value of the most recently acquired n data values in a real-time control scenario; in post-processing, each signal is estimated from an equal number of previous and future data points to avoid time-shift effects. The real-time unweighted moving average estimate usable for flight control is therefore given by:

    (7)

where  is a single sensor data value at time step k-i and  is the moving average estimate for time step k. A large value for n effectively eliminates high-frequency noise but has the disadvantages of introducing time delay into signal estimates. It can also filter out real, transient signals. To minimize the impact of old data on moving average estimates, data is often linearly or exponentially weighted so that the most recent data points influence moving average results more than older data values.

The median filter for single-channel signals is straightforward. The last d raw data values are collected in an array or set, then the median, i.e., the middle value or average of the two middle values given an even number of values, is returned:

    (8)

where  is a single sensor data value and  is the median filtered output at time step k. Data subject to both high-frequency noise and outliers are often sequentially processed through both median and moving average filters. To prevent outliers from influencing the moving average result, the median filter is typically applied first. Values for n and d are user-defined but are typically in the range [3, 10] unless data is acquired at much high rates than it is used in control decisions.