Robot Motion Planning: A Game-Theoretic Foundation

Analysis techniques and algorithms for basic path planning have become quite valuable in a variety of applications such as robotics, virtual prototyping, computer graphics, and computational biology. Yet, basic path planning represents a very restricted version of general motion planning problems often encountered in robotics. Many problems can involve complications such as sensing and model uncertainties, nonholonomy, dynamics, multiple robots and goals, optimality criteria, unpredictability, and nonstationarity, in addition to standard geometric workspace constraints. This paper proposes a unified, game-theoretic mathematical foundation upon which analysis and algorithms can be developed for this broader class of problems, and is inspired by the similar benefits that were obtained by using unified configuration-space concepts for basic path planning. By taking this approach, a general algorithm has been obtained for computing approximate optimal solutions to a broad class of motion planning problems, including those involving uncertainty in sensing and control, environment uncertainties, and the coordination of multiple robots. Received November 11, 1996; revised March 13, 1998.     

Improving Motion-Planning Algorithms by Efficient Nearest-Neighbor Searching

The cost of nearest-neighbor (NN) calls is one of the bottlenecks in the performance of sampling-based motion-planning algorithms. Therefore, it is crucial to develop efficient techniques for NN searching in configuration spaces arising in motion planning. In this paper, we present and implement an algorithm for performing NN queries in Cartesian products of R, S¹, and RP³, the most common topological spaces in the context of motion planning. Our approach extends the algorithm based on kd-trees, called ANN, developed by Arya and Mount for Euclidean spaces. We prove the correctness of the algorithm and illustrate substantial performance improvement over the brute-force approach and several existing NN packages developed for general metric spaces. Our experimental results demonstrate a clear advantage of using the proposed method for both probabilistic roadmaps and rapidly exploring random trees     

Localization With Limited Sensing

Localization is a fundamental problem for many kinds of mobile robots. Sensor systems of varying ability have been proposed and successfully used to solve the problem. This paper probes the lower limits of this range by describing three extremely simple robot models and addresses the active localization problem for each. The robot, whose configuration is composed of its position and orientation, moves in a fully-known, simply connected polygonal environment. We pose the localization task as a planning problem in the robot's information space, which encapsulates the uncertainty in the robot's configuration. We consider robots equipped with: 1) angular and linear odometers; 2) a compass and contact sensor and; 3) an angular odometer and contact sensor. We present localization algorithms for models 1 and 2 and show that no algorithm exists for model 3. An implementation with simulation examples is presented.     

Capnography: assessing end-tidal CO2 levels

The purpose of this article is to describe the nurse's role in caring for patients with capnography. Capnography provides a continuous and non-invasive measure of arterial partial pressure of carbon dioxide (PaCO2) throughout the entire respiratory cycle. Used correctly, this technology assists the critical care nurse in providing adequate oxygenation and ventilation to the unstable patient.     

Distance-Optimal Navigation in an Unknown Environment Without Sensing Distances

This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it to move toward discontinuities. The robot is incapable of performing localization or measuring any distances or angles. Nevertheless, when dropped into an unknown planar environment, the robot builds a data structure, called the gap navigation tree, which enables it to navigate optimally in terms of Euclidean distance traveled. In a sense, the robot is able to learn the critical information contained in the classical shortest-path roadmap, although surprisingly it is unable to extract metric information. We prove these results for the case of a point robot placed into a simply connected, piecewise-analytic planar environment. The case of multiply connected environments is also addressed, in which it is shown that further sensing assumptions are needed. Due to the limited sensor given to the robot, globally optimal navigation is impossible; however, our approach achieves locally optimal (within a homotopy class) navigation, which is the best that is theoretically possible under this robot model.     

A Bayesian segmentation methodology for parametric image models

Region-based image segmentation methods require some criterion for determining when to merge regions. This paper presents a novel approach by introducing a Bayesian probability of homogeneity in a general statistical context. The authors' approach does not require parameter estimation and is therefore particularly beneficial for cases in which estimation-based methods are most prone to error: when little information is contained in some of the regions and, therefore, parameter estimates are unreliable. The authors apply this formulation to three distinct parametric model families that have been used in past segmentation schemes: implicit polynomial surfaces, parametric polynomial surfaces, and Gaussian Markov random fields. The authors present results on a variety of real range and intensity images     

Optimal Navigation for a Differential Drive Disc Robot: A Game Against the Polygonal Environment

This paper considers the problem of globally optimal navigation with respect to minimizing Euclidean distance traveled by a disc-shaped, differential-drive robot (DDR) to reach a landmark. The robot is equipped with a gap sensor, which indicates depth discontinuities and allows the robot to move toward them. In this work we assume that a topological representation of the environment called GNT has already been built, and that the landmark has been encoded in the GNT. A motion strategy is presented that optimally navigates the robot to any landmark in the environment, without the need of using a previously known geometric map of the environment. To our knowledge this is the first time that the shortest path for a DDR (underactuated system) is found in the presence of obstacle constraints without knowing the complete geometric representation of the environment. The robot’s planner or navigation strategy is modeled as a Moore Finite State Machine (FSM). This FSM includes a sensor-feedback motion policy. The motion policy is based on the paradigm of avoiding the state estimation to carry out two consecutive mappings, that is, from observation to state and then from state to control, but instead of that, there is a direct mapping from observation to control. Optimality is proved and the method is illustrated in simulation.     

Field validation of a milk line sampling device for monitoring milk quality and udder health

The objective of this study was to investigate the ability of a milk line sampling device to obtain a representative sample by comparing SCC and bacterial culture results between milk line and bulk tank samples for milk harvested from the same group of cows at the same milking. A total of 42 paired milk line and bulk tank samples were collected at separate milking events from 21 different herds. Concordance correlation coefficients showed a high level of agreement between the two sample types, with values ranging between 0.74 and 0.99 for all parameters and bacterial species measured. ANOVA showed that SCC and bacterial culture results for Streptococcus agalactiae, Staphylococcus aureus, Streptococcus non-agalactiae, Coliforms, and coagulase-negative staphylococci were neither numerically or statistically different between milk line and bulk tank samples. KAPPA analysis showed that overall agreement beyond chance between milk line and bulk tank samples in determining whether a herd was positive or negative for either Strep. agalactiae or Staph. aureus were 100 and 75%, respectively. While further research is needed to fully assess the utility of this tool for the purpose of bacterial culture, the results of this study suggest that the strategy of milk line sampling is a very promising monitoring tool. This sampling strategy should provide producers with inexpensive and timely information that will help to improve programs for monitoring milk quality and udder health in commercial dairy herds.     

Surface Loading from Pollutants in Precipitation in Southern Ontario: Some Climatic and Statistical Aspects

Monthly samples of precipitation during the period June 1975 to June 1977 from bulk type precipitation gauges located in six watersheds in southern Ontario were analyzed for sulphate, nitrogen, phosphate, chloride, calcium, sodium, potassium, magnesium, heavy metals, and PCBs. The relationship between the surface loading of the pollutant and the amount of precipitation during the observation period was investigated and a significant relationship at the .05 level was found for all pollutants except sodium. The loadings in g/ha/d were tested statistically for spatial and temporal variability. All parameter loadings showed a downward trend over time and it was suggested that this is due to decreased precipitation during the second year of observation. No significant seasonal differences were found in the surface loadings. Analysis of variance tests indicated that at the .05 level of significance, no significant differences in monthly loadings were observed for all parameters except calcium and magnesium, although some locations were very near and others hundreds of kilometers distant from the major sources of industrial pollutants.