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presentation by: Alon Baruch
Deep Learning and Its Applications to Signal and Image Processing and Analysis presentation by: Alon Baruch
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A Sensor Fusion Method Based on an Integrated Neural Network and Kalman Filter for Vehicle Roll Angle Estimation By: Leandro Vargas-Meléndez, Beatriz L. Boada, María Jesús L. Boada, Antonio Gauchía and Vicente Día
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outline Introduction – “smart” vehicle safety.
9/17/2018 Introduction – “smart” vehicle safety. Problem description – vehicle roll angle estimation. Presented solution – NN + Kalman Filter architecture. Validation of a simulation model. Simulation and experimental Tests. Conclusions.
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Introduction “smart” vehicles – vehicle safety.
9/17/2018 “smart” vehicles – vehicle safety. Electronic Stability Control (ESC) Roll Stability Control (RSC) Detecting and reducing loss of traction. Applies the breaks to help “steer” the vehicle.
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Lateral stability ex 9/17/2018
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Lateral stability ex 9/17/2018
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Introduction - Roll Stability Control
9/17/2018 State Estimation – High accuracy Inertial Measurement Unit (IMU). Physical vehicle model. Low cost sensors – sensor fusion algorithms. Dual-antenna GPS. And more types of specially designed and expensive sensors such as suspension deflection sensors…
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Problem definition 9/17/2018 To estimate the vehicle roll angle 𝜙 in order to control the vehicle angle and prevent a roll over.
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The presented solution:
9/17/2018 To train a Neuron Network to identify different states of the vehicle in according with the roll angle and to use the Network output as a pseudo measurement in the Kalman Filter
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Estimator architecture
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Neural Network architecture
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NN- training The training data set is comprised of:
9/17/2018 The training data set is comprised of: 𝑥= 𝑎 𝑦𝑚 , 𝑎 𝑥𝑚 , 𝜙 𝑚 , 𝜓 𝑚 𝑎𝑛𝑑 𝑑= 𝜙 𝑑 Obtained from a simulator (TruckSim), which is experimentally validated. The training data contain different movement types: Double Lane Change(DLC) – from 30 to 140 km/h Lane Change (LC) – from 30 to 140 km/h J-turn maneuver– from 30 to 140 km/h With different road friction coefficient.
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Kalman Filter Optimal estimator (linear case).
9/17/2018 Optimal estimator (linear case). In the discrete state space system: 𝑥 𝑘 =𝐴 𝑥 𝑘−1 + 𝑤 𝑘 𝑦 𝑘 =𝐻 𝑥 𝑘 + 𝑣 𝑘 estimate the state vector 𝑥 given the measurement 𝑦. 𝐴 is the state evolution matrix. 𝐻 is the observation matrix. 𝑤 𝑘 , 𝑣 𝑘 are process uncertainty and measurement noise respectively assumed to be Gaussian, zero mean stationary and uncorrelated. 𝑤~𝑁 0,𝑄 𝑣~𝑁 0,𝑅
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Side note: Kalman Filter equations
9/17/2018 Prediciton: 𝑥 𝑘+1 − =𝐴 𝑥 𝑘 + 𝑃 𝑘+1 − =𝐴 𝑃 𝑘 + 𝐴 𝑇 +𝑄 Correction: 𝐾 𝑘 = 𝑃 𝑘+1 − 𝐻 𝑇 𝐻 𝑃 𝑘+1 − 𝐻 𝑇 +𝑅 −1 𝑥 𝑘+1 + = 𝑥 𝑘+1 − + 𝐾 𝑘 𝑦−𝐻 𝑥 𝑘+1 − 𝑃 𝑘+1 + =(𝐼− 𝐾 𝑘 𝐻) 𝑃 𝑘+1 −
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State space model The state vector: 𝑥 𝑠 = Δ 𝐹 𝑧𝑙 , 𝑎 𝑦 , 𝑎 𝑦 ,𝜙, 𝜙
9/17/2018 The state vector: 𝑥 𝑠 = Δ 𝐹 𝑧𝑙 , 𝑎 𝑦 , 𝑎 𝑦 ,𝜙, 𝜙 The measurement vector: 𝑦 𝑘 = 𝑎 𝑦 ,𝜙, 𝜙 ,Δ 𝐹 𝑧𝑙 Notice that the measurement 𝜙= 𝜙 𝑁𝑁 is the output of the NN
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Experimental validation of the simulation
An experiment to adjust the model parameters The target vehicle: 9/17/2018
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Experimental validation of the simulation
9/17/2018 TruckSim is widely-used simulation software in the automotive industry. The simulation parameters should be adjusted to the vehicle model. Simulation parameter adjustment:
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Validation results 9/17/2018 DLC maneuver at 70 km/h
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Validation results 9/17/2018 Good Enough? DLC maneuver at 70 km/h
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Validation results 𝐸 𝑡 - MSE normalized error
9/17/2018 𝐸 𝑡 - MSE normalized error 𝐸 𝑚𝑎𝑥 - maximum MSE error
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Simulation test After the simulation was validated in respect to the real vehicle, the estimator can be tested in simulation 2 maneuvers were tested: Sine sweep at 50/70 km/h Slalom at 35 km/h Comparison between the proposed architecture and a pseudo measurement taken by suspension deflection sensors: Δ 𝑖𝑗 - suspension deflection at position 𝑖,𝑗 (back-forth,front-rear) 𝑚 𝑣 - vehicle weight. 𝑘 𝑡 - roll stiffness (tire stiffness) 9/17/2018
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Simulation test 1 LKF – Linear Kalman Filter NN – Neuron Network
9/17/2018 LKF – Linear Kalman Filter NN – Neuron Network DEF – Suspension deflection Measured - simulated Slalom maneuver at 35 km/h with a friction coefficient of 0.3
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Simulation test 2 LKF – Linear Kalman Filter NN – Neuron Network
9/17/2018 LKF – Linear Kalman Filter NN – Neuron Network DEF – Suspension deflection Measured - simulated Sweep maneuver at 70 km/h with a friction coefficient of 0.3
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Simulation summary 9/17/2018 The normalized error of the proposed method is smaller. But the maximum error isn’t smaller for half of the presented cases.
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Experimental test Experimental testing of different maneuvers between:
9/17/2018 Experimental testing of different maneuvers between: DEF-LKF NN NN-LKF 2 maneuvers were tested: Sine sweep at 50/70 km/h Slalom at 35 km/h
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Experimental test 1 9/17/2018 (a)-DLC at 70 km/h (b)-LC at 70 km/h
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Experimental test 3 J-turn and Slalom maneuver 9/17/2018
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Experimental test 3 9/17/2018
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Results summary 100% better result for the norm error
80% better result for the maximum error In the worst case the maximum difference between the estimators roll angle is 0.197° which is negligible. Using just the NN isn’t enough 9/17/2018
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Conclusion The NN module estimate a pseudo measurement that is feed into a linear KF. The proposed method only use an IMU and doesn’t require more sensors which are expensive and aren’t always available. The estimator was validated by a simulation and an experiment, with different maneuvers, speed and friction coefficients. The proposed estimator improved the overall results in 71% of the cases that were analyzed. Using just the NN isn’t enough 9/17/2018
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Appendix A1: KF equations
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Appendix A2: KF equations
9/17/2018 The lateral load transfer function: Where ℎ 𝑓 , h r are the heights of the front and rear roll centers respectively, 𝑘 𝑓 , 𝑘 𝑟 - roll stiffness 𝑒 𝑓 , 𝑒 𝑟 - vehicle tracks 𝑙 𝑓 , 𝑙 𝑟 - distance from the Center Of Gravity (COG) to the front and rear axles. Lateral acceleration measurement: Assuming small 𝜙:
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Appendix B: vehicle model parameters
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Appendix C: Experimental test 2
9/17/2018 Slalom maneuver at 45 km/h
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Appendix D: Experimental test 3
J-turn and DLC maneuver 9/17/2018
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Appendix D: Experimental test 3
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