Functional Discretization of Space Using Gaussian Processes for - - PowerPoint PPT Presentation

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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

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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 Ñ E Z - G U Z M Á N 2

1I 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 2R E N A U L T S A S , F R A N C E
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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 maps Actuators Decision making

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Problem definition

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Multiple

  • verlapping

areas Dynamic behaviours

Functional discretization

Velocity profiles

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Problem definition

Challenges:

  • Learning with various behaviours
  • Scalable and adaptable to any layout
  • Representation within map standard

How to represent in map a space discretization taking into account dynamic behaviours?

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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]

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Discretization framework

Data set

  • f trajectories

Learning process Predict trajectories pattern Determine overlapping areas Determine approaching areas Merge and store

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Discretization framework

Data set

  • f trajectories

Learning process Predict trajectories pattern Determine overlapping areas Determine approaching areas Merge and store

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Data set of trajectories

A measure that contains : Timestamp when the measure has been taken, with the moment when the car is 50m away from the entrance

t0=0s,x0=2,y0=50,h0=pi/2 ti=5s,x=1.05,yi=68,hi=pi/3

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Pre-processing for learning step 1

Several trajectories with different duration

  • Solution=>Temporal normalization

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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

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Discretization framework

Data set

  • f trajectories

Learning process Predict trajectories pattern Determine overlapping areas Determine approaching areas Merge and store

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Learning process using GP

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

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Learning process

Data Hyper-parameters proposition Log marginal likelihood Hyper-parameters Minimized

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Discretization framework

Data set

  • f trajectories

Learning process Predict trajectories pattern Determine overlapping areas Determine approaching areas Merge and store

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Trajectories pattern from prediction

Learned trajectory Summation

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Discretization framework

Data set

  • f trajectories

Learning process Predict trajectories pattern Determine overlapping areas Determine approaching areas Merge and store

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Determine overlapping areas

Traji Trajj P(overlap) Condition Zone processing

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Discretization framework

Data set

  • f trajectories

Learning process Predict trajectories pattern Determine overlapping areas Determine approaching areas Merge and store

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Determine approaching areas

Traji Condition stop Zone processing Condition slow1 Condition slow2 Zone merging

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Experimentation

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Experimentation

Intersection layout Velocity profiles Path Simulator: Scaner Use in automotive industry

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Discretization framework

Data set

  • f

trajectories Learning process Predict trajectories pattern Determine

  • verlapping areas

Determine approaching areas Merge and store

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Experimentation: Simulation

lower its speed Continue Stop pass get to top speed

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1 2 3 4 5 5

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Experimentation : Real data

Experimental platform Xsens (IMU+GPS)to record trajectory Video Camera for context A X-shaped intersection

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Results: Real data

Simulation & Real-Data results are the same Observation from the front camera Elements availables for the reasoning

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5

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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

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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

  • n, 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.

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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

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Motivations

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From sensors =>Dynamic: pedestrians,

  • ther cars

From maps =>Static : layout, road signs