Qualitative Topological Coverage of Unknown Environments by Mobile Robots

Wong, S. C. (2006) Qualitative Topological Coverage of Unknown Environments by Mobile Robots. PhD thesis, The University of Auckland, New Zealand.

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Abstract

This thesis considers the problem of complete coverage of unknown
environments by a mobile robot. The goal of such navigation is for
the robot to visit all reachable surfaces in an environment. The task
of achieving complete coverage in unknown environments can be broken
down into two smaller sub-tasks. The first is the construction of a
spatial representation of the environment with information gathered by
the robot's sensors. The second is the use of the constructed model
to plan complete coverage paths.

A topological map is used for planning coverage paths in this thesis.
The landmarks in the map are large scale features that occur naturally
in the environment. Due to the qualitative nature of topological
maps, it is rather difficult to store information about what area the
robot has covered. This difficulty in storing coverage information is
overcome by embedding a cell decomposition, called slice
decomposition, within the map. This is achieved using landmarks in
the topological map as cell boundaries in slice decomposition. Slice
decomposition is a new cell decomposition method which uses the
landmarks in the topological map as its cell boundaries. It
decomposes a given environment into non-overlapping cells, where each
cell can be covered by a robot following a zigzag pattern. A new
coverage path planning algorithm, called topological coverage
algorithm, is developed to generate paths from the incomplete
topological map/slice decomposition, thus allowing simultaneous
exploration and coverage of the environment.

The need for different cell decompositions for coverage navigation was
first recognised by Choset. Trapezoidal decomposition, commonly used
in point-to-point path planning, creates cells that are unnecessarily
small and inefficient for coverage. This is because trapezoidal
decomposition aims to create only convex cells. Thus, Choset proposed
boustrophedon decomposition. It introduced ideas on how to create
larger cells that can be covered by a zigzag, which may not
necessarily be convex. However, this work is conceptual and lacking
in implementation details, especially for online creation in unknown
environments. It was later followed by Morse decomposition,
which addressed issues on implementation such as planning with partial
representation and cell boundary detection with range sensors. The
work in this thesis was developed concurrently with Morse
decomposition.

Similar to Morse decomposition, slice decomposition also uses the
concepts introduced by boustrophedon decomposition. The main
difference between Morse decomposition and slice decomposition is in
the choice of cell boundaries. Morse decomposition uses surface
gradients. As obstacles parallel to the sweep line are
non-differentiable, rectilinear environments cannot be handled by
Morse decomposition. Also, wall following on all side boundaries of a
cell is needed to discover connected adjacent cells. Therefore, a
rectangular coverage pattern is used instead of a zigzag. In comparison,
slice decomposition uses topology changes and range sensor
thresholding as cell boundaries. Due to the use of simpler landmarks,
slice decomposition can handle a larger variety of environments,
including ones with polygonal, elliptical and rectilinear obstacles.
Also, cell boundaries can be detected from all sides of a robot,
allowing a zigzag pattern to be used. As a result, the coverage path
generated is shorter. This is because a zigzag does not have any
retracing, unlike the rectangular pattern.

The topological coverage algorithm was implemented and tested
in both simulation and with a real robot. Simulation tests proved the
correctness of the algorithm; while real robot tests demonstrated its
feasibility under inexact conditions with noisy sensors and actuators.

To evaluate experimental results quantitatively, two performance
metrics were developed. While there are metrics that measure the
performance of coverage experiments in simulation, there are no
satisfactory ones for real robot tests. This thesis introduced
techniques to measure effectiveness and efficiency of real robot
coverage experiments using computer vision techniques. The two
metrics were then applied to results from both simulated and real
robot experiments. In simulation tests, 100% coverage was achieved
for all experiments, with an average path length of 1.08. In real
robot tests, the average coverage and path length attained were 91.2%
and 1.22 respectively.

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