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UKF estimated robot position with IA based adaptive mechanism using IMAGESP
X coordinate (m)
Y coordinate (m)
Obstacles or
Land Marks
Actual robot
position
Interval robot
position
IA based adaptive
UKF robot position
estimate
Figure 9: Fused robot position using IMAGESP algorithm
as adaptive mechanism in UKF
estimate using the SIVIA interval robot position esti-
mate for adaptation. It can be seen that the interval po-
sition estimate is very conservative when there are no
land marks in one coordinate, for example at the be-
ginning of the robot path in Figure 8. Moreover it can
be observed that the UKF estimate with the interval
analysis based adaptive mechanism has significantly
improved the UKF robot position estimate when com-
pared with the UKF position estimate without the IA
adaptive mechanism shown in Figure 7. Similarly the
Figure 9 shows the UKF robot position estimation us-
ing the IMAGESP algorithm for the adaptive mecha-
nism. It should be noted that the SIVIA interval posi-
tion uncertainty is more when compared with the IM-
AGESP algorithm, but the computational complexity
for the IMAGESP algorithm is more when compared
with the SIVIA algorithm.
5 CONCLUSION
An Unscented Kalman filter (UKF) using an Inter-
val Analysis based adaptive mechanism has been de-
scribed. The UKF uses accelerometers, gyroscopes
and encoders to measure the robots speed and head-
ing angle, so that the robots position can be estimated.
But the UKF robot position estimate is affected by er-
rors in robot model, sensor bias, drift etc. The Interval
Analysis (IA) is a deterministic approach to estimat-
ing the robots position without using a model of the
robot system, thereby minimizing errors due to robot
model. The interval analysis algorithm with ultra-
sonic sensor measurement to estimate robot position
has been described. Additionally previous work on
robot localisation and navigation using interval anal-
ysis has been extended so to incorporate sensor range
limitation. Moreover instead of using dynamic inter-
val model of the robot to predict the next step of the
interval robot position while tracking the robot posi-
tion, the physical limitations of the robot are used to
predict the next step in the interval analysis algorithm.
The IA robot position estimate is then used for an
adaptive mechanism to correct the errors in the UKF
robot position estimate. Then the newly implemented
approach to fuse both these robot position estimation
has been described and it can be observed that the
UKF with the IA based adaptive mechanism gives a
much accurate estimate when compared to estimates
with UKF without the adaptive mechanism.
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