Guiding Vector Fields for Robot Motion Control

Using a designed vector field to guide robots to follow a given geometric desiredpath has found a range of practical applications, such as underwater pipelineinspection, warehouse navigation and highway traffic monitoring. It is thus ingreat need to build a rigorous theory to guide practical implementations withformal guarantees. It is even so when multiple robots are required to followpredefined desired paths or maneuver on surfaces and coordinate their motionsto efficiently accomplish repetitive and laborious tasks.In this thesis, we propose and study a specific class of vector field, called guidingvector fields, on the Euclidean space and a general Riemannian manifold, for singlerobotand multi-robot path following and motion coordination. A guiding vectorfield is generally composed of two terms: a convergence term which enablesthe integral curves of the vector field to converge to the desired path, and apropagation term which is tangent to the desired path such that propagation alongthe desired path is ensured. The guiding vector field is completely determined(up to positive coefficients) by a number of twice continuously differentiablereal-value functions (called level functions). The intersection of the zero-level setsof these level functions is the desired path to be followed. Since the guiding vectorfield is not the gradient of any potential function, and also due to the existence ofsingular points where the vector field vanishes, the theoretical analysis becomeschallenging. Therefore, in Part I of the thesis, we derive extensive theoreticalresults. And then in Part II, we elaborate on how to utilize guiding vector fieldswith variations in practical applications.