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... then applied to the problem of vanishing point detection. 2.2.1 Vanishing Points. Under perspective projection, lines that are parallel in nature appear to intersect at a common point on the horizon =-=[10]-=-, as shown in Figure 2.6. In the Manhattan world, a set of mutually orthogonal vanishing points can be located. A set of vectors pointing to these orthogonal vanishing points can then be used to const...

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...c characteristics are the camera’s focal length, principal point, and distortion coecients. A common method for determining these parameters is through an iterative optimization process described in =-=[24]-=-. 12 Figure 2.6: Under perspective projection two parallel lines in a scene appear to intersect at a point on the horizon, the vanishing point V. Vector v can be used to form a basis set for a referen...

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...ice. When measurements from multiple devices need to be combined, they must be combined in a common frame of reference. This section contains a brief overview of coordinate transforms as presented in =-=[9]-=-. A reference frame is defined by an origin and a number of orthonormal vectors known as basis vectors. The number of basis vectors depends on the dimensionality of the reference frame. For example, a...

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... the image white and the non-edge pixels black. This black and white image is then processed by 25 a line extraction algorithm based on the Hough transform. These algorithms are discussed in detail in=-=[20]-=-. If a predicted vanishing point is available from the state estimation algorithm, the lines that don’t pass within five degrees of the predicted vanishing point are discarded. If no vanishing point e...

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... planning. As a result, the robot can spend a large amount of time wandering around a relatively small area. Examples of systems that use mapless navigation techniques can be found in [11], [16], and =-=[19]-=-. This research is focused on combining the on-board attitude and velocity measurements of the ARDrone with information extracted from a forward facing video camera to estimate the vehicle’s trajector...

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...ommon solution to all of these problems is to utilize a Kalman filter for state estimation. The following sections provide a brief discussion of the Kalman filter based on Dr. Peter Maybeck’s work in =-=[14]-=- and [15]. 15 The Kalman filter is a recursive estimation algorithm based on Baysian statistics that provides an optimal estimate of the mean and covariance of a stochastic linear system based on all ...

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...’s execution time is described by a function T (n) where n is the size of the input, and there exists some c that satisfies T (n) c f (n) where c > 0 (2.9) then the algorithm is said to be O( f (n))=-=[12]-=-. 2.4 Kalman Filtering Deterministic system models are built from a system of linear, partial dierential equations. In such models, each state can be precisely determined and is a function of the sys...

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...ture route planning. As a result, the robot can spend a large amount of time wandering around a relatively small area. Examples of systems that use mapless navigation techniques can be found in [11], =-=[16]-=-, and [19]. This research is focused on combining the on-board attitude and velocity measurements of the ARDrone with information extracted from a forward facing video camera to estimate the vehicle’s...

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... to future route planning. As a result, the robot can spend a large amount of time wandering around a relatively small area. Examples of systems that use mapless navigation techniques can be found in =-=[11]-=-, [16], and [19]. This research is focused on combining the on-board attitude and velocity measurements of the ARDrone with information extracted from a forward facing video camera to estimate the veh...

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...vehicle to operate over a wider range of floor surfaces. Methods such as feature tracking or “optical sonar” could be included to provide a more robust estimation of velocity and improve localization =-=[13]-=-. 5.1.3 Improved Vanishing Point Algorithm. The vanishing point algorithm used in this research did not take into account the uncertainty of the heading estimate used to predict the location of the va...

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...ues developed to date fit into three categories: 2 map-based navigation, map-building-based navigation, and mapless navigation [8]. This topic area has been broadly surveyed by the authors of [8] and =-=[4]-=-. In map-building-based navigation, the robot builds a geometric model as it observes features in its environment. These techniques work well when the robot has a reliable set of sensors that it can u...

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...s of a total of 27 images collected from nine dierent positions in front of a standard calibration board. The same calibration board is used for 40 each of the drones. The camera calibration toolbox =-=[5]-=- for MATLAB, is used to determine the values of the camera matrix and distortion coecients for each of the drone’s cameras. This procedure is only conducted once prior to running the experiments deve...

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... of map-building techniques is that any uncertainty in the measurement system that is not accounted for is compounded over time. Examples of systems using map-building techniques can be found in [6], =-=[21]-=-, and [23]. A robot using mapless navigation techniques makes navigation decisions based on what the robot is currently observing. These algorithms work well when the robot is simply required to move ...

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...d on the system dynamic model and the available measurements. The state propagation equations require the computation of the matrix exponential function, which has a computational complexity of O(n3) =-=[7]-=-. If the rate the system changes is small compared to the rate at which measurements are available, the first order approximations of the propagation equations can be used. Using the approximations is...

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...back to the ARDrone. The company that developed the ARDrone has released an SDK for a desktop computer system that gives a software developer documented access to the video and telemetry data streams =-=[17]-=-. This requires that any algorithms developed for this project be implemented on the laptop rather than on the drone’s internal processor. Implementing new software to run on the vehicle’s on-board pr...

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...ation of map-building techniques is that any uncertainty in the measurement system that is not accounted for is compounded over time. Examples of systems using map-building techniques can be found in =-=[6]-=-, [21], and [23]. A robot using mapless navigation techniques makes navigation decisions based on what the robot is currently observing. These algorithms work well when the robot is simply required to...

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...e all subject to drift over time. The notion of using visual cues from an on-board camera to aid the on-board inertial sensors is not a new concept. This research follows on research done by Prahl in =-=[18]-=-. 3 Prahl focused on demonstrating that vanishing points extracted from a perspective image could be used to constrain the errors in a Micro-Electro-Mechanical Systems (MEMS) grade Inertial Navigation...

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...1.5° when compared to the tactical grade INS. Prahl’s work demonstrated the feasibility of using vanishing points to constrain the errors inherent in a navigation system based on inertial sensors. In =-=[3]-=-, vanishing point estimation was used to guide an ARDrone through a corridor in a building. Bills [3] developed a real-time algorithm that located the vanishing point at the end of a corridor and used...

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...door environment is a broad and very active area of research. The techniques developed to date fit into three categories: 2 map-based navigation, map-building-based navigation, and mapless navigation =-=[8]-=-. This topic area has been broadly surveyed by the authors of [8] and [4]. In map-building-based navigation, the robot builds a geometric model as it observes features in its environment. These techni...

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...ilding techniques is that any uncertainty in the measurement system that is not accounted for is compounded over time. Examples of systems using map-building techniques can be found in [6], [21], and =-=[23]-=-. A robot using mapless navigation techniques makes navigation decisions based on what the robot is currently observing. These algorithms work well when the robot is simply required to move through an...