Significant progress has been achieved for research on coordination of networked
robotic systems in the past few years. Not only many theoretical results, but also
a lot of experimental and practical results have been obtained, covering topics of
consensus algorithms, graph theory, stochastic networks, animal swarming, agent
flocking, robot formation, sensor coverage, information fusion, and so on. In all
networked agent systems, the status of communication link is always a key factor in
system analysis and control law design. As is well-known, the manner of information
exchanging and sharing is determined by the communication topology of an agent
system. Thus the status of communication links is crucial for system stability and
task achievement. As a result, great effort has been devoted to investigation of the
following two problems. One is under what communication link conditions can the
networked system obtain the desired status, such as achieving an average consensus.
The other is how to design a control scheme for agents to meet these conditions
required by the specific practical tasks.
In this thesis, we consider the problem of the coordinated control in a basic group
task, called the rendezvous task. The goal of this task is to design distributed control
algorithms to drive all the agents to arrive at the same position in the work space in a
finite time or as time goes to infinity. Under the condition of limited communication
range, some new approaches have been developed to solve the rendezvous related
problems of multi-agent systems, including the weighted digraph balancing, the coordinated
control with unreliable communication links, and connectivity control with
bounded control inputs. These approaches enjoy significant advantages over existing
ones in literature, for example, less design conservatism and easier implementation in practice. Moreover, some of the problems, such as multi-agent connectivity control
with both unreliable communication and bounded control inputs, to the best of our
knowledge, are considered for the first time in research.
As is well-known, network consensus algorithms have extensive applications in coordination
of robot groups and decision making of agents, such as rendezvous control
and formation control. Among consensus algorithms, the so-called average consensus
algorithm is important for its wide application in signal processing such as sensor
fusion. Since balanced graphs play an important role in the average consensus problem
and many other coordination problems for directed communication networks, we
explore the conditions and algorithms for the digraph balancing problem. It is known
that a digraph can be balanced if and only if it is strongly semiconnected. Based on
this observation, we prove that a directed graph can be balanced if and only if the
null space of its incidence matrix contains positive vectors. Then, based on this result
and the corresponding analysis, two weight balance algorithms have been proposed.
We also point out the relationship between the weight balance problem and the features
of the corresponding underlying Markov chain. Compared with the existing
balancing algorithms, our algorithms are easier to be implemented in practice.
Another topic studied in this thesis is the rendezvous algorithms design problem
for multi-agent systems with discrete time setups, that is, for agents with a waypoint
control manner. Firstly, the agent system with limited communication ranges
and reliable communication is considered. We present a novel rendezvous algorithm
framework - the combination framework, which is named after the term convex combination
in computational geometry. The convergence of the proposed algorithms is
proved based on the novel tools from the recent results in graph theory and consensus
study. It has been observed that the extensively studied circumcenter algorithm can
be considered as a special case of the combination framework. Secondly, we investigate
the coordination problem of multiple agents with limited communication ranges
and unreliable communications. A novel coordination algorithm via the so-called
proximity graph is developed so that the agent group can achieve rendezvous when
the communication links satisfy an ergodic assumption. The convergence proof of the algorithm is established based on the tools from rooted graph theory.
The rendezvous algorithms design problem for multi-agent systems with continuous
time setups is also considered. Since in almost all existing studies on connectivity
control, control inputs may go unbounded when agents tend to go out of the
communication range of their neighbors, our attention is focused on design of connectivity
control laws with bounded inputs for multi-agents with limited communication
ranges. A general potential based control law is investigated and sufficient conditions
for preserving connectivity are presented. A necessary condition for preserving connectivity
with bounded control inputs is then obtained. Based on this condition, a
novel control law with bounded inputs is proposed and the selection of appropriate
parameters for the corresponding control law is also discussed. Obviously, compared
with the existing control design approaches, the proposed control law with bounded
inputs is easier to be implemented in practice.
Finally, we revisit the rendezvous algorithms with way-point setup in the presence
of unreliable communication and the connectivity preserving control approach
with bounded inputs. To the best of our knowledge, this is the first time to study
the rendezvous problem of multi-agent systems with limited communication range,
unreliable communication, and bounded control inputs. Combining the reference
point approach and the indicating function approach, we explicitly define a virtual
neighbor for each pair of proximity neighbors, and develop a connectivity control law
with bounded input for each agent. As a result, the proximity graph connectivity of
the agent group has been preserved with controls that are easy for implementation
in practice. It is also proved that the proposed control law can drive the agents to
rendezvous.
| Date of Award | 15 Jul 2011 |
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| Original language | English |
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| Awarding Institution | - City University of Hong Kong
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| Supervisor | Gang Gary FENG (Supervisor) |
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