Solving navigational uncertainty using grid cells on robots

To successfully navigate their habitats, many mammals use a combination of two mechanisms, path integration and calibration using landmarks, which together enable them to estimate their location and orientation, or pose. In large natural environments, both these mechanisms are characterized by uncertainty: the path integration process is subject to the accumulation of error, while landmark calibration is limited by perceptual ambiguity. It remains unclear how animals form coherent spatial representations in the presence of such uncertainty. Navigation research using robots has determined that uncertainty can be effectively addressed by maintaining multiple probabilistic estimates of a robot's pose. Here we show how conjunctive grid cells in dorsocaudal medial entorhinal cortex (dMEC) may maintain multiple estimates of pose using a brain-based robot navigation system known as RatSLAM. Based both on rodent spatially-responsive cells and functional engineering principles, the cells at the core of the RatSLAM computational model have similar characteristics to rodent grid cells, which we demonstrate by replicating the seminal Moser experiments. We apply the RatSLAM model to a new experimental paradigm designed to examine the responses of a robot or animal in the presence of perceptual ambiguity. Our computational approach enables us to observe short-term population coding of multiple location hypotheses, a phenomenon which would not be easily observable in rodent recordings. We present behavioral and neural evidence demonstrating that the conjunctive grid cells maintain and propagate multiple estimates of pose, enabling the correct pose estimate to be resolved over time even without uniquely identifying cues. While recent research has focused on the grid-like firing characteristics, accuracy and representational capacity of grid cells, our results identify a possible critical and unique role for conjunctive grid cells in filtering sensory uncertainty. We anticipate our study to be a starting point for animal experiments that test navigation in perceptually ambiguous environments.

Efficient computation of volume fractions for multi-material cell complexes in a grid by slicing

The paper presents a novel slicing based method for computation of volume fractions in multi-material solids given as a B-rep whose faces are triangulated and shared by either one or two materials. Such objects occur naturally in geoscience applications and the said computation is necessary for property estimation problems and iterative forward modeling. Each facet in the model is cut by the planes delineating the given grid structure or grid cells. The method, instead of classifying the points or cells with respect to the solid, exploits the convexity of triangles and the simple axis-oriented disposition of the cutting surfaces to construct a novel intermediate space enumeration representation called slice-representation, from which both the cell containment test and the volume-fraction computation are done easily. Cartesian and cylindrical grids with uniform and non-uniform spacings have been dealt with in this paper. After slicing, each triangle contributes polygonal facets, with potential elliptical edges, to the grid cells through which it passes. The volume fractions of different materials in a grid cell that is in interaction with the material interfaces are obtained by accumulating the volume contributions computed from each facet in the grid cell. The method is fast, accurate, robust and memory efficient. Examples illustrating the method and performance are included in the paper.

Airfoil flow and noise computation using monotonically integrated large eddy simulation and acoustic analogy: Effect of the grid resolution.

A new scalable Monotonically Integrated Large Eddy Simulation (MILES) method based on the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) has been applied for the simulation of unsteady flow around NACA0012 airfoil at Re = 400,000 and M = 0.058. The flow solution is coupled with the Ffowcs Williams-Hawkings formulation for far-field noise prediction. The computational modeling results are presented for several computational grid resolutions: 8, 16, and 32 million grid cells and compared with the experimental data available.

Grid Cell Hexagonal Patterns Formed by Fast Self-Organized Learning within Entorhinal Cortex

Grid cells in the dorsal segment of the medial entorhinal cortex (dMEC) show remarkable hexagonal activity patterns, at multiple spatial scales, during spatial navigation. How these hexagonal patterns arise has excited intense interest. It has previously been shown how a selforganizing map can convert firing patterns across entorhinal grid cells into hippocampal place cells that are capable of representing much larger spatial scales. Can grid cell firing fields also arise during navigation through learning within a self-organizing map? A neural model is proposed that converts path integration signals into hexagonal grid cell patterns of multiple scales. This GRID model creates only grid cell patterns with the observed hexagonal structure, predicts how these hexagonal patterns can be learned from experience, and can process biologically plausible neural input and output signals during navigation. These results support a unified computational framework for explaining how entorhinal-hippocampal interactions support spatial navigation.

Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields.

The discovery of grid cells in the medial entorhinal cortex (MEC) permits the characterization of hippocampal computation in much greater detail than previously possible. The present study addresses how an integrate-and-fire unit driven by grid-cell spike trains may transform the multipeaked, spatial firing pattern of grid cells into the single-peaked activity that is typical of hippocampal place cells. Previous studies have shown that in the absence of network interactions, this transformation can succeed only if the place cell receives inputs from grids with overlapping vertices at the location of the place cell's firing field. In our simulations, the selection of these inputs was accomplished by fast Hebbian plasticity alone. The resulting nonlinear process was acutely sensitive to small input variations. Simulations differing only in the exact spike timing of grid cells produced different field locations for the same place cells. Place fields became concentrated in areas that correlated with the initial trajectory of the animal; the introduction of feedback inhibitory cells reduced this bias. These results suggest distinct roles for plasticity of the perforant path synapses and for competition via feedback inhibition in the formation of place fields in a novel environment. Furthermore, they imply that variability in MEC spiking patterns or in the rat's trajectory is sufficient for generating a distinct population code in a novel environment and suggest that recalling this code in a familiar environment involves additional inputs and/or a different mode of operation of the network.

A navigating rat animat

This paper presents a new rat animat, a rat-sized bio-inspired robot platform currently being developed for embodied cognition and neuroscience research. The rodent animat is 150mm x 80mm x 70mm and has a different drive, visual, proximity, and odometry sensors, x86 PC, and LCD interface. The rat animat has a bio-inspired rodent navigation and mapping system called RatSLAM which demonstrates the capabilities of the platform and framework. A case study is presented of the robot's ability to learn the spatial layout of a figure of eight laboratory environment, including its ability to close physical loops based on visual input and odometry. A firing field plot similar to rodent 'non-conjunctive grid cells' is shown by plotting the activity of an internal network. Having a rodent animat the size of a real rat allows exploration of embodiment issues such as how the robot's sensori-motor systems and cognitive abilities interact. The initial observations concern the limitations of the deisgn as well as its strengths. For example, the visual sensor has a narrower field of view and is located much closer to the ground than for other robots in the lab, which alters the salience of visual cues and the effectiveness of different visual filtering techniques. The small size of the robot relative to corridors and open areas impacts on the possible trajectories of the robot. These perspective and size issues affect the formation and use of the cognitive map, and hence the navigation abilities of the rat animat.

Automatic in-bucket volume estimation for dragline operations

This paper presents a method for calculating the in-bucket payload volume on a dragline for the purpose of estimating the material’s bulk density in real-time. Knowledge of the bulk density can provide instant feedback to mine planning and scheduling to improve blasting and in turn provide a more uniform bulk density across the excavation site. Furthermore costs and emissions in dragline operation, maintenance and downstream material processing can be reduced. The main challenge is to determine an accurate position and orientation of the bucket with the constraint of real-time performance. The proposed solution uses a range bearing and tilt sensor to locate and scan the bucket between the lift and dump stages of the dragline cycle. Various scanning strategies are investigated for their benefits in this real-time application. The bucket is segmented from the scene using cluster analysis while the pose of the bucket is calculated using the iterative closest point (ICP) algorithm. Payload points are segmented from the bucket by a fixed distance neighbour clustering method to preserve boundary points and exclude low density clusters introduced by overhead chains and the spreader bar. A height grid is then used to represent the payload from which the volume can be calculated by summing over the grid cells. We show volume calculated on a scaled system with an accuracy of greater than 95 per cent.

Using strategic movement to calibrate a neural compass : a spiking network for tracking head direction in rats and robots

The head direction (HD) system in mammals contains neurons that fire to represent the direction the animal is facing in its environment. The ability of these cells to reliably track head direction even after the removal of external sensory cues implies that the HD system is calibrated to function effectively using just internal (proprioceptive and vestibular) inputs. Rat pups and other infant mammals display stereotypical warm-up movements prior to locomotion in novel environments, and similar warm-up movements are seen in adult mammals with certain brain lesion-induced motor impairments. In this study we propose that synaptic learning mechanisms, in conjunction with appropriate movement strategies based on warm-up movements, can calibrate the HD system so that it functions effectively even in darkness. To examine the link between physical embodiment and neural control, and to determine that the system is robust to real-world phenomena, we implemented the synaptic mechanisms in a spiking neural network and tested it on a mobile robot platform. Results show that the combination of the synaptic learning mechanisms and warm-up movements are able to reliably calibrate the HD system so that it accurately tracks real-world head direction, and that calibration breaks down in systematic ways if certain movements are omitted. This work confirms that targeted, embodied behaviour can be used to calibrate neural systems, demonstrates that ‘grounding’ of modeled biological processes in the real world can reveal underlying functional principles (supporting the importance of robotics to biology), and proposes a functional role for stereotypical behaviours seen in infant mammals and those animals with certain motor deficits. We conjecture that these calibration principles may extend to the calibration of other neural systems involved in motion tracking and the representation of space, such as grid cells in entorhinal cortex.

The impact of spatial scales and spatial smoothing on the outcome of Bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matern correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

A hierarchical model of goal directed navigation selects trajectories in a visual environment

We have developed a Hierarchical Look-Ahead Trajectory Model (HiLAM) that incorporates the firing pattern of medial entorhinal grid cells in a planning circuit that includes interactions with hippocampus and prefrontal cortex. We show the model’s flexibility in representing large real world environments using odometry information obtained from challenging video sequences. We acquire the visual data from a camera mounted on a small tele-operated vehicle. The camera has a panoramic field of view with its focal point approximately 5 cm above the ground level, similar to what would be expected from a rat’s point of view. Using established algorithms for calculating perceptual speed from the apparent rate of visual change over time, we generate raw dead reckoning information which loses spatial fidelity over time due to error accumulation. We rectify the loss of fidelity by exploiting the loop-closure detection ability of a biologically inspired, robot navigation model termed RatSLAM. The rectified motion information serves as a velocity input to the HiLAM to encode the environment in the form of grid cell and place cell maps. Finally, we show goal directed path planning results of HiLAM in two different environments, an indoor square maze used in rodent experiments and an outdoor arena more than two orders of magnitude larger than the indoor maze. Together these results bridge for the first time the gap between higher fidelity bio-inspired navigation models (HiLAM) and more abstracted but highly functional bio-inspired robotic mapping systems (RatSLAM), and move from simulated environments into real-world studies in rodent-sized arenas and beyond.

Development and parameterization of a rain- and fire-driven model for exploring elephant effects in African savannas

We describe the development and parameterization of a grid-based model of African savanna vegetation processes. The model was developed with the objective of exploring elephant effects on the diversity of savanna species and structure, and in this formulation concentrates on the relative cover of grass and woody plants, the vertical structure of the woody plant community, and the distribution of these over space. Grid cells are linked by seed dispersal and fire, and environmental variability is included in the form of stochastic rainfall and fire events. The model was parameterized from an extensive review of the African savanna literature; when available, parameter values varied widely. The most plausible set of parameters produced long-term coexistence between woody plants and grass, with the tree-grass balance being more sensitive to changes in parameters influencing demographic processes and drought incidence and response, while less sensitive to fire regime. There was considerable diversity in the woody structure of savanna systems within the range of uncertainty in tree growth rate parameters. Thus, given the paucity of height growth data regarding woody plant species in southern African savannas, managers of natural areas should be cognizant of different tree species growth and damage response attributes when considering whether to act on perceived elephant threats to vegetation. © 2007 Springer Science+Business Media B.V.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Lahopuumäärän ennustaminen ja kartoitus lentokonelaserkeilauksen avulla

Lahopuun määrästä ja sijoittumisesta ollaan kiinnostuneita paitsi elinympäristöjen monimuotoisuuden, myös ilmakehän hiilen varastoinnin kannalta. Tutkimuksen tavoitteena oli kehittää aluepohjainen laserkeilausdataa hyödyntävä malli lahopuukohteiden paikantamiseksi ja lahopuun määrän estimoimiseksi. Samalla tutkittiin mallin selityskyvyn muuttumista mallinnettavan ruudun kokoa suurennettaessa. Tutkimusalue sijaitsi Itä-Suomessa Sonkajärvellä ja koostui pääasiassa nuorista hoidetuista talousmetsistä. Tutkimuksessa käytettiin harvapulssista laserkeilausdataa sekä kaistoittain mitattua maastodataa kuolleesta puuaineksesta. Aineisto jaettiin siten, että neljäsosa datasta oli käytössä mallinnusta varten ja loput varattiin valmiiden mallien testaamiseen. Lahopuun mallintamisessa käytettiin sekä parametrista että ei-parametrista mallinnusmenetelmää. Logistisen regression avulla erikokoisille (0,04, 0,20, 0,32, 0,52 ja 1,00 ha) ruuduille ennustettiin todennäköisyys lahopuun esiintymiselle. Muodostettujen mallien selittävät muuttujat valittiin 80 laserpiirteen ja näiden muunnoksien joukosta. Mallien selittävät muuttujat valittiin kolmessa vaiheessa. Aluksi muuttujia tarkasteltiin visuaalisesti kuvaamalla ne lahopuumäärän suhteen. Ensimmäisessä vaiheessa sopivimmiksi arvioitujen muuttujien selityskykyä testattiin mallinnuksen toisessa vaiheessa yhden muuttujan mallien avulla. Lopullisessa usean muuttujan mallissa selittävien muuttujien kriteerinä oli tilastollinen merkitsevyys 5 % riskitasolla. 0,20 hehtaarin ruutukoolle luotu malli parametrisoitiin muun kokoisille ruuduille. Logistisella regressiolla toteutetun parametrisen mallintamisen lisäksi, 0,04 ja 1,0 hehtaarin ruutukokojen aineistot luokiteltiin ei-parametrisen CART-mallinnuksen (Classification and Regression Trees) avulla. CARTmenetelmällä etsittiin aineistosta vaikeasti havaittavia epälineaarisia riippuvuuksia laserpiirteiden ja lahopuumäärän välillä. CART-luokittelu tehtiin sekä lahopuustoisuuden että lahopuutilavuuden suhteen. CART-luokituksella päästiin logistista regressiota parempiin tuloksiin ruutujen luokituksessa lahopuustoisuuden suhteen. Logistisella mallilla tehty luokitus parani ruutukoon suurentuessa 0,04 ha:sta(kappa 0,19) 0,32 ha:iin asti (kappa 0,38). 0,52 ha:n ruutukoolla luokituksen kappa-arvo kääntyi laskuun (kappa 0,32) ja laski edelleen hehtaarin ruutukokoon saakka (kappa 0,26). CART-luokitus parani ruutukoon kasvaessa. Luokitustulokset olivat logistista mallinnusta parempia sekä 0,04 ha:n (kappa 0,24) että 1,0 ha:n (kappa 0,52) ruutukoolla. CART-malleilla määritettyjen ruutukohtaisten lahopuutilavuuksien suhteellinen RMSE pieneni ruutukoon kasvaessa. 0,04 hehtaarin ruutukoolla koko aineiston lahopuumäärän suhteellinen RMSE oli 197,1 %, kun hehtaarin ruutukoolla vastaava luku oli 120,3 %. Tämän tutkimuksen tulosten perusteella voidaan todeta, että maastossa mitatun lahopuumäärän ja tutkimuksessa käytettyjen laserpiirteiden yhteys on pienellä ruutukoolla hyvin heikko, mutta vahvistuu hieman ruutukoon kasvaessa. Kun mallinnuksessa käytetty ruutukoko kasvaa, pienialaisten lahopuukeskittymien havaitseminen kuitenkin vaikeutuu. Tutkimuksessa kohteen lahopuustoisuus pystyttiin kartoittamaan kohtuullisesti suurella ruutukoolla, mutta pienialaisten kohteiden kartoittaminen ei onnistunut käytetyillä menetelmillä. Pienialaisten kohteiden paikantaminen laserkeilauksen avulla edellyttää jatkotutkimusta erityisesti tiheäpulssisen laserdatan käytöstä lahopuuinventoinneissa.

Evaluation of spatial variation of peak horizontal acceleration and spectral acceleration for south India: a probabilistic approach

In this work, an attempt has been made to evaluate the spatial variation of peak horizontal acceleration (PHA) and spectral acceleration (SA) values at rock level for south India based on the probabilistic seismic hazard analysis (PSHA). These values were estimated by considering the uncertainties involved in magnitude, hypocentral distance and attenuation of seismic waves. Different models were used for the hazard evaluation, and they were combined together using a logic tree approach. For evaluating the seismic hazard, the study area was divided into small grids of size 0.1A degrees A xA 0.1A degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources within a radius of 300 km. Rock level PHA values and SA at 1 s corresponding to 10% probability of exceedance in 50 years were evaluated for all the grid points. Maps showing the spatial variation of rock level PHA values and SA at 1 s for the entire south India are presented in this paper. To compare the seismic hazard for some of the important cities, the seismic hazard curves and the uniform hazard response spectrum (UHRS) at rock level with 10% probability of exceedance in 50 years are also presented in this work.