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Functional Discretization of Space Using Gaussian Processes for Road Intersection Crossing M A T H I E U B A R B I E R 1 , 2 , C H R I S T I A N L A U G I E R 1 , O L I V I E R S I M O N I N 1 , J A V I E R I B A E Z - G U Z M N 2 1 I


  1. Functional Discretization of Space Using Gaussian Processes for Road Intersection Crossing M A T H I E U B A R B I E R 1 , 2 , C H R I S T I A N L A U G I E R 1 , O L I V I E R S I M O N I N 1 , J A V I E R I B A Ñ E Z - G U Z M Á N 2 1 I N R I A R H Ô N E - A L P E S , C H R O M A T E A M , F R A N C E 2 R E N A U L T S A S , F R A N C E

  2. Motivations Intersections are the most dangerous situation of the road network ◦ 3384 deaths in France in 2014 ◦ Even complex for autonomous vehicles What does an Autonomous vehicle need to understand? Different behaviors and actions regarding the context ◦ Dynamic : pedestrians, other cars ◦ Static : layout, road signs Perception Decision Actuators making maps 2 11/1/2016

  3. Problem definition Multiple overlapping areas Functional discretization Dynamic behaviours Velocity profiles 3 11/1/2016

  4. Problem definition How to represent in map a space discretization taking into account dynamic behaviours? Challenges: ◦ Learning with various behaviours ◦ Scalable and adaptable to any layout ◦ Representation within map standard 4 11/1/2016

  5. Modeling trajectories : Gaussian processes ◦ Trajectories models [Tay and Laugier, 2007] ◦ Used to learn velocities profile approaching a stop intersection [Armand et al., 2013] ◦ From motion pattern to context [Liu et al., 2015] 5 11/1/2016

  6. Discretization framework Determine overlapping areas Merge and Data set Predict trajectories Learning process store of trajectories pattern Determine approaching areas 6 11/1/2016

  7. Discretization framework Determine overlapping areas Merge and Data set Predict trajectories Learning process store of trajectories pattern Determine approaching areas 7 11/1/2016

  8. Data set of trajectories : Timestamp when the measure has been taken, with the moment when the car is 50m away from the entrance A measure that contains t i =5s,x=1.05,y i =68,h i =pi/3 t 0 =0s,x 0 =2,y 0 =50,h 0 =pi/2 8 11/1/2016

  9. Pre-processing for learning step 1 Several trajectories with different duration ◦ Solution=>Temporal normalization 9 11/1/2016

  10. Pre-processing for learning step 2 Clustering 12 clusters for each possible direction Each trajectory is assigned by looking at its first and last observation 10 11/1/2016

  11. Discretization framework Determine overlapping areas Merge and Data set Predict trajectories Learning process store of trajectories pattern Determine approaching areas 11 11/1/2016

  12. Learning process using GP are supposed independent A Gaussian process is a collection of random variables, any finite number of which have a joint Gaussian distribution, [Rasmussen, 2006] GP aims to recover from the data set How: Squared exponential covariance function: 12 11/1/2016

  13. Learning process Minimized Hyper-parameters Log marginal Hyper-parameters Data proposition likelihood 13 11/1/2016

  14. Discretization framework Determine overlapping areas Merge and Data set Predict trajectories Learning process store of trajectories pattern Determine approaching areas 14 11/1/2016

  15. Trajectories pattern from prediction Summation Learned trajectory 15 11/1/2016

  16. Discretization framework Determine overlapping areas Merge and Data set Predict trajectories Learning process store of trajectories pattern Determine approaching areas 16 11/1/2016

  17. Determine overlapping areas Traj i P(overlap) Zone processing Condition Traj j 17 11/1/2016

  18. Discretization framework Determine overlapping areas Merge and Data set Predict trajectories Learning process store of trajectories pattern Determine approaching areas 18 11/1/2016

  19. Determine approaching areas Condition stop Zone Condition Zone slow1 merging processing Traj i Condition slow2 19 11/1/2016

  20. Experimentation 20 11/1/2016

  21. Experimentation Path Intersection layout Simulator: Scaner Velocity profiles Use in automotive industry 21 11/1/2016

  22. Discretization framework Determine overlapping areas Data set Predict Merge and Learning of trajectories store process Determine trajectories pattern approaching areas 22 11/1/2016

  23. Experimentation: Simulation lower its speed 1 Continue 2 Stop 3 pass 4 get to top speed 5 5 23 11/1/2016

  24. Experimentation : Real data A X-shaped intersection Experimental platform Xsens (IMU+GPS)to record trajectory Video Camera for context 24 11/1/2016

  25. Results: Real data Simulation & Real-Data results are the same 5 Observation from the front camera Elements availables for the reasoning 25 11/1/2016

  26. Conclusion Formulation of a discretization of space for decision making ◦ Applied to intersections ◦ Validation with experimentations Future work ◦ Improvement on the thresholds determination ◦ Trade off between Simulated and real-data in the dataset 26 11/1/2016

  27. References [Rasmussen, 2006] Rasmussen, C. E. (2006). Gaussian processes for machine learning. MIT Press. [Darpa, 2007] Darpa (2007). Urban Challenge Route Network Definition File (RNDF) and Mission Data File (MDF) Formats. [Tay and Laugier, 2007] Tay, C. and Laugier, C. (2007). Modelling smooth paths using gaussian processes. In Proc. of the Int. Conf. on Field and Service Robotics, Chamonix, France. voir basilic :http://emotion.inrialpes.fr/bibemotion/2007/TL07/. [Aoude et al., 2012] Aoude, G., Desaraju, V., Stephens, L., and How, J.(2012). Driver behavior classification at intersections and validation on large naturalistic data set. Intelligent Transportation Systems, IEEE Transactions on, 13(2):724 – 736. [Armand et al., 2013] Armand, A., Filliat, D., and Ibanez-Guzman, J. (2013). Modelling stop intersection approaches using gaussian processes. In ITSC, page xx, Netherlands. [Bender et al., 2014] Bender, P., Ziegler, J., and Stiller, C. (2014). Lanelets: Efficient map representation for autonomous driving. In Intelligent Vehicles Symposium Proceedings, 2014 IEEE, pages 420 – 425. [Liu et al., 2015] Liu, W., Kim, S.-W., and Ang, M. H. (2015). Probabilistic road context inference for autonomous vehicles. In 2015 IEEE International Conference on Robotics and Automation (ICRA), pages 1640 – 1647. [national interministériel de la sécurité routiere, 2015] national interministériel de la sécurité routiere, O. (2015). Bilan de l’accidentalité de l’année 2014. Technical report, ONISR. 27 11/1/2016

  28. To delete Support: Maps Maps as prior information, Different representation and information ◦ RNDF [Darpa, 2007], Lanelet [Bender et al., 2014] ◦ Crowd sourced maps New information: sematic and dynamic 28 11/1/2016

  29. Motivations From sensors =>Dynamic : pedestrians, other cars From maps =>Static : layout, road signs 29 11/1/2016

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