Evaluation of Gaussian Processes for Large Scale Terrain Modeling Shrihari Vasudevan, Fabio Ramos, Eric Nettleton and Hugh Durrant-Whyte Australian Centre for Field Robotics The University of Sydney, NSW 2006, Australia {s.vasudevan,f.ramos,e.nettleton,hugh}@acfr.usyd.edu.au Abstract This paper addresses the problem of large scale terrain modeling for a mobile robot. Build- ing a model of large scale terrain that can ad- equately handle uncertainty and incomplete- ness in a statistically sound way is a challeng- ing problem. A recent work [Vasudevan et al., 2009] proposed non-stationary Gaussian pro- cesses (GP’s) based on the neural network ker- nel as a solution to the problem. GP’s natu- rally provide a multi-resolution representation of space, incorporate and handle uncertainty aptly and cope with incompleteness of sensory information. GP regression techniques may be applied to estimate and interpolate (to fill gaps in occluded areas) elevation information across the field. This paper presents results evaluating GP’s for the problem of large scale terrain mod- eling. Extensive cross validation experiments were conducted on real world datasets obtained from different mine sites. These experiments are used to report statistically representative results that characterize the performance of the GP method for large scale and complex terrain modeling. They also compare its performance with grid based representations using many dif- ferent interpolation techniques as well as trian- gulated irregular networks (TIN’s); these rep- resent the state-of-the-art in large scale terrain modeling. 1 Introduction and Related Work Large scale terrain mapping is a difficult problem with wide-ranging applications in robotics, from space ex- ploration to mining and more. For autonomous robots to function in such high-value applications, an efficient, flexible and high-fidelity representation of space is criti- cal. The key challenges posed by this problem are that of dealing with the problems of uncertainty, incompleteness and handling unstructured terrain. Uncertainty and in- completeness are virtually ubiquitous in robotics as sen- sor capabilities are limited. The problem is magnified in a field robotics scenario due to the significant scale of many domains. State-of-the-art terrain representations used in appli- cations such as mining, space exploration and other field robotics scenarios as well as in geospatial engineering are typically limited to elevation maps, triangulated irregu- lar networks (TIN’s), contour models and their variants or combinations ([Durrant-Whyte, 2001] and [Moore et al., 1991]). Each of them have their own strengths and preferred application domains. The former two are more popular in robotics. The latter represents the terrain as a succession of “isolines” of specific elevation (from min- imum to maximum). They are particularly suited for modeling hydrological phenomena but otherwise offer no particular computational advantages in the context of this paper. Each of them, in their native form, do not handle spatially correlated data effectively. Grid based methods represent space in terms of eleva- tion data corresponding to each cell of a regularly spaced grid structure. The outcome is a 2.5D representation of space. The main advantage of this representation is simplicity. Limitations include the inability to handle abrupt changes, the dependence on grid size and the is- sue of scalability in large environments. In robotics, grid based methods have been exemplified by numerous works such as [Krotkov and Hoffman, 1994], [Ye and Boren- stein, 2003], [Lacroix et al., 2002] and more recently [Triebel et al., 2006]. The main weaknesses observed in grid based representations are the lack of a statistically direct way of incorporating and managing uncertainty and the inability to appropriately handle spatial corre- lation. Triangulated Irregular Networks (TIN’s) usually sam- ple a set of surface specific points that capture im- portant aspects of the terrain surface to be modeled - bumps/peaks, troughs, breaks for example. The repre- sentation typically takes the form of an irregular network Australasian Conference on Robotics and Automation (ACRA), December 2-4, 2009, Sydney, Australia