Peter Cheeseman

Estimating uncertain spatial relationships in robotics

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information. The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships. The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions.

On the representation and estimation of spatial uncertainly

This paper describes a general method for estimating the nominal relationship and expected error (covariance) between coordinate frames representing the relative locations of ob jects. The frames may be known only indirectly through a series of spatial relationships, each with its associated error, arising from diverse causes, including positioning errors, measurement errors, or tolerances in part dimensions. This estimation method can be used to answer such questions as whether a camera attached to a robot is likely to have a particular reference object in its field of view. The calculated estimates agree well with those from an independent Monte Carlo simulation. The method makes it possible to decide in advance whether an uncertain relationship is known accu rately enough for some task and, if not, how much of an improvement in locational knowledge a proposed sensor will provide. The method presented can be generalized to six degrees offreedom and provides a practical means of esti mating the relationships ( position and orientation) among objects, as well as estimating the uncertainty associated with the relationships.

A Method of Computing Maximum Entropy Probability Values for Expert Systems

This paper presents a new method for calculating the conditional probability of any attribute value, given particular information about the individual case. The calculation is based on the principle of maximum entropy and yields the most unbiased probability estimate, given the available evidence. Previous methods for computing maximum entropy values are either very restrictive in the probabilistic information (constraints) they can use or are combinatorially explosive. The computational complexity of the new procedure depends on the interconnectedness of the constraints, but in practical cases it is small.