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 thesis, we propose and study a specific class of vector field, called guiding
vector fields, on the Euclidean space and a general Riemannian manifold, for singlerobot
and multirobot 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
realvalue functions (called level functions). The intersection of the zerolevel 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, in Part I of the thesis, we derive extensive theoretical
results. And then in Part II, we elaborate on how to utilize guiding vector fields
with variations in practical applications.
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 thesis, we propose and study a specific class of vector field, called guiding
vector fields, on the Euclidean space and a general Riemannian manifold, for singlerobot
and multirobot 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
realvalue functions (called level functions). The intersection of the zerolevel 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, in Part I of the thesis, we derive extensive theoretical
results. And then in Part II, we elaborate on how to utilize guiding vector fields
with variations in practical applications.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  8Oct2021 
Place of Publication  [Groningen] 
Publisher  
DOIs  
Publication status  Published  2021 