The typical inverse modeling approach involves finding a partial di?®erential
equation and corresponding boundary conditions to express the evolution
of the field variables in the 4D position-time space, based on a set of observation
samples. In this context, measurement uncertainty has also been
addressed using Kalman-filter estimation [3].
Some mobile robot navigation research has been addressed using potential
fields. Obstacle avoidance or goal attainment schemes often use penalty
functions to bend feasible paths around obstacles, or to reposition holonomic
or nonholonomic wheeled robots at an end point attractor, such as it was
originally presented in [26] and [24]. Path planning algorithms for mobile
robots now routinely employs potential fields [27, 44, 45]. In [31], an artifi-
cial repelling field is used to reposition mobile sensor nodes within an area
of interest. In [59] robot group uniformity is maintained through the use of
artificial potentials. In Robocup 2002, the Sony legged league was won using
a heuristic algorithm with shared potential functions [52]. The potentials are
formed from estimates of the environment together with control forces, and
local stability analysis is provided using Lyapunov functions. As with many
optimization schemes, only convergence to a local minima can be guaranteed
[23, 38, 51].
Extensive research has also been done in the context of ad-hoc sensor networks,
in particular in finding heuristic solutions for network routing [19],
deployment [22, 29], and congestion control [35, 55].
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