Path Integration Errors Research Articles

Spatiotemporal structure of foraging and path integration errors by fiddler crabs, Leptuca pugilator

Path integration is the navigational process by which animals construct a memory of a previous location by continuously measuring and summing their movements to form a single home vector pointing to the starting location. It is intrinsically error prone, subject to random errors and, potentially, to systematic errors in either measurement or the summing algorithm. Both types of errors lead to an incorrect vector memory and thus to an error in homing. Because the errors are incurred when animals move, they are theoretically predictable from the movements. We analyzed the behavior of fiddler crabs (Leptuca pugilator) as they performed foraging excursions followed by homing with varying degrees of error. From video recordings we measured body orientations and locations and computed these spatiotemporal path characteristics: duration, distance, turns, bearing and arc sector. These were analyzed for their effect on, separately, the magnitude, and the direction, of crabs’ homing error. The magnitude of the homing error was predicted by arc sector, Δbearing and path length, and several interactions. The direction of the homing error was predicted by interactions including arc sector x Δbearing, arc sector x turns, and Δbearing x turns. Covariance among these factors results in a path that traces a large arc while maintaining body orientation toward the burrow direction and leads to an error with the same clockwise/counterclockwise sign as the arc and the body turns. These results place L. pugilator’s path integration mechanism among others with known systematic errors.

Sources of systematic errors in human path integration.

Triangle completion is a task widely used to study human path integration, an important navigation method relying on idiothetic cues. Systematic biases (compression patterns in the inbound responses) have been well documented in human triangle completion. However, the sources of systematic biases remain controversial. We used cross-validation modeling to compare three plausible theoretical models that assume that systematic errors occur in the encoding outbound path solely (encoding-error model), executing the inbound responses solely (execution-error model), and both (bicomponent model), respectively. The data for cross-validation modeling are from a previous study (Qi et al., 2021), in which participants learned three objects' locations (one at the path origin, that is, home) very well before walking each outbound path and then pointed to the objects' original locations after walking the outbound path. The modeling algorithm used one inbound response (i.e., response to the home) or multiple inbound responses (i.e., responses to two nonhome locations and the home) for each outbound path. The algorithm of using multiple inbound responses demonstrated that the bicomponent model outperformed the other models in accounting for the systematic errors. This finding suggests that both encoding the outbound path and executing the inbound responses contribute to the systematic biases in human path integration. In addition, the results showed that the algorithm using only the home response could not distinguish among these 3 models, suggesting that the typical triangle-completion task with only the home response for each outbound path cannot determine the sources of the systematic biases. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Supplemental Material for Sources of Systematic Errors in Human Path Integration

Supplemental Material for Sources of Systematic Errors in Human Path Integration

Brain-Inspired Navigation Model Based on the Distribution of Polarized Sky-Light

This paper proposes a brain-inspired navigation model based on absolute heading for the autonomous navigation of unmanned platforms. The proposed model combined the sand ant’s strategy of acquiring absolute heading from the sky environment and the brain-inspired navigation system, which is closer to the navigation mechanism of migratory animals. Firstly, a brain-inspired grid cell network model and an absolute heading-based head-direction cell network model were constructed based on the continuous attractor network (CAN). Then, an absolute heading-based environmental vision template was constructed using the line scan intensity distribution curve, and the path integration error was corrected using the environmental vision template. Finally, a topological cognitive node was constructed according to the grid cell, the head direction cell, the environmental visual template, the absolute heading information, and the position information. Numerous topological nodes formed the absolute heading-based topological map. The model is a topological navigation method not limited to strict geometric space scale, and its position and absolute heading are decoupled. The experimental results showed that the proposed model is superior to the other methods in terms of the accuracy of visual template recognition, as well as the accuracy and topology consistency of the constructed environment topology map.

Executing the homebound path is a major source of error in homing by path integration.

Path integration-the constant updating of position and orientation in an environment-is an important component of spatial navigation, however, its mechanisms are poorly understood. The aims of this study are (a) to test the encoding-error model of path integration, which focuses solely on encoding as a potential source of error, and (b) to develop a model of path integration that best predicts path integration errors. We tested the encoding-error model by independently measuring participants' encoding errors in distance and angle reproduction tasks, and then using those reproduction errors to predict individual participants' errors in a triangle completion task. We sampled the distribution of encoding errors using Monte Carlo methods to predict the homebound path, and then compared the predictions to observed triangle completion behavior. The correlation between predicted errors and actual errors in the triangle completion task was extremely weak, whereas an alternative model using execution error alone was sufficient to describe the observed errors. A model incorporating both encoding and execution errors best described the triangle completion errors. These results suggest that errors in executing the response may contribute more to overall errors in path integration than do encoding errors, challenging the assumption that errors reflect encoding alone. Errors in triangle completion might not arise from failing to know where you are, but from an inability to get back home. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Sources of path integration error in young and aging humans

Path integration plays a vital role in navigation: it enables the continuous tracking of one's position in space by integrating self-motion cues. Path integration abilities vary widely across individuals, and tend to deteriorate in old age. The specific causes of path integration errors, however, remain poorly characterized. Here, we combine tests of path integration performance in participants of different ages with an analysis based on the Langevin equation for diffusive dynamics, which allows us to decompose errors into distinct causes that can corrupt path integration computations. We show that, across age groups, the dominant error source is unbiased noise that accumulates with travel distance not elapsed time, suggesting that the noise originates in the velocity input rather than within the integrator. Age-related declines are primarily traced to a growth in this noise. These findings shed light on the contributors to path integration error and the mechanisms underlying age-related navigational deficits.

Learning Cognitive Map Representations for Navigation by Sensory-Motor Integration.

How to transform a mixed flow of sensory and motor information into memory state of self-location and to build map representations of the environment are central questions in the navigation research. Studies in neuroscience have shown that place cells in the hippocampus of the rodent brains form dynamic cognitive representations of locations in the environment. We propose a neural-network model called sensory-motor integration network model (SeMINet) to learn cognitive map representations by integrating sensory and motor information while an agent is exploring a virtual environment. This biologically inspired model consists of a deep neural network representing visual features of the environment, a recurrent network of place units encoding spatial information by sensorimotor integration, and a secondary network to decode the locations of the agent from spatial representations. The recurrent connections between the place units sustain an activity bump in the network without the need of sensory inputs, and the asymmetry in the connections propagates the activity bump in the network, forming a dynamic memory state which matches the motion of the agent. A competitive learning process establishes the association between the sensory representations and the memory state of the place units, and is able to correct the cumulative path-integration errors. The simulation results demonstrate that the network forms neural codes that convey location information of the agent independent of its head direction. The decoding network reliably predicts the location even when the movement is subject to noise. The proposed SeMINet thus provides a brain-inspired neural-network model for cognitive map updated by both self-motion cues and visual cues.

Visual cue-related activity of cells in the medial entorhinal cortex during navigation in virtual reality.

During spatial navigation, animals use self-motion to estimate positions through path integration. However, estimation errors accumulate over time and it is unclear how they are corrected. Here we report a new cell class ('cue cell') encoding visual cues that could be used to correct errors in path integration in mouse medial entorhinal cortex (MEC). During virtual navigation, individual cue cells exhibited firing fields only near visual cues and their population response formed sequences repeated at each cue. These cells consistently responded to cues across multiple environments. On a track with cues on left and right sides, most cue cells only responded to cues on one side. During navigation in a real arena, they showed spatially stable activity and accounted for 32% of unidentified, spatially stable MEC cells. These cue cell properties demonstrate that the MEC contains a code representing spatial landmarks, which could be important for error correction during path integration.

Path integration error and adaptable search behaviors in a mantis shrimp.

Mantis shrimp of the species Neogonodactylus oerstedii occupy small burrows in shallow waters throughout the Caribbean. These animals use path integration, a vector-based navigation strategy, to return to their homes while foraging. Here, we report that path integration in N. oerstedii is prone to error accumulated during outward foraging paths and we describe the search behavior that N. oerstedii employs after it fails to locate its home following the route provided by its path integrator. This search behavior forms continuously expanding, non-oriented loops that are centered near the point of search initiation. The radius of this search is scaled to the animal's positional uncertainty during path integration, improving the effectiveness of the search. The search behaviors exhibited by N. oerstedii bear a striking resemblance to search behaviors in other animals, offering potential avenues for the comparative examination of search behaviors and how they are optimized in disparate taxa.

NeuroSLAM: a brain-inspired SLAM system for 3D environments.

Roboticists have long drawn inspiration from nature to develop navigation and simultaneous localization and mapping (SLAM) systems such as RatSLAM. Animals such as birds and bats possess superlative navigation capabilities, robustly navigating over large, three-dimensional environments, leveraging an internal neural representation of space combined with external sensory cues and self-motion cues. This paper presents a novel neuro-inspired 4DoF (degrees of freedom) SLAM system named NeuroSLAM, based upon computational models of 3D grid cells and multilayered head direction cells, integrated with a vision system that provides external visual cues and self-motion cues. NeuroSLAM's neural network activity drives the creation of a multilayered graphical experience map in a real time, enabling relocalization and loop closure through sequences of familiar local visual cues. A multilayered experience map relaxation algorithm is used to correct cumulative errors in path integration after loop closure. Using both synthetic and real-world datasets comprising complex, multilayered indoor and outdoor environments, we demonstrate NeuroSLAM consistently producing topologically correct three-dimensional maps.

Differentiation of mild cognitive impairment using an entorhinal cortex-based test of virtual reality navigation.

The entorhinal cortex is one of the first regions to exhibit neurodegeneration in Alzheimer's disease, and as such identification of entorhinal cortex dysfunction may aid detection of the disease in its earliest stages. Extensive evidence demonstrates that the entorhinal cortex is critically implicated in navigation underpinned by the firing of spatially modulated neurons. This study tested the hypothesis that entorhinal-based navigation is impaired in pre-dementia Alzheimer's disease. Forty-five patients with mild cognitive impairment (26 with CSF Alzheimer's disease biomarker data: 12 biomarker-positive and 14 biomarker-negative) and 41 healthy control participants undertook an immersive virtual reality path integration test, as a measure of entorhinal-based navigation. Behavioural performance was correlated with MRI measures of entorhinal cortex volume, and the classification accuracy of the path integration task was compared with a battery of cognitive tests considered sensitive and specific for early Alzheimer's disease. Biomarker-positive patients exhibited larger errors in the navigation task than biomarker-negative patients, whose performance did not significantly differ from controls participants. Path-integration performance correlated with Alzheimer's disease molecular pathology, with levels of CSF amyloid-β and total tau contributing independently to distance error. Path integration errors were negatively correlated with the volumes of the total entorhinal cortex and of its posteromedial subdivision. The path integration task demonstrated higher diagnostic sensitivity and specificity for differentiating biomarker positive versus negative patients (area under the curve = 0.90) than was achieved by the best of the cognitive tests (area under the curve = 0.57). This study demonstrates that an entorhinal cortex-based virtual reality navigation task can differentiate patients with mild cognitive impairment at low and high risk of developing dementia, with classification accuracy superior to reference cognitive tests considered to be highly sensitive to early Alzheimer's disease. This study provides evidence that navigation tasks may aid early diagnosis of Alzheimer's disease, and the basis of this in animal cellular and behavioural studies provides the opportunity to answer the unmet need for translatable outcome measures for comparing treatment effect across preclinical and clinical trial phases of future anti-Alzheimer's drugs.

Compromised Grid-Cell-like Representations in Old Age as a Key Mechanism to Explain Age-Related Navigational Deficits

SummaryA progressive loss of navigational abilities in old age has been observed in numerous studies, but we have only limited understanding of the neural mechanisms underlying this decline [1]. A central component of the brain’s navigation circuit are grid cells in entorhinal cortex [2], largely thought to support intrinsic self-motion-related computations, such as path integration (i.e., keeping track of one’s position by integrating self-motion cues) [3, 4, 5, 6]. Given that entorhinal cortex is particularly vulnerable to neurodegenerative processes during aging and Alzheimer’s disease [7, 8, 9, 10, 11, 12, 13, 14], deficits in grid cell function could be a key mechanism to explain age-related navigational decline. To test this hypothesis, we conducted two experiments in healthy young and older adults. First, in an fMRI experiment, we found significantly reduced grid-cell-like representations in entorhinal cortex of older adults. Second, in a behavioral path integration experiment, older adults showed deficits in computations of self-position during path integration based on body-based or visual self-motion cues. Most strikingly, we found that these path integration deficits in older adults could be explained by their individual magnitudes of grid-cell-like representations, as reduced grid-cell-like representations were associated with larger path integration errors. Together, these results show that grid-cell-like representations in entorhinal cortex are compromised in healthy aging. Furthermore, the association between grid-cell-like representations and path integration performance in old age supports the notion that grid cells underlie path integration processes. We therefore conclude that impaired grid cell function may play a key role in age-related decline of specific higher-order cognitive functions, such as spatial navigation.

Sensory feedback in a bump attractor model of path integration.

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.

Bias in Human Path Integration Is Predicted by Properties of Grid Cells

Accurate wayfinding is essential to the survival of many animal species and requires the ability to maintain spatial orientation during locomotion. One of the ways that humans and other animals stay spatially oriented is through path integration, which operates by integrating self-motion cues over time, providing information about total displacement from a starting point. The neural substrate of path integration in mammals may exist in grid cells, which are found in dorsomedial entorhinal cortex and presubiculum and parasubiculum in rats. Grid cells have also been found in mice, bats, and monkeys, and signatures of grid cell activity have been observed in humans. We demonstrate that distance estimation by humans during path integration is sensitive to geometric deformations of a familiar environment and show that patterns of path integration error are predicted qualitatively by a model in which locations in the environment are represented in the brain as phases of arrays of grid cells with unique periods and decoded by the inverse mapping from phases to locations. The periods of these grid networks are assumed to expand and contract in response to expansions and contractions of a familiar environment. Biases in distance estimation occur when the periods of the encoding and decoding grids differ. Our findings explicate the way in which grid cells could function in human path integration.

Walking and running in the desert ant Cataglyphis fortis.

Path integration, although inherently error-prone, is a common navigation strategy in animals, particularly where environmental orientation cues are rare. The desert ant Cataglyphis fortis is a prominent example, covering large distances on foraging excursions. The stride integrator is probably the major source of path integration errors. A detailed analysis of walking behaviour in Cataglyphis is thus of importance for assessing possible sources of errors and potential compensation strategies. Zollikofer (J Exp Biol 192:95–106, 1994a) demonstrated consistent use of the tripod gait in Cataglyphis, and suggested an unexpectedly constant stride length as a possible means of reducing navigation errors. Here, we extend these studies by more detailed analyses of walking behaviour across a large range of walking speeds. Stride length increases linearly and stride amplitude of the middle legs increases slightly linearly with walking speed. An initial decrease of swing phase duration is observed at lower velocities with increasing walking speed. Then it stays constant across the behaviourally relevant range of walking speeds. Walking speed is increased by shortening of the stance phase and of the stance phase overlap. At speeds larger than 370 mms−1, the stride frequency levels off, the duty factor falls below 0.5, and Cataglyphis transitions to running with aerial phases.Electronic supplementary materialThe online version of this article (doi:10.1007/s00359-015-0999-2) contains supplementary material, which is available to authorized users.

Oscillatory neurocomputing with ring attractors: a network architecture for mapping locations in space onto patterns of neural synchrony

Theories of neural coding seek to explain how states of the world are mapped onto states of the brain. Here, we compare how an animal's location in space can be encoded by two different kinds of brain states: population vectors stored by patterns of neural firing rates, versus synchronization vectors stored by patterns of synchrony among neural oscillators. It has previously been shown that a population code stored by spatially tuned ‘grid cells’ can exhibit desirable properties such as high storage capacity and strong fault tolerance; here it is shown that similar properties are attainable with a synchronization code stored by rhythmically bursting ‘theta cells’ that lack spatial tuning. Simulations of a ring attractor network composed from theta cells suggest how a synchronization code might be implemented using fewer neurons and synapses than a population code with similar storage capacity. It is conjectured that reciprocal connections between grid and theta cells might control phase noise to correct two kinds of errors that can arise in the code: path integration and teleportation errors. Based upon these analyses, it is proposed that a primary function of spatially tuned neurons might be to couple the phases of neural oscillators in a manner that allows them to encode spatial locations as patterns of neural synchrony.

Iterative Bayesian Estimation as an Explanation for Range and Regression Effects: A Study on Human Path Integration

Systematic errors in human path integration were previously associated with processing deficits in the integration of space and time. In the present work, we hypothesized that these errors are de facto the result of a system that aims to optimize its performance by incorporating knowledge about prior experience into the current estimate of displacement. We tested human linear and angular displacement estimation behavior in a production-reproduction task under three different prior experience conditions where samples were drawn from different overlapping sample distributions. We found that (1) behavior was biased toward the center of the underlying sample distribution, (2) the amount of bias increased with increasing sample range, and (3) the standard deviation for all conditions was linearly dependent on the mean reproduced displacements. We propose a model of bayesian estimation on logarithmic scales that explains the observed behavior by optimal fusion of an experience-dependent prior expectation with the current noisy displacement measurement. The iterative update of prior experience is modeled by the formulation of a discrete Kalman filter. The model provides a direct link between Weber-Fechner and Stevens' power law, providing a mechanistic explanation for universal psychophysical effects in human magnitude estimation such as the regression to the mean and the range effect.

Near exact correction of path integration errors by the grid cell-place cell system

Near exact correction of path integration errors by the grid cell-place cell system

Changes in the Limb Kinematics and Walking-Distance Estimation After Shank Elongation: Evidence for a Locomotor Body Schema?

When walking, step length provides critical information on traveled distance along the ongoing path [corrected] Little is known on the role that knowledge about body dimensions plays within this process. Here we directly addressed this question by evaluating whether changes in body proportions interfere with computation of traveled distance for targets located outside the reaching space. We studied locomotion and distance estimation in an achondroplastic child (ACH, 11 yr) before and after surgical elongation of the shank segments of both lower limbs and in healthy adults walking on stilts, designed to mimic shank-segment elongation. Kinematic analysis of gait revealed that dynamic coupling of the thigh, shank, and foot segments changed substantially as a result of elongation. Step length remained unvaried, in spite of the significant increase in total limb length ( approximately 1.5-fold). These relatively shorter strides resulted from smaller oscillations of the shank segment, as would be predicted by proportional increments in limb size and not by asymmetrical segmental increment as in the present case (length of thighs was not modified). Distance estimation was measured by walking with eyes closed toward a memorized target. Before surgery, the behavior of ACH was comparable to that of typically developing participants. In contrast, following shank elongation, the ACH walked significantly shorter distances when aiming at the same targets. Comparable changes in limb kinematics, stride length, and estimation of traveled distance were found in adults wearing on stilts, suggesting that path integration errors in both cases were related to alterations in the intersegmental coordination of the walking limbs. The results are consistent with a dynamic locomotor body schema used for controlling step length and path estimation, based on inherent relationships between gait parameters and body proportions.

Metric embedding of view-graphs

Most recent robotic systems, capable of exploring unknown environments, use topological structures (graphs) as a spatial representation. Localization can be done by deriving an estimate of the global pose from landmark information. In this case navigation is tightly coupled to metric knowledge, and hence the derived control method is mainly pose-based. Alternative to continuous metric localization, it is also possible to base localization methods on weaker constraints, e.g. the similarity between images capturing the appearance of places or landmarks. In this case navigation can be controlled by a homing algorithm. Similarity based localization can be scaled to continuous metric localization by adding additional constraints, such as alignment of depth estimates. We present a method to scale a similarity based navigation system (the view-graph-model) to continuous metric localization. Instead of changing the landmark model, we embed the graph into the three dimensional pose space. Therefore, recalibration of the path integrator is only possible at discrete locations in the environment. The navigation behavior of the robot is controlled by a homing algorithm which combines three local navigation capabilities, obstacle avoidance, path integration, and scene based homing. This homing scheme allows automated adaptation to the environment. It is further used to compensate for path integration errors, and therefore allows to derive globally consistent pose estimates based on "weak" metric knowledge, i.e. knowledge solely derived from odometry. The system performance is tested with a robotic setup and with a simulated agent which explores a large, open, and cluttered environment.