14:00 - 15:00
Online (please contact the organizer Bayu Jayawardhana to receive login details)
Title: Guiding vector fields for robot motion control
Abstract: Using a designed vector field to guide robots to follow a given geometric desired path has found a range of practical applications, such as underwater pipeline inspection, warehouse navigation and highway traffic monitoring. It is thus in great need to build a rigorous theory to guide practical implementations with formal guarantees. It is even so when multiple robots are required to follow predefined desired paths or maneuver on surfaces and coordinate their motions to efficiently accomplish repetitive and laborious tasks.
In this talk, I will introduce guiding vector fields on a Euclidean space and a general Riemannian manifold, for single-robot and multi-robot path following and motion coordination. A guiding vector field is generally composed of two terms: a convergence term which enables the integral curves of the vector field to converge to the desired path, and a propagation term which is tangent to the desired path such that propagation along the desired path is ensured. The guiding vector field is completely determined (up to positive coefficients) by a number of twice continuously differentiable real-value functions (called level functions). The intersection of the zero-level sets of these level functions is the desired path to be followed. Since the guiding vector field is not the gradient of any potential function, and also due to the existence of singular points where the vector field vanishes, the theoretical analysis becomes challenging. Therefore, I will present extensive theoretical results, and elaborate on how to utilize guiding vector fields with variations in practical applications.