Adaptive Sampling With Multiple Mobile Robots

Adaptive Sampling With Multiple Mobile Robots Bin Zhang and Gaurav S. Sukhatme Abstract— When a scalar field, such as temperature, is to be estimated from sensor readings corrupted by noise, the estimation accuracy can be improved by judiciously controlling the locations where the sensor readings (samples) are taken. In this paper, we solve the following problem: given a set of static sensors and a group of mobile robots equipped with the same sensors, how to determine the data collecting paths for the mobile robots so that the reconstruction error of the scalar field is minimized. In our scheme, the static sensors are used to provide an initial estimate and the mobile robots refine the estimate by taking additional samples at critical locations. Unfortunately, it is computationally expensive to search for the best set of paths that minimizes the field estimation errors and hence the field reconstruction errors as well). We propose a heuristic to find ‘good’ paths for the robots. Our approach first partitions the sensing field into equal gain subareas and then we use a single robot planning algorithm to generate a path for each robot separately. The properties of this approach are studied in simulation. Our approach also implicitly solves a multi-robot coordination/task allocation problem, where the robots are homogeneous and the size of task set might be large. I. INTRODUCTION A sensor actuator network (also a robotic sensor network), which consists of both static and mobile nodes, provides a new tool for measuring and monitoring the environment. On the one hand, with less energy consumed, the static sensor nodes are able to provide high resolution temporal sampling. On the other hand, with the ability to move, the mobile nodes (henceforth) are able to change the spatial distribution of the sensor readings leading (if running the appropriate algorithm) to a high density of readings in important areas. The key challenge is an adaptive sampling problem - come up with trajectories that the robots can follow, sampling alone which will improve the field reconstruction. In [1], we proposed an adaptive sampling algorithm for a system consisting of a set of static sensor nodes and one mobile robot, a robotic boat. The system, part of the NAMOS project at USC (http://robotics.usc.edu/ namos), is used for measuring scalar fields, such as temperature, salinity and chlorophyll concentration. We have shown [1] that by combining optimal experimental design and path planning, we are able to achieve an improved estimation performance, i.e., a lower Integrated Mean Square Error (IMSE) with the same (finite) initial energy available to the mobile robot. This work is supported in part by the National Science Fundation (NSF) under grants CNS-0325875, IIS-0133947, EIA-0121141 and grants CCR- 0120778, ANI-00331481 (via subcontract). B. Zhang binz@usc.edu and G. S. Sukhatme gaurav@usc.edu are with the Robotic Embedded Systems Laboratory, Computer Science Department, Unversity of Southern California, 941 W. 37th Place, Los Angeles, CA 90089, USA In [1], we assume that the scalar field to be reconstructed changes slowly. That is, during the time the mobile robot is sent out for a data collecting tour, the readings from the static sensors are still valid. However, this might not be true in practice since it takes a while for the mobile robot to finish a tour. One way to overcome this drawback is to use multiple mobile robots in parallel to accomplish the task. If we can generate ‘good’ paths for all the mobile robots and let them carry out the sampling task simultaneously, the speedup could be significant. Another advantage of a system with multiple mobile robots is energy efficiency. In many cases, the ideal distribution (leading to the best reconstruction of the field) of the sensor readings contains several clusters. Since normally, we already have static sensors covering the whole sensing field, the mobile robots may just need to take readings within each cluster. If only one mobile robot is deployed, it has to move between the clusters. If multiple mobile robots are used and the number of robots is more than the number of clusters, each robot only needs to stay within a cluster and the energy to move from one cluster to another could be saved. Fig. 1. One of the robotic boats used in the NAMOS project at USC. In this paper, we investigate the problem of adaptive sampling using multiple mobile robots. Specifically, given a set of static sensor nodes deployed uniformly across the sensing field, and a team of mobile robots each with the same energy, how to exploit the information collected by the static sensors and coordinate the motion of the mobile robots so that error associated with the reconstruction of the underlying scalar field is minimized. Here we assume that all the mobile robots have the same energy consumption profile and the underlying scalar field is continuous and has finite second order derivative at any point.