Estimating Uncertain Spatial Relationships in Robotics

Abstract

In many robotic applications the need to rep resent and reason about spatial relationships is of great importance. However, our knowledge of par ticular spatial relationships is inherently uncertain. The most used method for handling the uncertainty is to "pre-engineer" the problem away, by structur ing the working environment and using specially suited high-precision equipment. In some advanced robotic research domains, however, such as auto matic task planning, off-line robot programming, 267 and autonomous vehicle operation, prior structur ing will not be possible, because of dynamically changing environments, or because of the demand for greater reasoning flexibility. Spatial reasoning is further complicated because relationships are often not described explicitly, but are given by uncertain relative information. This is particularly true when many different frames of reference are used, produc ing a network of uncertain relationships. Rather than treat spatial uncertainty as a side issue in geo metrical reasoning, we believe it must be an intrin sic part of spatial representations. In this paper, we describe a representation for spatial informa tion, called the stochastic map, and associated pro cedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map always contains the best esti mates of relationships among objects in the map, and their uncertainties. The procedures provide a general solution to the problem of estimating un certain relative spatial relationships. The estimates are probabilistic in nature, an advance over the pre vious, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering the ory, which provides a solid basis for numerous ex tensions.

Principles of goal-directed spatial robot navigation in biomimetic models

“…A large range of algorithms [56,57,[63][64][65][66][67][68][69][70] have been developed to deal with the key issues in producing and maintaining a suitable metric map for robot navigation: sensor observation uncertainty, scalability to larger environments and the need to incorporate changes in the environment. Metric occupancy maps have been used extensively both in forming global representations of a robot's entire operating environment, as well Figure 3.…”

Orbital SLAM

“…Additionally, SLAM has been studied for years as its own problem, beginning with Smith, Self, and Cheeseman's 1990 text [10]. Sebastian Thrun's Probabilistic Robotics text includes a detailed review of the state of art in indoor SLAM techniques [11].…”

Error analysis of the extended Kalman filter applied to the simultaneous localization and mapping problem

“…Well known solutions [3][4][5] to the single robot SLAM problem include the extended Kalman filter (EKF) algorithm to estimate the position of landmarks and the pose (i.e., position and heading) of the robot as Gaussian distributions or particle filters 6-8 that allow for non-Gaussian representations or their combinations (known as FastSLAM). In order to estimate the position of the robotic vehicle and the landmarks in the environment, a motion model for the robotic vehicle and a measurement model for the sensors are used in the algorithms to create a map.…”