9th ITS European Congress, Dublin, Ireland, 4/7 June 2013 SP 0003 Energy efficient adaptive cruise control utilizing V2X information Philipp Themann 1*, Julian Bock 1, Lutz Eckstein 1 1. RWTH Aachen University - Institut für Kraftfahrzeuge (ika), Steinbachstr. 7, 52074 Aachen, Germany, TEL +49-241-80-25673, FAX +49-241-80-22147, themann@ika.rwth-aachen.de Abstract Predictive driving style considerably reduces vehicle s fuel consumption, while systems with autonomous cruise control achieve highest savings. This paper elaborates on the optimization of the vehicle s longitudinal dynamics to reduce fuel consumption using digital map data, V2X communication and radar sensor data. The approach deployed is highly modular with respect to the utilized sensor information and directly incorporates driver s preferences. Based on human decision finding rational and intuitive planning decisions are modelled in a cost function and represent optimization constraints resulting in a driving corridor. A prediction of driving style is employed to ensure driver acceptance and preferences. This paper describes the optimization approach, determination of optimization parameters and presents first results of fuel savings in a simulated test drive. Keywords: predictive driving; energy efficiency; driver acceptance; V2X; V2I; cooperative technologies; optimization; Dijkstra s algorithm. Introduction and motivation Currently the European Commission (EC) challenges automobile industry by setting a limit of 130 g CO 2 per km for a fleet average to be achieved in 2015, which will be lowered to a limit of 95 g CO 2 per km in 2020 [1]. Automobile industry has to face these challenges to find solutions to lowering CO 2 emissions significantly. As CO 2 emission is directly connected with fuel consumption, energy efficiency of vehicles gains crucial importance. Predictive driving provides great potentials in lowering fuel consumption [2]. Driver assistance systems can be used to support the driver incorporating fuel saving driving styles. In order to completely exploit the fuel saving potential of predictive driving, a driver assistance system with automatic longitudinal control is necessary. This allows to evaluate information not directly available for the driver and to perform energy efficient velocity trajectories. Besides information from vehicle sensors, also digital map data, vehicle to vehicle and vehicle to infrastructure communication (V2X) can be used with this approach. Considering these information a speed profile can be calculated, which is optimal with respect to fuel consumption. This speed profile can differ significantly from the uninfluenced driving style
and the driver might thus refuse using the system. If this results in switching off the system no fuel savings are possible. Thus, a driver assistance system with automatic longitudinal control needs to consider driver acceptance in speed profile planning, which is elaborated in following sections of this work. State of the art Some research projects elaborate on energy efficient Adaptive Cruise Control (ACC) systems. Volkswagen presented an energy efficient ACC system in a research project in 2012 [3]. It uses an electronic horizon to replace braking by energy efficient deceleration strategies like coasting in neutral or fuel cut-off. Driver input is considered in the determination of alternative deceleration strategies. An energy efficient ACC based on an optimization of the speed profile is presented in [4]. Thereby the method of dynamic programming is used for optimization. An optimal speed profile is calculated in real time while driving, but is purely based on static map data. Different driving styles, which can be chosen by the driver, are achieved by change of parameters in a cost function. The optimization of a speed profile, which uses a cost function with linear weighting between trip length and fuel consumption, is presented in [5]. Dynamic programming is also used for optimizations to deploy fuel savings based on the knowledge of future traffic light status information. However the optimization is not applied in a vehicle yet. Research approach and methodology The research approach described in this work is deduced from a state of the art analysis. Research projects currently do not fully exploit the predictive driving approach. Either information available by V2X communication aren t used or alternative energy efficient speed profiles are only calculated for specific driving situations and not for a longer distance in front of the vehicle. Further gaps are lacking implementations of optimization approaches in vehicles and a very primitive adaptability of system behaviour to different driver preferences. This work approaches these gaps and consequently requirements on the research approach are derived. The research energy efficient ACC system has to cope with following challenges: 1) Expand conventional ACC functionalities by optimization of energy efficiency 2) Deployment of energy efficient driving strategies such as coasting or fuel cut-off 3) Consideration of driver s preferences, while keeping legal and physical limits 4) Exploitation of digital map data incorporating information from V2X communication 5) Implementation on a test vehicle without restrictions on test routes 2
Modular prediction model In order to predict the velocity of the vehicle for an upcoming situation ahead the ecosituational Model (esim) is used. This is developed within the research project ecomove [6] and provides a short term prediction in form of a velocity profile versus distance. This velocity profile is used as a basic input for the optimization to derive suitable driving strategies minimizing fuel consumption on the road ahead. Furthermore esim provides a classification of current and predicted driving situations, which can be used to consider situation specific preferences of drivers with respect to different driving strategies. Hardware limitations as well as available sensor technologies form constraints in the design of the esim. Different information sources such as radar sensors, vehicle-to-vehicle or vehicle-toinfrastructure communication are evaluated by the esim, which enables a cooperative prediction [7]. To predict the velocity of a vehicle, the different entities traffic consists of need to be considered by the esim: environment, driver and vehicle. Each entity has an impact on the velocity profile the driver chooses in a specific traffic situation. The environment contains static and dynamic information about external influences on the driver and vehicle. Static information includes all information about the road such as slopes, curvatures or speed limits, while dynamic information represents traffic jams, construction sites or obstacles. In addition to the variation in environment, the driver of a vehicle can vary in driving behaviour or driving mood. A sporty driver e.g. results in totally different velocity profiles than a conservative driver. The third entity affecting the chosen velocity profile is the vehicle itself. Technical aspects such as total vehicle mass, drive train performance or aerodynamic resistances heavily affect the acceleration of the vehicle. A passenger car has different dynamics than a heavy commercial vehicle. Utility function modelling human preferences An approach to model human decision processes with respect to the choice of energy efficient driving strategies is presented in [8] and implemented in the optimization approach discussed in this work. The resulting utility function with fuel consumption f eco, trip length t eco, normalization parameter w and weighting parameter is shown in equation 1. u opt f eco,t eco w f eco - t eco Eq. 1 This allows deriving utility values for different driving strategies and choosing the best strategy by comparing these values. In the function the weighting parameter 3 can be set by the driver to choose between sporty ( = 0) and energy efficient driving ( 1). The normalization parameter w is adjusted dynamically to the present traffic situation, which
ensures a reasonable distribution of the weighting parameter. The Pareto front, shown in Figure 1, visualizes eleven different driving strategies in a traffic situation and corresponding values for fuel consumption f eco and trip length t eco. For each strategy the w value is given, resulting in the highest utility value of the utility function for this strategy. The resulting quite equal distribution of weighting parameters along the Pareto front allows to easily forsee the impact of this parameter and use this to define driver specific preferences between sporty driving ( = 0) and energy efficient driving ( = 1). Optimization approach Figure 1: Pareto distribution with varying weighting factor w The optimization algorithm needs to fulfil some requirements for the application in a driver assistance system. Most important requirements are real time computing and calculation of a globally optimal speed profile. Real time computing thereby has to be understood as correct computation finished in time. A discretized representation of the speed profile is used in order to fulfil these requirements. The optimization of one single parameter per route segment results from the discretization of driving routes, which is thus a multi stage decision process. Furthermore driving speed and the combination of acceleration and gear status (called longitudinal dynamics variants in the following) are discretized. Possible states of longitudinal dynamics variants are energy efficient deceleration strategies such as coasting in neutral and fuel cut-off as well as some discrete values for acceleration and braking. By these discretizations, the state space for optimization is represented as a directed graph with values of a cost function defining edge weights. Edges represent possible speed profiles of 4
longitudinal dynamics variants, while nodes are velocity states at discrete route points. Given a certain starting velocity at starting position and a target velocity at target position, the optimization problem is now to find the path with lowest cost between a starting and a target node. In graph theory this problem is called single-pair shortest path problem, which is often solved by Dij stra s algorithm (see e.g. [9]. Dij stra s algorithm [10] can also be seen as application of the principle of dynamic programming on the shortest path problem [11]. Dynamic programming is based on Richard Bellman s principle of optimality: An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision. [12]. In context of the shortest path problem this means that a shortest path between two nodes A and B, which follows across nodes M and N, also follows across the shortest path between M and N. The problem representation by a graph allows further techniques to reduce optimization time. Results, which need to be calculated by a vehicle model and are used to evaluate cost function, can be pre-calculated offline and saved in a look up table. This is valid since only discrete states are considered in the graph. The complexity of evaluating the cost function can be kept down to a few memory accesses and simple arithmetic operations. By that, simulation with a vehicle model is not necessary while driving and computational demand is reduced significantly. Furthermore, calculation time can be decreased by reducing the number of nodes and edges. Calculation time directly depends on the number of edges and nodes. Here, graph size can be determined and reduced by choosing a suitable boundary condition, which can be represented by a driving corridor. Using these techniques and Dij stra s algorithm, the mentioned requirements can be hold. It is guaranteed to find a global optimum and methods allow real-time computing. Loss of precision through discretization is a drawback, but for performing real-time optimization a certain loss of precision by simplifications like discretization cannot be avoided. A higher precision is likely to be achieved in future by first of all increasing computing power. Look up table and discretization parameters In order to make use of an offline preprocessing, fuel consumption, driving time and target velocity are calculated for a distance s depending on the starting velocity. Results of this calculation are stored in a lookup table. The calculation is performed with a vehicle model, which is based on the determination of driving resistances. The lookup table needs to fully cover the expected range of the most important input variables in vehicle model calculation influencing fuel consumption. Basically a lookup table approach allows the usage of any number of parameters, range or discretization accuracy. This results however in a huge lookup table and huge amount of data accompanied by high requirements on implementation and 5
poor performance. Therefore lookup table needs to be kept as small as possible. A sensitivity analysis reveals that first of all gradients and wind speed have the largest impact on fuel consumption [13]. The variables with a low impact are not taken into account for generating the lookup table. Besides, also the wind speed isn t considered since the experimental vehicle has no sensor to monitor this. Thus it suffices to consider gradients beside the starting velocity and longitudinal dynamics variants in the lookup table. Discretization parameters need to be determined for generating the lookup table. The vehicle velocity is discretized with v =1 km/h, which is also chosen in [5], and a maximum speed of 150 km/h. Gradients are discretized with g = 1% in a range of +/- 12%, which is oriented on German road construction regulations. For the choice of discretization parameters, resulting discretization error and calculation time are crucial. For this reason other parameters are chosen by means of these criteria. Both criteria can be examined by comparing optimization of single speed profiles. Discretization error produced by distance discretization is analyzed by a simulated test drive. The speed profile is compared with best discretized approximation. Using the root mean square error, a statement about the error size can be made. In Figure 2 a boxplot for 25 m, 50 m and 100 m discretization is visualized. While the values for 25 m and 50 m discretization are in the order of the velocity discretization, values for 100 m discretization exceed this order significantly. Figure 2: Discretization error (RMSE) Since 25 m and 50 m are both suitable by means of discretization error, calculation time needs to be taken in account. Thus for distance discretization and other parameters, a sensitivity analysis with respect to calculation time is performed. The goal is to choose parameters in a way that calculation time does not exceed a value of one second significantly. Table 1 summarizes this sensitivity analysis, while standard parameter values are shown in bold. Distance discretization Calculation time Horizon length Calculation time 100 m 0.399 s 2000 m 5.944 s 50 m 1.632 s 1500 m 1.644 s 25 m 19.660 s 1000 m 0.483 s 10 m >> 200 s 500 m 0.311 s 6
Velocity [km/h] Driver s preference Energy efficient adaptive cruise control utilizing V2X information Long. dynamics variants Calculation time Driving corridor width Calculation time 84 1.639 s 50 km/h 7.724 s 44 0.674 s 40 km/h 1.616 s 24 0.573 s 30 km/h 0.531 s 12 0.507 s 20 km/h 0.374 s Table 1: Sensitivity analysis with respect to calculation time Calculation time for 25 m distance discretization exceeds the target value clearly, while this is acceptable for 50m. The horizon length is set to 1500 m, in order to allow long coasting maneuvers at a reasonable calculation time. These values are also proposed in literature [14]. Discrete longitudinal dynamics variants are defined by some discrete accelerations as well as decelerations by braking, coasting with fuel cutoff and coasting in neutral. The total amount of these variants has a minor impact on calculation time. Contrary driving corridor width has a big influence on calculation time, but cannot be set to a constant value since it is calculated for every driving situation. However, the analysis shows, that the driving corridor should be kept as small as possible, without excluding useful speed profiles with coasting deceleration. The driving corridor can be narrowed for instance at constant driving situations, where only slight deviations from the uninfluenced driving behavior is accepted. Formulation of boundary conditions and graph set up Boundary conditions represented by limiting the driving corridor ensure the autonomous system to hold legal speed limits and limits of driving dynamics. Driver acceptance is considered by a velocity dependent maximum deviation from the uninfluenced average driving style, which is provided by the simulation model esim described above. Maximum tolerated deviations may vary between drivers in order to allow a more energy efficient driving style or just very small deviations. The width of the driving corridor hence depends on the chosen value of the weighting parameter representing driver s preferences. Predicted average behaviour Speed Limit 70 km/h Speed Limit 50 km/h Upper/lower bound of driving corridor C u r v e 100 km/h 0 Traffic Light Position along electronic horizon [m] Figure 3: Composition of boundary conditions 7
Figure 3 exemplary visualizes the composition of a driving corridor based on the predicted uninfluenced velocity profile as well as maximum tolerated deviations, speed limits, traffic lights and maximal curve speeds. Within this driving corridor the graph is set up representing velocity profiles by discrete states. Validation of the optimization approach First, optimizations of single speed profiles were performed for to test whether the optimization algorithm is working correct. Figure 4 shows the state graph, upper and lower bounds and optimization results for minimum fuel consumption and minimum trip length. One can see that for minimum trip length optimization the speed profile is at the upper bound, while the minimum fuel consumption tends to avoid full acceleration and resulting braking. Figure 4: Optimization of a single speed profile In order to analyze possible reductions of fuel consumption, a simulated test drive containing about 300 optimization horizons of 1500 m is performed. For every optimized speed profile fuel consumption and trip length of average and optimized driving behavior is derived. The simulated test drive is performed with five different driver preferences (w) to analyze the influence. Table 2 summarizes mean values over the complete trip for fuel consumption and trip length resulting from a comparison between optimized and uninfluenced driving for different driver settings. Additionally the range of these values for the different optimization horizons in the trip is given. With increasing w the mean of fuel consumption increases as expected, while the mean of trip length decreases. 8
Since the system aims to reduce fuel consumption, the optimal speed profile is replaced by the original speed profile for uninfluenced driving in case the calculated speed profile results in higher fuel consumption compared to the original one. For this reason the range of fuel consumption change is limited to 0 % uninfluenced by driver s settings. An optimization with w=0.75 yields great fuel saving potentials accompanied with even shorter trip length. This reveals the great advantage of the optimization approach described considering the whole speed profile not limited to single traffic situations. w = 0.05 w = 0.25 w = 0.5 w = 0.75 w = 0.95 Mean(Δ fuel consumption) -2,74 % -4,88 % -10,09 % -11,51 % -12,88 % Mean(Δ trip length) -1,67 % -5,41 % -2,90 % -2,74 % -2,48 % Range of Δ fuel consumption -27 to 0 % -23 to 0 % -26 to 0 % -28 to 0 % -67 to 0 % Range of Δ trip length -6 to 1 % -12 to -2 % -8 to 5 % -8 to 4 % -13 to 7 % Table 2: Optimized speed profiles compared to uninfluenced driving in simulated drives In this simulated test drive neither dynamic information from V2X communication nor from radar sensors is considered. However the procedure of defining the driving corridor based on the predicted speed profile and the electronic horizon as well as the optimization is independent of the information used. Thus, V2X communication or radar sensor data can easily be added, which is not the focus of this paper. With the developed energy efficient ACC system several test drives are performed in order to analyze the system s functionality in real world conditions. Tests proof the system to be able to calculate energy efficient speed profiles in real-time and execute the corresponding maneuvers such as coasting in neutral, while a particular challenge consists in the avoidance of frequent gear changes. Detailed investigations of test drives and reductions of fuel consumption is not the focus of this work and will be provided in additional publications. Conclusion and outlook This paper presents an energy efficient ACC system considering V2X information, radar sensor and digital map data. Based upon this data, an electronic horizon is set up and a speed profile of uninfluenced driving is simulated. Herewith a driving corridor is generated wherein the optimal speed profile with respect to the weighted cost function is calculated. The system is applied in an experimental vehicle. Simulations reveal promising reductions in fuel consumption at about constant trip lengths. In this work we present an approach to directly consider driver s preferences in a factor w weighting fuel consumption versus travel time in a utility function. Our simulations presented in this work prove this approach to be useful as it results in an equal distribution of the weighting parameters w along the Pareto front and 9
hence enables drivers to intuitively configure the system to their expectations. Additional research focuses on the optimization algorithm to avoid e.g. frequent gear changes. Also the consideration of cooperative information from V2X communication is analyzed in more detail and will be published separately. Especially the total calculation time necessary for the prediction and optimization needs to be assessed for different environmental conditions. References 1. European Parliament and Council. Regulation (EC) No 443/2009, 23 April 2009 2. J. N. Barkenbus. Eco-driving: An overlooked climate change initiating, in: Energy Policy Nr. 38, 2010, Pages 762 769 3. B.Dornieden, L.Junge, P.Pascheka. Anticipatory Energy-efficient Longitudinal Vehicle Control, in ATZ worldwide emagazines Edition, March 2012 4. P. Markschläger, H-G. Wahl, F. Weberbauer, M. Lederer. Assistance System for Higher Fuel Efficiency, in ATZ worldwide emagazines Edition, November 2012 5. S. Gausemeier, K.-P. Jäker, A. Trächtler. Multi-objective Optimization of a Vehicle Velocity Profile by Means of Dynamic Programming, 6th IFAC Symposium on Advances in Automotive Control AAC, Schwabing, July 2010 6. P. Themann, et Al., ecosituational Model, Deliverable D 2.9 of the ecomove project, 2012, published at: http:// www.ecomove-project.eu 7. P. Themann., et. Al., ecodriving Support based on cooperative prediction models, ITS World Congress, Vienna, Oct. 22-26, 2012, Paper EU-00374 8. P. Themann, L. Eckstein, Modular Approach to Energy Efficient Driver Assistance Incorporating Driver Acceptance, IEEE Intelligent Vehicles Symposium, Alcalá de Henares, Spain, June 05, 2012 9. D. Mount. Dijkstra s Algorithm for Shortest Paths, University of Maryland, available at: http://www.cs.umd.edu/class/fall2012/cmsc451/lects/lect06.pdf, December 2012 10. E. W. Dijkstra, A note on two problems in connexion with graphs, in Numerische Mathematik, Vol. 1, S.269-271, 1959 11. M. Sniedovich. Dijkstra s algorithm revisited: the dynamic programming connexion, Control and cybernetics, Number.35, Page. 599, 2006 12. R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957 13. B. Dornieden, P. Themann, A. Zlocki., L. Junge. Energy efficient longitudinal vehicle control based on analysis of driving situations, 20. Aachener Kolloquium Fahrzeug und Motorentechnik, Pages 1491-1511, Aachen, 2011 14. E. Hellström, Look-ahead control of heavy trucks utilizing road topography, Dissertation, Linköping University, Sweden, 2007. 10