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Adaptive Sampling for Multi Robot Wide Area Prospecting Kian Hsiang Low Geoffrey J Gordon Pradeep Khosla October 2005 CMU RI TR 05 51 October 2005 Robotics Institute Carnegie Mellon University Pittsburgh Pennsylvania 15213 c Carnegie Mellon University John M Dolan Abstract Prospecting for in situ mineral resources is essential for establishing settlements on the Moon and Mars To reduce human effort and risk it is desirable to build robotic systems to perform this prospecting An important issue in designing such systems is the sampling strategy how do the robots choose where to prospect next This paper argues that a strategy called Adaptive Cluster Sampling ACS has a number of desirable properties compared to conventional strategies 1 it reduces the total mission time and energy consumption of a team of robots and 2 returns a higher mineral yield and more information about the prospected region by directing exploration towards areas of high mineral density thus providing detailed maps of the boundaries of such areas Due to the adaptive nature of the sampling scheme it is not immediately obvious how the resulting sampled data can be used to provide an unbiased low variance estimate of the regional mineral density This paper therefore investigates new mineral density estimators which have lower error than previously developed estimators they are derived from the older estimators via a process called Rao Blackwellization Since the efficiency of estimators depends on the type of mineralogical population sampled the population characteristics that favor ACS estimators are also analyzed The ACS scheme and our new estimators are evaluated empirically in a detailed simulation of the prospecting task and the quantitative results show that our approach can yield more minerals with less resources and provide more accurate mineral density estimates than previous methods I Contents 1 Introduction 1 2 Robot Supervision Architecture 2 3 Adaptive Cluster Sampling 3 4 Unbiased ACS



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