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TRANSCRIPT
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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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