Abstract
The paper presents a novel approach by using multi- step predictions to
address the adaptive sampling problem in a resources and obstacles
constrained mobile robotic sensor network to efficiently monitor
environmental spatial phenomena. It is first proposed to employ the
Gaussian process (GP) to represent the spatial field, which can then be
used to predict the field at unmeasured locations. The adaptive sampling
problem aims to drive the mobile sensors to optimally navigate the
environment where the sensors adaptively take measurements of the
spatial phenomena at each sampling step. To this end, a conditional
entropy based optimality criterion is proposed, which aims to minimize
prediction uncertainty of the GP model. By predicting possible
measurements the mobile sensors potentially take in a horizon of
multiple sampling steps ahead and exploiting the chain rule of the
conditional entropy, a multi-step predictions based adaptive sampling
optimization problem is formulated. The objective of the optimization
problem is to find the optimal sampling paths for the mobile sensors in
multiple sampling steps ahead, which then provides their benefits in
terms of better navigation, deployment and data collection with more
informative sensor readings. However, the optimization problem is
nonconvex, complex, constrained and mixed-integer. Therefore, it is
proposed to employ the proximal alternating direction method of
multipliers algorithm to efficiently solve the problem. More
importantly, the solution obtained by the proposed approach is
theoretically guaranteed to be converged to a stationary value.
Effectiveness of the proposed algorithm was extensively validated by the
real- world dataset, where the obtained results are highly promising.