Navigation Representation Research Articles

Optimal Path Maps on the GPU.

We introduce a new method for computing optimal path maps on the GPU using OpenGL shaders. Our method explores GPU rasterization as a way to propagate optimal costs on a polygonal 2D environment, producing optimal path maps which can efficiently be queried at run-time. Our method is implemented entirely with GPU shaders, does not require pre-computation, addresses optimal path maps with multiple points and line segments as sources, and introduces a new optimal path map concept not addressed before: maps with weights at vertices representing possible changes in traversal speed. The produced maps offer new capabilities not explored by previous navigation representations and at the same time address paths with global optimality, a characteristic which has been mostly neglected in animated virtual environments. The proposed path maps partition the input environment into the regions sharing a same parent point along the shortest path to the closest source, taking into account possible speed changes at vertices. The proposed approach is particularly suitable for the animation of multiple agents moving toward the entrances or exits of a virtual environment, a situation which is efficiently represented with the proposed path maps.

Multimodal Parcellations and Extensive Behavioral Profiling Tackling the Hippocampus Gradient.

The hippocampus displays a complex organization and function that is perturbed in many neuropathologies. Histological work revealed a complex arrangement of subfields along the medial-lateral and the ventral-dorsal dimension, which contrasts with the anterior-posterior functional differentiation. The variety of maps has raised the need for an integrative multimodal view. We applied connectivity-based parcellation to 1) intrinsic connectivity 2) task-based connectivity, and 3) structural covariance, as complementary windows into structural and functional differentiation of the hippocampus. Strikingly, while functional properties (i.e., intrinsic and task-based) revealed similar partitions dominated by an anterior-posterior organization, structural covariance exhibited a hybrid pattern reflecting both functional and cytoarchitectonic subdivision. Capitalizing on the consistency of functional parcellations, we defined robust functional maps at different levels of partitions, which are openly available for the scientific community. Our functional maps demonstrated a head-body and tail partition, subdivided along the anterior-posterior and medial-lateral axis. Behavioral profiling of these fine partitions based on activation data indicated an emotion-cognition gradient along the anterior-posterior axis and additionally suggested a self-world-centric gradient supporting the role of the hippocampus in the construction of abstract representations for spatial navigation and episodic memory.

A Standard for Map Data Representation: IEEE 1873-2015 Facilitates Interoperability Between Robots

The availability of environment maps for autonomous robots enables them to complete several tasks. A new IEEE standard, IEEE 1873-2015, Robot Map Data Representation for Navigation (MDR) [15], sponsored by the IEEE Robotics and Automation Society (RAS) and approved by the IEEE Standards Association Standards Board in September 2015, defines a common representation for two-dimensional (2-D) robot maps and is intended to facilitate interoperability among navigating robots. The standard defines an extensible markup language (XML) data format for exchanging maps between different systems. This article illustrates how metric maps, topological maps, and their combinations can be represented according to the standard.

A representation method based on the probability of collision for safe robot navigation in domestic environments

This paper introduces a three-dimensional volumetric representation for safe navigation. It is based on the OctoMap representation framework that probabilistically fuses sensor measurements to represent the occupancy probability of volumes. To achieve safe navigation in a domestic environment this representation is extended with a model of the occupancy probability if no sensor measurements are received, and a proactive approach to deal with unpredictably moving obstacles that can arise from behind occlusions by always expecting obstacles to appear on the robot’s path. By combining the occupancy probability of volumes with the position uncertainty of the robot, a probability of collision is obtained. It is shown that by relating this probability to a safe velocity limit a robot in a real domestic environment can move close to a certain maximum velocity but decides to attain a slower safe velocity limit when it must, analogous to slowing down in traffic when approaching an occluded intersection.

The explicit construction of all dually flat Randers metrics

In this paper, we construct explicitly all dually flat Randers metrics by using the bijection between Randers metrics and their navigation representation.

A biologically inspired model based on a multi-scale spatial representation for goal-directed navigation

Inspired by the multi-scale nature of hippocampal place cells, a biologically inspired model based on a multi-scale spatial representation for goal-directed navigation is proposed in order to achieve robotic spatial cognition and autonomous navigation. First, a map of the place cells is constructed in different scales, which is used for encoding the spatial environment. Then, the firing rate of the place cells in each layer is calculated by the Gaussian function as the input of the Q-learning process. The robot decides on its next direction for movement through several candidate actions according to the rules of action selection. After several training trials, the robot can accumulate experiential knowledge and thus learn an appropriate navigation policy to find its goal. The results in simulation show that, in contrast to the other two methods(G-Q, S-Q), the multi-scale model presented in this paper is not only in line with the multi-scale nature of place cells, but also has a faster learning potential to find the optimized path to the goal. Additionally, this method also has a good ability to complete the goal-directed navigation task in large space and in the environments with obstacles.

Robust Topological Navigation via Convolutional Neural Network Feature and Sharpness Measure

Visual navigation for mobile robots has emerged in recent years. Among the various methods, topological navigation using visual information provides a scalable map representation for large-scale mapping and navigation. A topological map is essentially a graph with keyframes as its nodes and adjacency relations as its edges. Previous topological mapping uses local feature descriptors, such as scale-invariant feature transform or Speeded-Up Robust Features, to select keyframes in mapping, localization, and estimate relative pose. In practice, local features are not robust for severe motion blur or large illumination change. In this paper, we improve topological mapping to make it more efficient and robust. First, we use a convolutional neural network (CNN) feature as the holistic image representation. The CNN feature can be used to effectively retrieve keyframes that have similar appearance from a topological map, and it is robust to motion blur and illumination change. Thus, it improves the performance for place recognition and robot relocalization. Second, we use sharpness measure to select high-quality keyframes and avoid selecting blurry ones. Third, an efficient and robust non-rigid matching method, vector field consensus, is used for efficient geometric verification and to retrieve the most similar keyframe. The qualitative and quantitative experimental results demonstrate that our method is satisfactory.

Does spatial locative comprehension predict landmark-based navigation?

In the present study we investigated the role of spatial locative comprehension in learning and retrieving pathways when landmarks were available and when they were absent in a sample of typically developing 6- to 11-year-old children. Our results show that the more proficient children are in understanding spatial locatives the more they are able to learn pathways, retrieve them after a delay and represent them on a map when landmarks are present in the environment. These findings suggest that spatial language is crucial when individuals rely on sequences of landmarks to drive their navigation towards a given goal but that it is not involved when navigational representations based on the geometrical shape of the environment or the coding of body movements are sufficient for memorizing and recalling short pathways.

Self-motivated visual scanning predicts flexible navigation in a virtual environment

The ability to navigate flexibly (e.g., reorienting oneself based on distal landmarks to reach a learned target from a new position) may rely on visual scanning during both initial experiences with the environment and subsequent test trials. Reliance on visual scanning during navigation harkens back to the concept of vicarious trial and error, a description of the side-to-side head movements made by rats as they explore previously traversed sections of a maze in an attempt to find a reward. In the current study, we examined if visual scanning predicted the extent to which participants would navigate to a learned location in a virtual environment defined by its position relative to distal landmarks. Our results demonstrated a significant positive relationship between the amount of visual scanning and participant accuracy in identifying the trained target location from a new starting position as long as the landmarks within the environment remain consistent with the period of original learning. Our findings indicate that active visual scanning of the environment is a deliberative attentional strategy that supports the formation of spatial representations for flexible navigation.

Efficient grid-based spatial representations for robot navigation in dynamic environments

In robotics, grid maps are often used for solving tasks like collision checking, path planning, and localization. Many approaches to these problems use Euclidean distance maps (DMs), generalized Voronoi diagrams (GVDs), or configuration space (c-space) maps. A key challenge for their application in dynamic environments is the efficient update after potential changes due to moving obstacles or when mapping a previously unknown area. To this end, this paper presents novel algorithms that perform incremental updates that only visit cells affected by changes. Furthermore, we propose incremental update algorithms for DMs and GVDs in the configuration space of non-circular robots. These approaches can be used to implement highly efficient collision checking and holonomic path planning for these platforms. Our c-space representations benefit from parallelization on multi-core CPUs and can also be integrated with other state-of-the-art path planners such as rapidly-exploring random trees.In various experiments using real-world data we show that our update strategies for DMs and GVDs require substantially less cell visits and computation time compared to previous approaches. Furthermore, we demonstrate that our GVD algorithm deals better with non-convex structures, such as indoor areas. All our algorithms consider actual Euclidean distances rather than grid steps and are easy to implement. An open source implementation is available online.

Spatial navigation and multiscale representation by hippocampal place cells

Spatial navigation and multiscale representation by hippocampal place cells

A FAMILY OF EINSTEIN RANDERS METRICS

We classify all Einstein Randers metric on R4 constructed from ga, the Hawking Taub–NUT metric, and a homothetic vector field W for ga in the Zermelo navigation representation. All of these Einstein Randers metrics are Ricci-flat and are not of scalar flag curvature. Finally, the moduli space of constructed Randers metrics is obtained.

On Some Finsler Metrics of Non-positive Constant Flag Curvature

(α, β)-norms on \({\mathbb{R}^N}\) induce Minkowski metrics, and the construction of related homothetic vector fields gives a family of new Finsler metrics of non-positive constant flag curvature for each non-trivial (α, β)-norm. The dimension of this family is at least \({\tfrac{1}{2}(N^2 - N + 4)}\) . In particular, we generalize the Funk metric on the unit ball via navigation representation of the standard Euclidean norm and the radial vector field. Finally, we describe the geodesics of these new Finsler metrics with constant flag curvature.

Long-term experiments with an adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metric-topological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability.

On geodesics of Finsler metrics via navigation problem

This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced fromanyFinsler metric andanyhomothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constantSS-curvature. As its application, we present explicitly the geodesics of the Funk metric on a strongly convex domain.

Lateralized human hippocampal activity predicts navigation based on sequence or place memory

The hippocampus is crucial for both spatial navigation and episodic memory, suggesting that it provides a common function to both. Here we adapt a spatial paradigm, developed for rodents, for use with functional MRI in humans to show that activation of the right hippocampus predicts the use of an allocentric spatial representation, and activation of the left hippocampus predicts the use of a sequential egocentric representation. Both representations can be identified in hippocampal activity before their effect on behavior at subsequent choice-points. Our results suggest that, rather than providing a single common function, the two hippocampi provide complementary representations for navigation, concerning places on the right and temporal sequences on the left, both of which likely contribute to different aspects of episodic memory.

Maplets: local geometrical components of human cognitive maps

The cognitive representation underlying human spatial navigation is often dichotomized into “route knowledge” and “survey knowledge.” Motivated by concepts from studies of animal navigation, we propose a different form of underlying representation for human navigation. “Maplets” are small pieces of maps whose configural information can be encoded from a single location using vision. The maplet representation of a building's layout consists of a set of maplets each composed of a root node (corridor intersection) and the connecting links (branching corridors) to adjacent maplets. We have developed a computer algorithm that synthesizes global building layouts from a set of maplets, demonstrating that global layout information is implicitly retained in the maplet decomposition. Convergent evidence from two empirical studies, conducted for other purposes supports the psychological reality of maplets. In one experiment (Giudice et al., VSS 2002), human judges rated the accuracy of maps drawn by human subjects who learned building layouts by exploration. A maplet-matching score (computed by comparing the number of maplets in the subjects' drawings to the actual maplet representation of the layout) correlated better with the judges' ratings (R = .87 to .98) than did a global template matching method (R = .64 to .66). In a second experiment (Schlicht et al., ARVO 2001), subjects learned a building layout by free exploration. Then they drew a map of the layout and also performed a set of target-localization trials. The maplet-matching scores, derived from the subjects' drawings, correlated (R = 0.7) with the accuracy of performance in the localization trials. Our computational and empirical results support the proposal that configural information in human cognitive maps is stored in local maplets. Each maplet contains geometrical information that is accessible by visual inspection from within the maplet.

The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature

By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.

Processing Text on the Web: The Construction of Mental Representations

Aim of the present study was to identify an appropriate hypertext structure and navigation aids that enhance the comprehensibility of hypertext and support readers in building up a mental representation of the text. It is assumed that hypertext readers construct a content representation for the comprehension of the hypertext and a text structure representation for navigation within the hypertext. If relevant dimensions of these two representations cannot be mapped onto each other, orientation problems are likely to occur. The results of this experimental study show that disadvantages of hypertext concerning orientation problems can be compensated with the aid of a graphical overview which is usable for navigation. This orientation and navigation aid is also an advantage for the speed of information retrieval. However, the coherence of the reading sequence seems to the best predictor for the quality of the mental representations of both text content and hypertext structure. An influence of the availability of cognitive resources was also shown.

S-curvature of isotropic Berwald metrics

Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.