Multistep Predictions for Adaptive Sampling in Mobile Robotic Sensor Networks Using Proximal ADMM

This paper presents a novel approach, using multi-step predictions, to the adaptive sampling problem for efficient monitoring of environmental spatial phenomena in a mobile sensor network. We employ a Gaussian process to represent the spatial field of interest, which is then used to predict the field at unmeasured locations. The adaptive sampling problem aims to drive the mobile sensors to optimally navigate the environment while the sensors adaptively take measurements of the spatial phenomena at each sampling step. To this end, an optimal sampling criterion based on conditional entropy is proposed, which minimizes the prediction uncertainty of the Gaussian process model. By predicting the measurements the mobile sensors potentially take in a finite horizon of multiple future sampling steps and exploiting the chain rule of the conditional entropy, a multi-step-ahead adaptive sampling optimization problem is formulated. Its objective is to find the optimal sampling paths for the mobile sensors in multiple sampling steps ahead. Robot-robot and robot-obstacle collision avoidance is formulated as mixed-integer constraints. Compared with the single-step-ahead approach typically adopted in the literature, our approach provides better navigation, deployment, and data collection with more informative sensor readings. However, the resulting mixed-integer nonlinear program is highly complex and intractable. We propose to employ the proximal alternating direction method of multipliers to efficiently solve this problem. More importantly, the solution obtained by the proposed algorithm is theoretically guaranteed to converge to a stationary value. The effectiveness of our proposed approach was extensively validated by simulation using a real-world dataset, which showed highly promising results.