In this chapter we have introduced the mathematical background relevant to the work in this thesis. Specifically we introduced the notation and representations for rigid body transformations. We introduced the pinhole camera and FOV lens distortion models and discussed briefly how these are used to model observations made using a 2D camera. We then went on to discuss relevant topics in computer vision including feature extrac- tion, descriptors and feature tracking. The computer vision component of the chapter concluded with a look at the important topic of Structure from Motion in particular the PnP, triangulation and bundle adjustment problems and their solutions. We discussed how these solutions could be used for both incremental motion estimation (localisation) and recovering the 3D structure of an environment (mapping). The chapter concluded with a look at two related topics, State Estimation and Control. We introduced two important algorithms in these domains, the Kalman Filter and PID controller, and dis- cussed how they could be used in the context of autonomous navigation of MAVs.
Autonomous Navigation for
Micro Aerial Vehicles
One of the most difficult challenges in autonomous navigation is the localisation problem, localisation solutions for MAVs can be divided into two categories: (i) those that provide absolute positioning directly such as GPS, or a motion capture system and (ii) those that provide positioning via Simultaneous Localisation and Mapping (SLAM). In this chapter we will explore the related work in both areas; however given the focus of this thesis is visual navigation a large portion of this chapter is dedicated to exploring the related work in that area.
3.1
Absolute Positioning Approaches
Absolute position systems can be divided into two categories, radio based (this includes system such as GPS) and vision based (this includes motion capture systems). This section explores the related work of these systems and their application to MAV navi- gation.
3.1.1 Radio Based Navigation
The most common radio based navigation solution for autonomous vehicle is the Global Position System (GPS). The GPS system consists of a network of satellites in Medium Eath Orbit (MEO) which is an altitude of approximately 20,200 kilometres. Each satel- lite is equipped with an atomic clock which is synchronised with the clocks on-board other satellites and the ground. The satellites continuously broadcast a time coded sig- nal which includes the current position of the satellite. A receiver on the ground can use the time coded signal to calculate the distance between satellite and receiver. Typical GPS receivers do not include very precise clocks therefore it is also necessary for the receiver to compute it clock drift relative to the satellites. This means the system must compute four unknowns (3D position and clock dirft) which requires a signal from four or more satellites.
Figure 3.1: The two main sources of GPS interference, atmospheric (left) and multi- path (right) [19].
There has been much success both in research and industrial work with MAVs using GPS-based autonomous navigation. Several successful industrial applications such as aerial surveillance and mapping, aerial photography and even autonomous delivery rely on GPS for autonomous navigation. GPS navigation has been used for autonomous ground robots [53, 89] and for MAVs as part of the STARMAC project [44, 47] and even a 27 gram MAV platform [94]. There are two major drawbacks to GPS-based naviga- tion, namely the precision/reliability and the overall coverage of GPS navigation. The precision of GPS-based system is dependant on the sophistication of the GPS receivers used, most off-the-shelf UAS systems make use of GPS receivers with a best-case (i.e. clear line of sight to a number of GPS satellites) precision of 2.5 metres. GPS is pri- marily affected by two sources of interference see Figure 3.1. Atmospheric conditions both in the ionosphere and the troposphere can perturb the very weak signal sent by the orbiting satellites. However for MAVs multi-path interference has a much larger effect, that is where some or all of the signals do not travel directly to the receiver but instead are reflected off surrounding environmental features such as mountains and tall buildings. This can reduce the accuracy of GPS to up to 26 metres.
Differential GPS systems can improve this accuracy to 0.1 centimetres. Differential GPS is simply put another GPS receiver placed at a known location, this receiver will calculate it’s position based on satellite signals and compare this to it’s known position. The error between these two data points corresponds to error induced by local atmo- spheric conditions. This correction can then be broadcast to neighbouring (mobile) GPS receivers allowing them to correct for atmospheric errors. Even with the atmospheric error correction provided by Differential GPS, the sensitivity to multi-path interference and lack of coverage indoors makes GPS based navigation only applicable for large open area navigation.
Other radio based navigation solutions are also possible; in recent years with the growth in coverage of wireless local area networks (WLAN), radio based localisation using WLAN has become a popular research topic [8, 48, 88, 91]. In contrast to GPS which is purpose built for navigation WLAN is not. This means that is typical WLAN does not broadcast precisely timestamped signals that include the transmitters position, as GPS does. This means most WLAN approaches make use of the signal strength rather
than time of flight to determine the distance between the base station and receiver. The relationship between signal strength and distance can be modelled relatively easily when receiver and base station have line of sight between one another. However without line of sight modelling this relationship becomes difficult as the propagation of reflected wireless signals is dependant on many factors some of which include the properties of the occluding material and the frequency and signal strength of the base station.
Another radio based localisation technology is Ultra-Wide-Band (UWB) radio [1, 34, 61]; UWB systems are dedicated navigation systems, similar to GPS in that they broadcast time stamped messages and make use time of flight for distance measurements. A UWB localisation system typically consists of a number of base stations at fixed locations which broadcast time coded signals to moving receivers. UWB radio has several advantages over WLAN based systems, for example signals are transmitted over a larger frequency bandwidth (up to 500 Mhz) which allows the signals to penetrate barriers more easily (as the signal occupies a larger frequency spectrum it is more likely that some part of the signal will penetrate a barrier). While many other positioning techniques are possible one of the most accurate for UWB are the time-based approaches. In cases where the base station are synchronised a time of arrival scheme similar to GPS can be used. The use of a time of flight-based distance measurement approach produce more accurate and reliable distance measurements than signal strength as used with WLAN positions. The typical range of UWB systems is 300 metres in outdoor environment and 100 metres in indoor environments and their accuracy in with the range of 0.1 to 0.15 metres. UWB localisation has been applied to both ground-based robots [57] and aerial vehicles [7, 70].
3.1.2 Motion Capture Based Navigation
Another approach to autonomous navigation indoors is the use of high speed motion capture systems such as Vicon and Optitrack (see Figure 3.2). These systems use a set of high speed infra-red cameras coupled with infra-red emitters to precisely track reflective markers which can be attached to any object. Motion capture systems provide sub-millimetre precision at very high update rate 100-200 Hertz (Hz) which makes them very useful for the precise control of autonomous MAVs. In addition given that multiple sets of markers can be tracked these systems enable the autonomous indoor navigation for multiple MAVs. This facilitates research into a number of interesting applications such as : (i) aggressive manoeuvres [76], (ii) formation flight [59], (iii) object transportation [59] and (iv) bridge construction [3].
There are several drawbacks to using motion capture systems, primarily that entry level systems cost well over £30, 000. Additionally these systems have limited scalability and coverage, meaning they can only track a fixed number of MAVs (4-6 depending upon the configuration) and cover a limited area (for accurate localisation the MAV has to be within view of at least 3 cameras). This limits the autonomy of a MAV using such a system for localisation.
Figure 3.2: An example of using motion capture to control a palm sized Crazyflie Nano MAV in the University of Liverpool’s smARTLab.