Fast and accurate clothoid fitting

An effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is provided. At the beginning the problem is naturally formulated as a system of nonlinear equations with multiple solutions that is generally difficult to solve numerically. All the solutions of this nonlinear system are reduced to the computation of the zeros of a single nonlinear equation. A simple strategy, together with the use of a good and simple guess function, permits to solve the single nonlinear equation with a few iterations of the Newton--Raphson method. The computation of the clothoid curve requires the computation of Fresnel and Fresnel related integrals. Such integrals need asymptotic expansions near critical values to avoid loss of precision. This is necessary when, for example, the solution of interpolation problem is close to a straight line or an arc of circle. Moreover, some special recurrences are deduced for the efficient computation of asymptotic expansion. The reduction of the problem to a single nonlinear function in one variable and the use of asymptotic expansions make the solution algorithm fast and robust.Comment: 14 pages, 3 figures, 9 Algorithm Table

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Homeostatic action selection for simultaneous multi-tasking

Mobile robots are rapidly developing and gaining in competence, but the potential of available hardware still far outstrips our ability to harness. Domain-specific applications are most successful due to customised programming tailored to a narrow area of application. Resulting systems lack extensibility and autonomy, leading to increased cost of development. This thesis investigates the possibility of designing and implementing a general framework capable of simultaneously coordinating multiple tasks that can be added or removed in a plug and play manner. A homeostatic mechanism is proposed for resolving the contentions inevitably arising between tasks competing for the use of the same robot actuators. In order to evaluate the developed system, demonstrator tasks are constructed to reach a goal location, prevent collision, follow a contour around obstacles and balance a ball within a spherical bowl atop the robot. Experiments show preliminary success with the homeostatic coordination mechanism but a restriction to local search causes issues that preclude conclusive evaluation. Future work identifies avenues for further research and suggests switching to a planner with the sufficient foresight to continue evaluation."This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/K503162/1]." -- Acknowledgement