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Bayesian risk assessment of autonomous vehicles

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Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.

Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.

The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.

Published in: Automotive
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Bayesian risk assessment of autonomous vehicles

  1. 1. BAYESIAN RISK ASSESSMENT OF AUTONOMOUS VEHICLES Christos Katrakazas Mohammed Quddus Wen-Hua Chen* Transport Studies Group School of Civil and Building Engineering *Department of Aeronautics and Automobile Engineering Loughborough University NORTHMOST 01: ITS-Leeds Monday 12th Dec.
  2. 2. Overview  Introduction to the problem  Bayesian & Dynamic Bayesian Networks (DBN)  DBN models and risk assessment of autonomous vehicles - Variables, estimation of probabilities and inference  Preliminary findings  Potential contribution
  3. 3. 3 Introduction Human error is responsible for causing 75 – 90% traffic accidents Examples: • Blind-spots & line of sight • Risk perception • Reaction time • Impaired driving • Fails to look properly • Excessive/inappropriate speed Removing the human element from the task of driving Potential Solution? Autonomous vehicles
  4. 4. Road to Autonomy Potential obstacles? - Reliability - High quality data - Perception horizon How could Transport Professional help? 4 © European Commission Roadmap for automated driving
  5. 5. 5 Robotics  Expensive sensors  Real-time effectiveness  Lack of context Collision Prediction (vehicle-level) In-vehicle sensors Dangerous road user
  6. 6. 6 Transport Engineering  Aggregated data  Location-based variables  Spatio-temporal risk Could network-level collision predication in transport engineering be integrated to vehicle-level risk assessment of autonomous vehicles? - Bayesian Inference? Collision Prediction (network-level) Dangerous road segment Classification Real-time traffic data
  7. 7. Bayesian Networks  Directed Acyclic Probabilistic Graphs  Every node represents a random variable  Edges represent probabilistic dependencies or influences  Joint Probability Distribution shows how a situation is modelled (e.g. the probabilistic relationship between the variables of the whole system) 7
  8. 8. Bayesian Networks • Suitable for learning causal relationships • Ideal representation for combining prior knowledge and data • Help in modelling noisy systems • Can handle situations where data is incomplete BUT Are applied for events in a particular point in time! 8
  9. 9. Dynamic Bayesian Networks (DBN)  Bayesian Networks used to model a system that dynamically changes or evolves over time  Probabilistic reasoning over time  How do the variables affect each other over time?  Requirements for DBNs: 1. A prior probability P(x1) 2. A state-transition function P(xt|xt-1) 3. An observation function P(Yt|xt) Time slice 9
  10. 10. Dynamic Bayesian Networks (DBN) 1. A prior (initial) probability distribution P(x1) in the beginning of the process; 2. A state-transition function P(xt|xt-1) specifies time dependencies between states/variables; 3. An observation function P(Yt|xt) Specifies dependencies of observation nodes regarding to other nodes at time slice t. 10 Time slice
  11. 11. Dynamic Bayesian Network (DBN): Example Raint-1 P(Raint-1) True (T) 0.7 False (F) 0.3 Raint P(Umbrellat|Raint) T 0.9 F 0.1 Rain : Hidden Variable Umbrella : Observed Variable 11
  12. 12. Research Question How could fundamental principles of robotics and transport engineering be integrated in addressing research challenges associated with real-time crash prediction of autonomous vehicles?  Act proactively for the ego-vehicle  Improve real-time prediction by using network-level hint  Take traffic environment into account  May reduce the need for expensive (“super”- accurate) sensor measurements Potential improvements?
  13. 13. Modelling crash prediction in real-time Required variables:  Network-level Risk (CRN): “Is the road segment on which the vehicle travels dangerous or not?”  Vehicle-level Risk (CRV): “Are the vehicles in the vicinity of the ego- vehicle dangerous or not?”  Vehicle Kinematics (K): “How likely is that the vehicles will follow the same course according to a physical model of motion?”  Sensor Measurements (Z): “How likely is that the measurements from the sensors are giving the correct values?”
  14. 14. How are the variables connected? Observations (Z) Kinematics (K) Crash Risk Vehicle-Level (CRV) Crash Risk Network-Level (CRN) What happens on the road segment influences the behaviour of the vehicles If a situation between vehicles is dangerous, their motion will be affected The motion of the vehicles is depicted in the sensors’ observations
  15. 15. Variable relationship depicted as a DBN t t + 1 t+2 Figure: Dynamic Bayesian Network Markov State Space model Multi-vehicle dependencies Single vehicle dependencies
  16. 16.  Use traffic flow parameters to estimate the risk of an accident happening in real-time  Compare & Contrast traffic conditions just before an accident with normal conditions Data: Highways England & DfT • 15-min Traffic flow data (HATRIS JTDB) • Historical Accident data (STATS 19) • Traffic microsimulation (PTV VISSIM) -> 30second traffic data Method : Machine learning classifiers (i.e. SVMs, RVMs, Random Forests, k-Nearest Neighbours) Network – Level Risk
  17. 17.  Represents the probability of a crash happening between two vehicles  Needs a well-calibrated metric or risk indicator Data  Sensor measurements, Maps, Vehicle trajectories  Methods  Unscented Kalman Filter for sensor data fusion, Time-to- collision metrics  Problems: Efficient data fusion, crashes in real-world environments Vehicle – Level Risk
  18. 18. Safe and dangerous vehicle contexts Which of the vehicle trajectories end up in a collision? Vehicle – Level Risk 𝑓𝐾 = 𝑓(TTCn t−1 ) = ቊ 1: dangerous 𝑖𝑓 TTCn t < 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑇𝑇𝐶 0: 𝑠𝑎𝑓𝑒; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
  19. 19. Kinematics/ Vehicle motion Kinematics • Kinematics variable describes the probability that the vehicle will follow a certain course according to the context. • Uses information on position, heading and speed to distinguish between contexts
  20. 20. Kinematics/ Vehicle motion Kinematics Bicycle model Compromise between bicycle model estimations and context thresholds Accuracy of the sensors’ system
  21. 21. Sensor measurements • Each measurement from the sensors contains only partial information about the environment • This variable (Z) describes the probability that the sensor readings correspond correctly to the real values of the attributes that are measured Sensor Measurements
  22. 22. Correct measurements probability Sensor Measurements 𝑃 Τ𝑍 𝑛 𝑡 𝐾 𝑛 𝑡 ~ 𝑆𝑡𝑢𝑑𝑒𝑛𝑡 𝐶 𝑇 𝐾 𝑛 𝑡 , 𝜎2 𝛪, 𝜈 where C is a rectangular matrix that selects entries from the kinematic (physical state), ν are the degrees of freedom, Ι is the identity matrix and σ is related to the accuracy of the sensor system.
  23. 23. Inference t t + 1 t+2 𝑷 𝑪𝑹𝑽 𝒏 𝒕 = 𝒅 𝑪𝑹𝑽 𝑵 𝒕−𝟏 𝑲 𝑵 𝒕−𝟏 𝑪𝑹𝑵 𝒏 𝒕 > λ
  24. 24. Preliminary Findings: Vehicle-level risk estimation 𝑷 𝑪𝑹𝑽 𝒏 𝒕 = 𝒅 𝑪𝑹𝑽 𝑵 𝒕−𝟏 𝑲 𝑵 𝒕−𝟏 𝑪𝑹𝑵 𝒏 𝒕 and assuming 6 vehicles are sensed by the ego-vehicle With network-level hint σ 𝒏=𝟏 𝑵 (𝒇 𝑲 𝒏 = 𝟏) + σ 𝒏=𝟏 𝑵 (𝒇 𝑪𝑹𝑽 𝒏 = 𝟏) + σ 𝒏=𝟏 𝑵 (𝒇 𝑪𝑹𝑵 𝒏 = 𝟏) 𝑵 = 𝟏+𝟏+𝟏 𝟔 = 𝟎. 𝟓 Without network-level hint σ 𝒏=𝟏 𝑵 (𝒇 𝑲 𝒏 = 𝟏) + σ 𝒏=𝟏 𝑵 (𝒇 𝑪𝑹𝑽 𝒏 = 𝟏) 𝑵 = 𝟏 + 𝟏 𝟔 = 𝟎. 𝟑𝟑 By simply adding a function checking the network-level collision risk, hazardous vehicle identification is potentially improved!
  25. 25. 25 Potential contribution  Improve real-time effectiveness of vehicle-level collision prediction by making use of network-level risk - Knowing the road segment where an accident is likely to happen - Find faster which car is going to trigger the accident in this road segment  Make AVs drive in a human-like cautious way in road segments which are flagged dangerous (e.g reduce speed)  Assist obstructed or low-cost AV sensor’ systems.
  26. 26. Inspiring Winners Since 1909 Thank you! Christos Katrakazas c.katrakazas@lboro.ac.uk

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