A DRIVING OPERATIONAL BEHAVIOR ANALYSIS BASED ON THE STATE - PowerPoint PPT Presentation

A DRIVING OPERATIONAL BEHAVIOR ANALYSIS BASED ON THE STATE TRANSITION MODEL FOR AUTONOMOUS VEHICLES Yasuhiro, Akagi*, Pongsathorn Raksincharoensak* * Tokyo University of Agriculture and Technology akagi-y@cc.tuat.ac.jp

Introduction Shared control / Cooperative driving is a practical method for complicated traffic environment like urban areas. Role of systems: instruct the safe driving plan trough display, sound, haptic and force feedback HMI devices. Cooperative Role of human drivers: follow (override) the system instructions to keep safety. Complementing the weak points of both the human and systems realizes safe driving.

Problems If systems present the multiple operational orders to the driver through multiple HMI devices at the same time. HUD shows slow down operation. Steering wheel gives force feedback for avoidance operation. Warning: person Sound explains the situations. approaching! Gas pedal gives haptic feedback to release. It is difficult for the driver to understand the multiple kind instructions in a short time.

Goal An evaluation model gives the feasibility of switching driving behaviors by using the state transition model. Input: state of driving operational behaviors Braking C Cruising Acceleration 1 Continuation probability of Feasibility to switch 0.8 the current state = Cruising 0.6 Output: 0.4 Transition probability 0.2 of next state = Braking 0 Time

State transition model of driving behaviors Longitudinal state transition model Lateral state transition model C H A B L R A:Acceleration L:Left B:Braking R:Right C:Cruising H:Holding State transition probability is denoted by the conditional probability model. A C P C A

State transition model of driving behaviors State transition model of the steering wheel State transition model of the foot pedal operations when a foot pedal is operated. operations when a steering wheel is operated. C H H C or or A L L A or or B R R B This model represents the co-occurrence probability of the state transition of a driving interface (foot pedal or steering wheel) while the driver is operating another interface.

Data collection Subjects ： 6 instructors of a driving school Time ： 9 am, 4 pm ： 4 km × 2 sessions Route Area : Residential area near the train station Data types: � GNSS positioning Elementary � Steering wheel angle School � Gas pedal operation � Brake pedal operation � Velocity � Acceleration Station � Yaw rate https://www.openstreetmap.org/#map=17/35.70374/139.51991

Initial labeling of driving behaviors The input motion data is divided every 0.1 second to classify. x i , y i , v i , θ i X ( a > a t) Acceleration The pedal control state is decided Cruising ( −a t ≥ a ≥ at ) S p a = with the acceleration value a . (a < −a t) Braking at=0.1 m/s2 Threshold: ( 𝜔 < − 𝜔 t) Left The steering wheel operation state is decided ( − with the yaw rate 𝜔 . 𝜔 = Holding 𝜔 t ≥ 𝜔 ≥ 𝜔 t ) S s Right ψt=0.05 rad/s ( 𝜔 > 𝜔 t) Threshold: Initial label list: many discontinuous state transitions.

Integration of the driver states based on minimum cut algorithm By applying the minimum cut algorithm, the driver states are classified in two states. Initial state sequence A A C C B B B Min-cut for B or others B (source) A (source) 1.0 Physical distance A Min-cut A A A as weight 1.0 C C C 1.0 Cost for B B B changing state 1.0 Others (sink) Others (sink) B C B C A C B C

Probabilistic models of the driver state transition Longitudinal state transition model Actual state transition probability 1.00 Transition probability Destination state P(C|C) Source state C 0.75 C A B P(A|C) P(B|C) 0.50 C A B P(C|C) P(A|C) P(B|C) 0.25 0.00 0 2 4 6 8 10 Time (s) Approximation function: 1 Cumulative distribution function of k=1,θ=1 Gamma distribution (CDFG) 0.8 k=1,θ=3 Value of CDFG CDFG t ,k,θ = γ(k,t/θ) k=1,θ=5 0.6 Γ(k) × k=3,θ=1 0.4 ＊ k=3,θ=3 0.2 t : Continues time of the current state k=3,θ=5 ● Γ : Gamma function 0 0 5 10 γ : Incomplete Gamma function Time

Results and discussions Destination state P A t,C = CDFG t,kca,θca /2 C A B P C t,C = 1 − P A t,C − P B t,C P B t,C = CDFG t,kcb,θcb /2 C P(C|t,C) P A t,C P(B|t,C) Source state P C t,A = CDFG t,kac,θac A P A t,A = 1 − P C t,A P(C|t,A) P(A|t,A) 0 P C t,B = CDFG t,kbc,θbc B P(C|t,B) 0 P(B|t,B) P B t,B = 1 − P C t,B 1.00 1.00 1.00 1.00 Transition probability P B t,B P A t,A P C t,C 0.75 0.75 0.75 0.75 P C t,B P A t,C P B t,C P C t,A data$IdolOrg data$AccOrg data$Acc data$Idol 0.50 0.50 0.50 0.50 0.25 0.25 0.25 0.25 0.00 0.00 0.00 0.00 0 10 20 30 40 0 2 4 6 8 10 0 0 2 2 4 4 6 6 8 8 10 10 Time (s)

Results and discussions Destination state P L t,H = CDFG t,khl,θhl /2 H L R P H t,H = 1 − P L t,H − P R t,H P R t,H = CDFG t,k hr ,θ hr /2 H Source state P(H|t,H) P(L|t,H) P(R|t,H) P H t,L = CDFG t,klh,θlh L P(H|t,L) P(L|t,L) 0 P L t,L = 1 − P H t,L R P H t,R = CDFG t,krh,θrh P(H|t,R) 0 P(R|t,R) P R t,R = 1 − P H t,R Transition probability 1.00 1.00 1.00 P H t,H 0.75 P H t,L P H t,R 0.75 0.75 P L t,H P R t,H 0.50 0.50 0.50 P R t,R P L t,L 0.25 0.25 0.25 0.00 0.00 0.00 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time (s)

Results and discussions Lat c Lat={H ⋃ L ⋃ R} C H P(Latc,C|t,Lat,C) C or A L P(Latc,A|t,Lat,A) A = CDFG t,klat,θlat or B R P(Latc,B|t,Lat,B) B 1.00 State transition model of the steering wheel Transition probability operations when a foot pedal is operated. 0.75 0.50 0.25 Feasibility of switching the steering wheel operation is not related to the operation 0.00 type of the pedals. 0 2 4 6 8 10 Time (s)

Results and discussions Lonc Lon={C ⋃ A ⋃ B} H C or P(Lonc,H|t,Lon,H) H = CDFG t,klonH,θlonH L A P(Lonc,L|t,Lon,L) L or = CDFG t,k lonLR ,θ lonLR R B P(Lonc,R|t,Lon,R) R 1.00 1.00 State transition model of the foot pedal Transition probability operations when a steering wheel is operated. 0.75 0.75 0.50 0.50 0.25 0.25 Feasibility of switching the foot pedal operation depends on the operation type 0.00 0.00 of the steering wheel. 0 0 2 2 4 4 6 6 8 8 10 10 Time (s)

Results and discussions Parameters of the state transition probabilities Longitudinal control state Lateral control state K θ K θ transition transition P A t,C 0.5 1.31 P L t,H 0.43 2.27 P B t,C 1.31 0.82 P R t,H 0.43 2.27 P C t,A 1.18 6.81 P H t,L 0.75 0.95 P C t,B 0.58 2.8 P H t,R 0.68 1.12 Longitudinal co-occurrence state Lateral co-occurrence state P Lat C ,C t,Lat,C P L on C ,H t,Lon,H 0.37 9.2 P LatC,A t,Lat,A P L on C ,L t,Lon,L 0.31 2.96 P LatC,B t,Lat,B 0.63 2.84 P L on C,R t,Lon,R

Application Behavior Planner for Autonomous Vehicles which translates the motion plan can be easier to control by the driver. Input: motion plan generated by a driving support system • Frequent B C B C A C B C • Simultaneous R H L H R H L H R H operation switching Arbitration layer: replaces the complex operations based on the proposed state transition model. • Reduce switching B C A B C Is it possible to follow R H L H R L R the original path?

Application The control parameters are Target section of the Pri,0 = { a i,0, a i,0, ψ i,0, ψ i,0} state transition. optimized to minimize the sum Pei,0 of the difference from the input Pri,1 = { a i,1, a i,1, ψ i,1, ψ i,1} Pri,2 = { a i,2, a i,2, ψ i,2, ψ i,2} path plan. Pei,1 Pei,2 Waypoint: Wpi Modification error. Results: Input Trajectory Plan Simplification level and path error 1 0 Y (m) Feasibility Mean Standard -1 -2 threshold (%) error (m) deviation (m) -3 0 50 100 150 0 0.11 0.20 X (m) 5 0.13 0.30 Velocity Headway angle 0.15 8 10 0.17 0.41 V (m/s) (rad) 6 15 0.59 1.90 0.00 4 20 1.22 3.87 2 -0.15 0 25 1.97 5.46 0 50 100 150 0 50 100 150 X (m) X (m)

Conclusion • The state transition models of the driving operations are proposed. • The feasibility of the operation switching of drivers can be approximated by using Cumulative distribution function of Gamma distribution. • The driving behavior planner for the arbitration layer between the motion planner and HMI devices is shown as the application. • As a future work, the comparative experiments of the acceptability of HMI devices equipped with/without the arbitration layer will be performed.

A DRIVING OPERATIONAL BEHAVIOR ANALYSIS BASED ON THE STATE TRANSITION MODEL FOR AUTONOMOUS VEHICLES http://www.coi.nagoya-u.ac.jp/en This research is supported by the Center of Innovation (COI) Program from Japan Science and Technology Agency, JST.