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K00363313, TEXAS A&M UNIVERSITY KINGSVILLE

Abstract Robot is an intelligent device. It comes under the category of automation vehicle (AV). Robots are developed to carry

out specific tasks autonomously with no human intervention. Common issue for any application using robots is navigation which

includes localization, path planning, path execution and obstacle avoidance. The computation of the robot’s pose estimate will

never be error free. Therefore, localization involves two different challenges: computing a pose estimate and its associated

uncertainty. In robotics, the notion of a cognitive mechanism that binds ode metric and perceptual information into maps suitable

for navigation is certainly appealing. The current simultaneous localization and mapping (SLAM) solutions are taken from rat’s

spatial cognitive mechanism. In this article we propose a novel solution for calculation of cross-covariance terms through which

we are able to catch the highly nonlinear behavior of the pose uncertainty while estimating it. We compare our pose uncertainty

calculation and propagation approach to existing propagation approach such as classic Jacobian approach. Here in this article we

also describe key elements of the known biology of rat brain in relation to navigation. We outline RatSLAM’s performance to

produce results for rival state-of-the-art approach in robotics. Here a decentralized platform for SLAM with multiple robots is

developed. In this paper a novel occupancy grid map fusion algorithm is proposed. This map fusion is mapped from the data of

image processing, clustering, relative orientation extraction, relative translation extraction and then verification of results. The

obstacles of the map are learned from Clustering.

Index Terms— Uncertainty position estimation, robot localization, robot navigation, Map fusion, Radon transform, self-organizing

map, simultaneous localization and mapping (SLAM), Neuro robotics, biologically inspired robots, learning and adaptive systems.

I. INTRODUCTION1

HIS article is fixated on how we can precisely gauge

the robot pose vulnerability and how this instability is

proliferated to future states. A min/max error bound

approach is proposed resulting in bigger and bigger circles

in the x-y plane representing the possible positions for the

robot. A strategy for deciding the pose instability

covariance matrix utilizing a Jacobian methodology is given

for the exceptional instance of circular motion with a steady

radius of curvature. The spatial abilities of rats have been

extensively studied for several decades. Early experiments

assumed that the rat’s ability was based on a generic

concept of learning and memory, and many behavioral

studies were performed to find the limits of the rodent’s

abilities. The breakthrough came in 1971 with the discovery

of the rat’s cognitive map in the cells of the hippocampus, a

region of themidbrain common to all mammals, including

rodents and humans.

II. CURRENT POSE UNCERTAINTY: ACCURATE

COMPUTATION AND PROPAGATION [1]

In [4] the uncertainty of accurately estimating and

propagating future states was computed using

We propose here an efficient method to compute such

cross-covariance between the previous pose and actual

pose

To obtain an expression for the cross-covariance terms

and because of the mathematical complexity of the problem,

an equation representation of the covariance at step k -1 is

obtained, by assuming an error vector for the robot’s pose in

time k-1.

Multiple Robot Simultaneous Localization and

Mapping using Neural Networks

Chunduri Anil Venkata Sivarama Reddy (K00363313), TEXAS A&M UNIVERSITY Kingsville

T


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considered errors are independent and zero mean; hence,

the resultant covariance matrix can be written as follows:

A. Approach Validation

Figure 1. Comparison for state (x,y,ϴ) covariance values

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of the circular trajectory between Monte Carlo simulation,

Jacobian, the presented formulation, and UT. Values used

in this run are Δdk=0.2 m, σΔdk,=0.01 m, Фk,=1.1250

,σФk,=30,L=1.25 m, number of steps=2,000. (a) cov(x,x).

(b) cov(x,y). (c) cov(y,y). All covariance values are given in

m2.

Figure 2. Comparison for the state (x,y,ϴ) covariance

values of the S trajectory (x,y, ϴ) between Monte Carlo

simulation, Jacobian, the presented formulation, and UT.

Values used in this run are Δdk=0.2 m, σΔdk,=0.01 m,

Ф1…1,000,=1.1250,Ф1.001…2,000,=-1.1250σФk,=30,L=1.25 m,

number of steps=2,000. (a) cov(x,x). (b) cov(x,y). (c)

cov(y,y). All covariance values are given in m2.

For each experiment, four different methods to obtain the

pose uncertainty have been used. First, a Monte Carlo

simulation for the path the vehicle performs has been made.

Figure 3. Comparison for the state (x,y,ϴ) covariance

values of the rectangular trajectory (x,y, ϴ) between Monte

Carlo simulation, Jacobian, the presented formulation, and

UT. Values used in this run are σΔdk,vary accordingly

σФk,=30,L=1.25 m, number of steps=2,000. (a) cov(x,x). (b)

cov(x,y). (c) cov(y,y). All covariance values are given in m2.

Carlo simulation was performed by averaging the

covariances for each sample time in a total of 30,000

simulations to have a good estimation of the real value for

the pose uncertainty. Foundations of this technique can be

found in [5] and [6]. The other three methods shall be

compared to this simulation.

On the other hand, as the covariance in the orientation of

the vehicle grows (as the case at hand, where the robot is

trying to perform paths involving high changes in

orientation using measures from internal noisy sensors), the

computed uncertainty by either the Jacobian method, UKF

method, or the one presented here differs from the Monte


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Carlo simulation results.

B. Kinetic Model of AV

We provide in this section an overview of the method

proposed in [4] and [8]. The formulation is particularized

for an AV for which a bicycle kinematic model is

considered (see Figure A1) [9]. The vehicle’s pose can be

fully determined from

Here Δdk measured displacement

Фk measured steering angle

Δd^k and Δϴ^

k independent errors with gaussian

probability distributions

In order that (A2) and (A3) perform correctly, the

systematic errors of the vehicle need to be corrected and

compensated [25].

Uncertainty of the pose estimate is then given by the

covariance matrix cov(^Pk), which can be further

decomposed into the following expression:

E expected value of the corresponding function.

Finally, to obtain a better evaluation of these methods,

the covariance eigenvalues obtained with the presented

formulation, Jacobian, and UT are compared to those

obtained with the Monte Carlo simulation.

where (*) could be Jacobian, UT, or the developed

formulation, and diff represents how close the different

methods are to the covariance obtained with Monte Carlo

approach.

Results are shown in below Figure 4, in which the

developed formulation is closer than the other two

techniques.

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Figure 4. Eigenvector comparison of Monte Carlo

approach against Jacobian, UT, and the presented

formulation approaches for the three trajectories performed

in the experiments: (a) circular, (b) S, and (c) rectangular

real trajectories.

III. HOW A RAT BRAIN WORKS. [2]

Evidence for the neural basis of spatial encoding has

principally been gleaned from recordings of the activity in a

single cell (or small group of cells) when the rodent moves

through space. A complete pattern of brain activity cannot

be compiled in this way, but the correlation between rodent

pose and single-cell firing over time provides strong insight

into the nature of the biological system. A review of the

current understanding of the neural basis of spatial encoding

can be found in [7].

A. Connectivity of Regions

Figure 5. Idealized place and head direction specificity for

various cell types involved in spatial encoding: (a) place

cell,(b) head-direction cell, (c) grid cell, and (d)

conjunctive grid cell.

B. Spatial Encoding Behaviour

Recordings from spatially selective cells have shown that

a rodent will observe the layout of key features in the

environment to reset pose estimates. The rodent brain is

using external perception to correct its pose estimation,

performing a similar function to the update process in robot

SLAM.

Recordings taken in complete darkness show that the

spatially selective cells continue to fire even though there is

no sensory stimulus. As with robots, pose estimates degrade

with time in the absence of external cues [9], suggesting

similar computation to the prediction process in robot

SLAM. A roboticist versed in probabilistic SLAMmight

expect the activity in the head-direction cells to represent a

broader range of absolute heading in the absence of

perceptual cues to correct bearing drift.

Figure 6. Connectivity of the brain regions containing

various spatial encoding cell types.

C. Experience mapping for path planning

Over time, the (x’, y’, ϴ’) arrangement of the pose cells

corresponds decreasingly to the spatial arrangement of the

physical environment. The wrapping connectivity leads to

pose ambiguity, where a pose cell encodes multiple

locations in the environment, forming the tessellated firing

fields seen in grid cells in the rat.

We combine the activity pattern of the pose cells with the

activity of the local view cells to create a topologically

consistent semi metric map in a separate coordinate space

called the experience map.

The experience map contains representations of places

combined with views, called experiences (ei)

lij describe the spatiotemporal relationships between

places

Pi position at a location Vi

local view cell


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Figure 7. The RatSLAM system. Each local view cell is

associated with a distinct visual scene in the environment

and becomes active when the robot sees that scene. A 3-D

CAN forms the pose cells, where active pose cells encode

the estimate of the robot’s pose. Each pose cell is connected

to proximal cells by excitatory (red arrows) and inhibitory

connections with wrapping across all six faces of network.

Intermediate layers in the ðx0; y0Þ plane are not shown.

The network connectivity leads to clusters of active cells

known as activity packets. Active local view and pose cells

drive the creation of experience nodes in the experience

map, a semimetric graphical representation of places in the

environment and their interconnectivity.

Figure 8. Robot in the indoor test environment

Figure 9. (a) Plan view of the testing environment. (b)

The experience map state after 5h in the testing

environment (rotated for comparison

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Figure 10. Path planning, showing the temporal map and planned route. The temporal map shows the predicted travel times to any other location in the environment from the robot’s current (start) location, whereas the route is calculated from a gradient climbing process. The temporal map and goal route are calculated continually enabling path planning to adapt to map changes instantaneously.

Figure 11. (a) The car with the laptop mounted on the roof and (b) the scanline intensity profile of a typical image.

Figure 12. (a) Aerial photo of St. Lucia and (b) corresponding experience map.

IV. ALGORITHM [3]


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Figure 13. map segmentation as described in algorithm 1

V. CONCLUSION

This paper has focused on how the robot’s pose

uncertainty can be accurately estimated and howthis

uncertainty is propagated to future states. This is important

since, in any outdoor mobile robot application, we need to

knowas accurate as possible the error in the robot’s pose

estimation. Although the presented method has been

particularized to an Ackerman vehicle platform, it is general

and valid for all types of robotic vehicles. We found that

building a mapping system based on an understanding of the

highly competent spatial cognition system evidenced by the

rat’s remarkable navigation abilities has produced new

insights into developing long-term and largescale navigation

competence in a robot.

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