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Experimental Validation: Perception and Localization Systems for Autonomous Vehicles using the Extended Kalman Filter Algorithm

Bambang Lelono Widjiantoro

Bambang Lelono Widjiantoro

Department of Engineering Physics, Sepuluh Nopember Institute of Technology (ITS)Surabaya, Indonesia
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Widjiantoro, Bambang Lelono
, 
Katherin Indriawati

Katherin Indriawati

Department of Engineering Physics, Sepuluh Nopember Institute of Technology (ITS)Surabaya, Indonesia
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Indriawati, Katherin
, 
T. S. N. Alexander Buyung

T. S. N. Alexander Buyung

Department of Engineering Physics, Sepuluh Nopember Institute of Technology (ITS)Surabaya, Indonesia
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Alexander Buyung, T. S. N.
 and 
Kadek Dwi Wahyuadnyana

Kadek Dwi Wahyuadnyana

  • Department of Engineering Physics, Sepuluh Nopember Institute of Technology (ITS)Surabaya, Indonesia
  • Beehive Intelligent Robotics Laboratory (BIRL)Yogyakarta, Indonesia
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Wahyuadnyana, Kadek Dwi
  
Feb 07, 2024
Experimental Validation: Perception and Localization Systems for Autonomous Vehicles using the Extended Kalman Filter Algorithm's Cover Image
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Article Category: Article
Published Online: Feb 07, 2024
Received: Aug 28, 2023
DOI: https://doi.org/10.2478/ijssis-2024-0002
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© 2024 Bambang Lelono Widjiantoro et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1:

The hardware wiring and schematics.
The hardware wiring and schematics.

Figure 2:

The physical look of a robot.
The physical look of a robot.

Figure 3:

The scenario of physical world and measurement.
The scenario of physical world and measurement.

Figure 4:

Encoders' schematic diagram.
Encoders' schematic diagram.

Figure 5:

The Localization and perception block diagram. ROS, robot operating system.
The Localization and perception block diagram. ROS, robot operating system.

Figure 6:

The map generated using the Hector-SLAM algorithm. SLAM, Simultaneous localization and mapping.
The map generated using the Hector-SLAM algorithm. SLAM, Simultaneous localization and mapping.

Figure 7:

Comparison of EKF position estimation results with references. During the experiment, we focus on two coordinates as the mobile robot moves—namely, the X and Y coordinates. Label A represents the robot's motion along the X coordinate, while label B corresponds to its movement along the Y coordinate. EKF, extended Kalman filter.
Comparison of EKF position estimation results with references. During the experiment, we focus on two coordinates as the mobile robot moves—namely, the X and Y coordinates. Label A represents the robot's motion along the X coordinate, while label B corresponds to its movement along the Y coordinate. EKF, extended Kalman filter.

Figure 8:

RViz visualization.
RViz visualization.

The EKF parameter details_

Parameter Information
β^k− \hat \beta_k^- The estimated state
f Non-linear model system
h Measurement model system
vk Measurement noise
zk IMU measurement
Wk − 1 Dynamic system noise
β^k−1+ \hat \beta_{k - 1}^+ The estimated updates state
V The linear velocity of the robot
Δt Time derivative
θ The steering angle of the robot
Qk Dynamic system noise matrix Q=[10−40000010−40000010−40000010−40000010−4] Q = \left[ {\matrix{{{{10}^{- 4}}} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & {{{10}^{- 4}}} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & {{{10}^{- 4}}} \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & {{{10}^{- 4}}} \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {{{10}^{- 4}}} \hfill \cr}} \right]
Hk IMU measurement matrix Hodometry+IMU=[1000001000001000001000001] {H_{{\rm{odometry+}}IMU}} = \left[ {\matrix{1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 1 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & 1 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 1 \hfill \cr}} \right]
Rk Measurement noise matrix R=[10−40000010−40000010−40000010−40000010−4] R = \left[ {\matrix{{{{10}^{- 4}}} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & {{{10}^{- 4}}} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & {{{10}^{- 4}}} \hfill & 0 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & {{{10}^{- 4}}} \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {{{10}^{- 4}}} \hfill \cr}} \right]
Fk Jacobians matrix, Fk=[10−Vk−1ΔtsinθkΔtcosθk001Vk−1ΔtcosθkΔtsinθk00010Δt0001000001] {F_k} = \left[ {\matrix{1 \hfill & 0 \hfill & {- {V_{k - 1}}\Delta t\sin {\theta_k}} \hfill & {\Delta t\cos {\theta_k}} \hfill & 0 \hfill \cr 0 \hfill & 1 \hfill & {{V_{k - 1}}\Delta t\cos {\theta_k}} \hfill & {\Delta t\sin {\theta_k}} \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 1 \hfill & 0 \hfill & {\Delta t} \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & 1 \hfill & 0 \hfill \cr 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 1 \hfill \cr}} \right]

The steps of the EKF-SLAM Algorithm_

EKF-SLAM Algorithm

The initial step is to initialize the previous estimated value (b_prev) and the previous covariance error (p_prev) with a value of 0.

Initialize the predicted state (b_new) based on Eq. (1)

Initialize the prediction error covariance (p_new) based on Eq. (2)

Obtain the optimal gain (K) based on Eq. (3)

Obtain an estimate of the state of the update (b) based on Eq. (4)

The estimation of the state of the update is the result of the KF displayed

Get the updated covariance error (K) based on Eq. (5)

The updated state estimate value is stored as the previous estimate, and then the state estimation algorithm returns to step 2

The error covariance update value is stored as the prior covariance, and then the error covariance algorithm returns to step 3.

The comparison of the encoder results and the reference in X-axis_

X position from odometry X reference Error
0.95 0.97 0.02
0.95 0.97 0.03
0.95 0.97 0.03
0.95 0.97 0.03
0.95 0.98 0.03
0.95 0.98 0.04
0.95 0.98 0.04
0.95 0.99 0.04
0.95 0.99 0.04
0.95 1.00 0.05
Error in average (%) 3

The details of robot parameters_

Parameter Value
Battery 12.6 V (DC)
Dimension 242.9 × 192.2 mm
Steering servo 9 kg/cm torque
Wheel motor 240 RPM
Wireless 2.4G/5G dual-band WIFI, Bluetooth 4.2
Driving type Ackerman steering dual gearmotor rear wheel drive

Comparison between the EKF positions and the reference_

X position (EKF) X reference Y position (EKF) Y reference Error X Error Y
0.97 0.97 0.02 0.02 0.00 0.00
0.98 0.97 0.02 0.02 0.01 0.00
0.98 0.97 0.02 0.02 0.01 0.01
0.98 0.97 0.02 0.02 0.01 0.01
0.99 0.98 0.02 0.02 0.01 0.02
0.99 0.98 0.02 0.02 0.01 0.04
1.00 0.98 0.02 0.02 0.02 0.04
1.01 0.99 0.02 0.02 0.02 0.04
1.01 0.99 0.02 0.02 0.02 0.04
1.02 1.00 0.02 0.02 0.02 0.05
Error in average (%) 1 3
RMSE 0.11 0.15

Accelerometer measurements_

X Y X reference Y reference X error Y error
0.02 −0.02 0 0 0.02 −0.02
0.01 −0.01 0 0 0.01 −0.01
−0.03 −0.02 0 0 −0.03 −0.02
−0.06 −0.02 0 0 −0.06 −0.02
−0.07 −0.02 0 0 −0.07 −0.02
−0.06 0.01 0 0 −0.06 0.01
−0.06 −0.03 0 0 −0.06 −0.03
0.01 0.01 0 0 0.01 0.01
−0.01 0.00 0 0 −0.01 0.00
−0.06 −0.02 0 0 −0.06 −0.02
Error in average (%) 4 2

The maximum and minimum distance values of the LiDAR data_

Maximum (m) Minimum (m)
Measured data 6.808 0.15
Actual value (reference) 6.54 0.09
Error (%) 4 67

Gyroscope orientation measurements_

X orientation Y orientation X reference Y reference X error Y error
−0.01 −0.01 0 0 −0.01 −0.01
−0.01 −0.01 0 0 −0.01 −0.01
−0.01 0.02 0 0 −0.01 0.02
−0.01 0.03 0 0 −0.01 0.03
−0.01 0.03 0 0 −0.01 0.03
0.00 0.03 0 0 0.00 0.03
−0.01 0.03 0 0 −0.01 0.03
0.00 0.00 0 0 0.00 0.00
0.00 0.00 0 0 0.00 0.00
−0.01 0.03 0 0 −0.01 0.03
Errors in average (%) 1 2

The comparison of the encoder results and the reference in Y-axis_

Y position from odometry Y reference Error
0.02 0.02 0.00
0.02 0.02 0.00
0.02 0.02 0.00
0.02 0.02 0.00
0.02 0.02 0.00
0.01 0.02 0.01
0.01 0.02 0.01
0.02 0.02 0.02
0.07 0.02 0.05
0.07 0.02 0.05
Error in average (%) 2
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