1 Challenge the future M.Wang, W.Daamen, S. P. Hoogendoorn and B. van Arem Driver Assistance Systems Modeling by Optimal Control Department of Transport & Planning Delft University of Technology

2 Challenge the future Outline Context Control framework for car-following support Adaptive Cruise Control (ACC) model EcoACC control model Simulation results Summary and outlook

3 Challenge the future Context Global interests in Advanced Driver Assistance Systems (ADAS). ACC are earliest ADAS in market. Public concern on environment stimulates Eco-driving assistance systems, i.e. EcoACC. Needs for model EcoACC and evaluate the effects on driving behavior.

4 Challenge the future Existing ACC Feedback controller, not optimal behavior Often be switched off at low speeds Cannot satisfy multiple control objectives Not able to model Eco-driving

5 Challenge the future This paper An optimal control framework to model ACC/EcoACC systems based on assumptions that: Other vehicles driving at constant speed within a prediction horizon; Accelerations are controlled to minimize a cost function; Costs are chosen to reflect multiple control objectives.

6 Challenge the future Schematic diagram for vehicle following control

7 Challenge the future Control framework (Local traffic) system state: x = (x 1, x 2 ) T = (s i, Δv i ) T s i - following gap Δv i - relative speed to predecessor State dynamics: u i-1 - follower acceleration u i - follower acceleration

8 Challenge the future Control framework 2 Objective function s.t. state dynamics Applying Pontryagin’s Minimum Principle entails solving coupled ODE: 1) state dynamics with initial conditions x(t 0 ) 2) co-state dynamics with terminal conditions λ(t 0 +T) λ : co-states or marginal costs of the state x

9 Challenge the future ACC model Functional requirements: Maintaining desired speed at cruising mode; Maintaining desired time gap at following mode. Control objectives: Maximize travel efficiency; Minimizing risk; Maximizing comfort.

10 Challenge the future ACC running cost with s*: desired gap, s*= v t* + s 0 ; v 0 : desired speed. The controller aims to: 1) Minimize accelerations 2) Maintain a gap close to some desired gap s * 3) Match the speed of the predecessor. Applying the solution approach yields: The optimal control law equals the marginal cost of relative speed.

11 Challenge the future Tuning of prediction horizon Leader with constant speed of 72 km/h Initial gap: s (0) = 50 m Initial speed difference: Δv (0) = 0 km/h Desired time gap: t* = 1.5 s Desired speed: v 0 = 120 km/h Prediction horizon: T = [2:20] s

12 Challenge the future Simulation results

13 Challenge the future Choice of prediction horizon Large enough to ensure expected behavior; Not too large to avoid computational complexicity. A prediciton horizon of 5 s is recommanded from the results. Intel Core 2, 2.4 GHz

14 Challenge the future EcoACC model Control objectives: ACC controller objectives + minimizing fuel consumption Running cost: ACC controller running cost + Eco cost Calculation of Eco cost: Spatial fuel consumption rate Microscopic fuel consumption model from ARRB

15 Challenge the future Comparison of ACC/EcoACC Simulation setup: Disturbance in leader speed; Initial speed difference: Δv (0) = 0 km/h; Initial gap: s (0) = 30 m; 100 m; Desired time gap: t* = 1.5 s; Desired speed: v 0 = 120 km/h; Prediction horizon: T = 5 s. Comparison 1) ACC; 2) EcoACC1, Eco cost weight = 5; 3) EcoACC2, Eco cost weight = 10.

16 Challenge the future Simulation: Ｉ nitial gap 100 m

17 Challenge the future Results (with reference to ACC) EcoACC1EcoACC2 Scenario 1 (30m) Mean speed-0.5%-1.2% Fuel consumed-3.5%-5.1% VKT * -0.5%-1.2% Scenario 2 (100m) Mean speed-0.3%-0.8% Fuel consumed-9.9%-15.2% VKT-0.3%-0.8% * VKT: Vehicle Kilometers Travelled

18 Challenge the future Summary An optimal control framework to model/design ADAS and Eco-DAS. Flexible state and running cost specifications reflecting control objectives. In our simple examples, the Eco costs result in higher fuel efficiency and similar distance traveled. Stochastic case Local and string stability Cooperation between vehicles M. Wang, S.P. Hoogendoorn, W. Daamen, R.G. Hoogendoorn and B. van Arem. Driver Support and Cooperative Systems Control Design American Control Conference. Montreal, Canada. Outlook

19 Challenge the future Questions?