A Hierarchical Model-based Optimization Control Method for Merging of Connected Automated Vehicles. Na Chen, Meng Wang, Tom Alkim, Bart van Arem

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1 A Hierarchical Model-based Optimization Control Method for Merging of Connected Automated Vehicles Na Chen, Meng Wang, Tom Alkim, Bart van Arem 1

2 Background Vehicle-to-Vehicle communication Vehicle-to-Infrastructure communication Small Inter-vehicle gap... Connected Automated Vehicle (CAV) Traffic capacity increase (efficiency) 2

3 Background Mainstream lane Acceleration lane On-ramp merging scenario Which slot is the best option for the on-ramp vehicle to merge? How to generate optimal trajectories then? 3

4 Relevant research Existing methods: Control zone s exit boundary 1. Mapping Control zone s entry boundary Times-to-go comparison: 2. Heuristic approach Passing time comparison: 3. First-in-first-out 4. Optimization control method : Predefining vehicle geometrical lotus or not 4

5 Research objective Objective: to design an efficient and safe control strategy for merging of CAVs. Vehicles positions and velocities Upper level controller Future vehicle order; lane change preparation time A CAV system Lower level controller Longitudinal accelerations; lane change initiation time Actuator Centralized control method Model-based optimization 5

6 Upper level controller State variable X u : vehicle positions x i and speeds v i Control variable U u : future vehicle order r and on-ramp vehicle s lane change preparation time l p. Vehicle dynamics: dx/dt = v; dv/dt = a Car-following mode: a i = C 1 s i + C 2 v i (Helly model) s i = Real gap desired gap (v i t d + s 0 ); v i relative speed Cooperation mode: if x i-1 < x i, a i-1 = a com accelerate and a i = d com decelerate Car-following Cooperation Car-following l p d t 1) s r (d t ) and s r-1 (d t ) are large enough 2) a r (d t ), a r-1 (d t ) ϵ [d com, a com ] t 6

7 Upper level controller t1 T Objective function min l p, r t 1 N N N c1 si c2 vi c3 aix dt i 1 i 1 i 1 Subject to: (1) a i ϵ [a min, a max ]; (2) v i ϵ [0, v limits ]; (3) r ϵ {2,3,..,N-1}; (4) Car-following mode and cooperation mode (5) Vehicle dynamics (6) The on-ramp vehicle completes lane changing when it is on the acceleration lane Quadratic mixed integer programming problem 7

8 Lower level controller Model Predictive Control (MPC) An objective function Optimizer An explicit Model Independent variables; t [t 0, t 0 +T p ] Plant Output t= t 0 + t Measurements (t 0 ) A new cycle t 0 = t 0 + t State variable X l : vehicle positions x i and speeds v i Control variable U l : Vehicles longitudinal accelerations a ix and on-ramp vehicles lane change initiation time l t 8

9 Lower level controller t0 Tp l l Objective function min L, l X U U [ t, t T ] 0 0 p t 0 dt N N N L c s c v c a 1 i 2 i 3 ix i 1 i 1 i 1 safety efficiency control to reach equilibrium states to have smooth accelerations l t : s r (l t ) and s r-1 (l t ) are large enough to change lane Trajectory equation: to generate lateral motion for the merging vehicle Subject to same constraints as upper level controller excluding cooperation mode. 9

10 Experiment design & Results Controller parameters: 1) t d = 1 s 2) v i ϵ [0, 30] m/s 3) a i ϵ [-5, 2] m/s 2 Initial states: v i = 25 m/s r ϵ {2,3,4,5}; Decision from different methods: r=4, l p =0 s. (first-in-first-out) r=3, l p =4 s. (designed upper level controller) 10

11 Experiment design & Results l t =9.6 s r=4, l p =0 s. (first-in-first-out) l t =8.2 s r=3, l p =4 s. (designed upper level controller) 11

12 Experiment design & Results Table 1 Objective function values comparison r=3, l p =4 s r=3, l p =3 s r=4, l p =0 s Upper level 283,97 290,38 305,19 Lower level 1725, , ,38 Different time steps Comparison: % decrease Advantages of the proposed control method: 1. to consider the lane change preparation time 2. to choose a reasonable vehicle order 3. to have small sizes of dimension for control variables 12

13 Conclusion The proposed control method vehicle order + lane change preparation time safe and efficient trajectories for CAVs Future research direction Multiple mainstream lanes Mixed traffic 13

14 A Hierarchical Model-based Optimization Control Method for Merging of Connected Automated Vehicles Mainstream lane Acceleration lane On-ramp merging scenario 14