Relative Position Sensing by Fusing Monocular Vision
and Inertial Rate Sensors
Andreas Huster
July 2003
A dissertation submitted to the department of Electrical Engineering
and the Committee on Graduate Studies of Stanford University
in partial fulfillment of the requirements
for the degree of Doctor of Philosophy.

Abstract
Sensing the relative position between a robot and objects in its
environment is a core requirement for many robot tasks and is an area
of active research. This dissertation describes the development of a
new, robust, relative-position sensing strategy suitable
for unstructured and unprepared environments. Underwater
manipulation, the use of underwater vehicles to perform object
manipulation tasks in the ocean, is the particular application that
motivated this research. Although many relative position sensing
systems have already been developed, achieving the level of robustness
that is required for operation in the underwater environment is
very challenging.
The new sensing strategy is based on fusing bearing measurements from
computer vision and inertial rate sensor measurements. These
measurements are fused to compute the relative position between a
moving observer and a stationary object. Inertial rate sensors are
composed of accelerometers and rate gyros.
The requirements on the vision system have been chosen to be as simple
as possible: tracking a single feature on the object of interest with
a single camera. This is equivalent to a bearing measurement.
Simplifying the vision system has the potential to create a more
robust sensing system. The relative position between a moving
observer and a stationary object is observable if these bearing
measurements, acquired at different observer positions, are combined
with the inertial rate sensor measurements, which describe the motion
of the observer.
The main contribution of this research is the development of a new,
recursive estimation algorithm which enables the sensing strategy by
providing a solution to the inherent sensor fusion problem. Fusing
measurements from a single bearing sensor with inertial rate sensor
measurements is a nonlinear estimation problem that is difficult to
solve with standard recursive estimation techniques, like the Extended
Kalman Filter (EKF). A new, successful estimator design---based on
the Kalman Filtering approach but adapted to the unique requirements
of this sensing strategy---was developed. The new design avoids the
linearization of the nonlinear system equations. This has been
accomplished by developing a special system representation with a
linear sensor model and by incorporating the Unscented Transform to
propagate the nonlinear state dynamics.
The dissertation describes how the sensing strategy can be implemented
to determine the relative position between a moving observer and a
stationary object. A demonstration task is developed that illustrates
how a real-time implementation of this sensing strategy can be
incorporated into the closed-loop control of an autonomous robot to
perform an object manipulation task. The performance of the sensing
strategy is evaluated with this hardware experiment and extensive
computer simulations. Centimeter-level position sensing for a typical
underwater vehicle scenario has been achieved.

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