KTH Royal Institute of Technology and Scania are entering the GCDC 2011 under the name Scoop –Stockholm Cooperative Driving. This paper is an introduction to their team and to the technical approach theyare using in their prototype system for GCDC 2011.
The current system of global trade is largely based on transportation and communication technology from the 20th century. Advances in technology have led to an increasingly interconnected global market and reduced the costs of moving goods, people, and technology around the world [1]. Transportation is crucial to society, and the demand for transportation is strongly linked to economic development. Specifically, road transportation is essential since about 60% of all surface freight transportation (which includes road and rail transport) is done on roads [2]. Despite the important role of road freight transportation in the economy, it is facing serious challenges, such as those posed by increasing fuel prices and the need to reduce greenhouse gas emissions. On the other hand, the integration of information and communication technologies to transportation systems-leading to intelligent transportation systems-enables the development of cooperative methods to enhance the safety and energy efficiency of transportation networks. This article focuses on one such cooperative approach, which is known as platooning. The formation of a group of heavy-duty vehicles (HDVs) at close intervehicular distances, known as a platoon (see Figure 1) increases the fuel efficiency of the group by reducing the overall air drag. The safe operation of such platoons requires the automatic control of the velocity of the platoon vehicles as well as their intervehicular distance. Existing work on platooning has focused on the design of controllers for these longitudinal dynamics, in which simple vehicle models are typically exploited and perfect environmental conditions, such as flat roads, are generally assumed. The broader perspective of how platooning can be effectively exploited in a freight transportation system has received less attention. Moreover, experimental validations of the fuel-saving potential offered by platooning have typically been performed by reproducing the perfect conditions as assumed in the design of the automatic controllers. This article focuses on these two aspects by addressing the following two objectives.
In this paper, we consider the problem of finding decentralized controllers for heavy-duty vehicle (HDV) platooning by establishing empiric results for a qualitative verification of a control design methodology. We present a linear quadratic control framework for the design of a high-level cooperative platooning controller suitable for modern HDVs. A nonlinear low-level dynamical model is utilized, where realistic response delays in certain modes of operation are considered. The controller performance is evaluated through numerical and experimental studies. It is concluded that the proposed controller behaves well in the sense that experiments show that it allows for short time headways to achieve fuel efficiency, without compromising safety. Simulation results indicate that the model mimics real life behavior. Experiment results show that the dynamic behavior of the platooning vehicles depends strongly on the gear switching logic, which is confirmed by the simulation model. Both simulation and experiment results show that the third vehicle never displays a bigger undershoot than its preceding vehicle. The spacing errors stay bounded within 6.8. m in the simulation results and 7.2. m in the experiment results for varying transient responses. Furthermore, a minimum spacing of -0.6. m and -1.9. m during braking is observed in simulations and experiments, respectively. The results indicate that HDV platooning can be conducted at close spacings with standardized sensors and control units that are already present on commercial HDVs today.
Vehicle platooning has become important for thevehicle industry. Yet conclusive results with respect to thefuel reduction possibilities of platooning remain unclear, inparticular when considering constraints imposed by the topography.The focus of this study is to establish whether itis more fuel-efficient to maintain or to split a platoon that isfacing steep uphill and downhill segments. Two commercialcontrollers, an adaptive cruise controller and a look-aheadcruise controller, are evaluated and alternative novel controlstrategies are proposed. The results show that an improvedfuel-efficiency can be obtained by maintaining the platoonthroughout a hill. Hence, a cooperative control strategy basedon preview information is presented, which initiates the changein velocity at a specific point in the road for all vehiclesrather than simultaneously changing the velocity to maintainthe spacing. A fuel reduction of up to 14% can be obtainedover a steep downhill segment and a more subtle benefit of0.7% improvement over an uphill segment with the proposedcontroller, compared to the combination of the commerciallyavailable cruise controller and adaptive cruise controller thatcould be used for platooning. The findings show that it isboth fuel-efficient and desirable in practice to consider previewinformation of the topography in the control strategy.
The transport-related externalities of the urban logistics system impact the urban environment and the health of the citizens: there is a need to improve the sustainability of the system. In this paper, we use a framework for sustainability performance abessment and a literature review to analyse the urban logistics concepts of electrification, consolidation, cargo bikes and automation. In the literature, there is a focus on pollution, while a holistic perspective on sustainability is lacking. A Sustainability Performance Abessment (SPA) matrix is the main result of this paper, as a tool for comparing the concepts and understanding how they can be combined to achieve integrated benefits. To make informed decisions, stakeholders need knowledge from a holistic perspective. The findings presented in this paper are a first step to achieving this required knowledge.
Truck drivers are required to stop and rest with a certain regularity according to the driving and rest time regulations, also called Hours-of-Service (HoS) regulations. This paper studies the problem of optimally forming platoons when considering realistic HoS regulations. In our problem, trucks have fixed routes in a transportation network and can wait at hubs along their routes to form platoons with others while fulfilling the driving and rest time constraints. We propose a distributed decision-making scheme where each truck controls its waiting times at hubs based on the predicted schedules of others. The decoupling of trucks' decision-makings contributes to an approximate dynamic programming approach for platoon coordination under HoS regulations. Finally, we perform a simulation over the Swedish road network with one thousand trucks to evaluate the achieved platooning benefits under the HoS regulations in the European Union (EU). The simulation results show that, on average, trucks drive in platoons for 37 % of their routes if each truck is allowed to be delayed for 5 % of its total travel time. If trucks are not allowed to be delayed, they drive in platoons for 12 % of their routes.
This paper considers the problem of hub-based platoon coordination for a large-scale transport system, where trucks have individual utility functions to optimize. An event-triggered distributed model predictive control method is proposed to solve the optimal scheduling of waiting times at hubs for individual trucks. In this distributed framework, trucks are allowed to decide their waiting times independently and only limited information is shared between trucks. Both the predicted reward gained from platooning and the predicted cost for waiting at hubs are included in each truck's utility function. The performance of the coordination method is demonstrated in a simulation with one hundred trucks over the Swedish road network.
We model a platooning system including trucks and a third-party service provider that performs platoon coordination, distributes the platooning profit within platoons, and charges the trucks in exchange for its services. This paper studies one class of pricing rules, where the third-party service provider keeps part of the platooning profit each time a platoon is formed. Furthermore, we propose a platoon coordination solution based on distributed model predictive control in which the pricing rule is integrated. To evaluate the effect of the pricing on the platooning system, we perform a simulation over the Swedish road network. The simulation shows that the platooning rate and profit highly depend on the pricing. This suggests that pricing needs to be set carefully to obtain a satisfactory platooning system in the future.
Freight drivers of electric trucks need to design charging strategies for where and how long to recharge the truck in order to complete delivery missions on time. Moreover, the charging strategies should be aligned with drivers' driving and rest time regulations, known as hours-of-service (HoS) regulations. This letter studies the optimal charging problems of electric trucks with delivery deadlines under HoS constraints. We assume that a collection of charging and rest stations is given along a pre-planned route with known detours and that the problem data are deterministic. The goal is to minimize the total cost associated with the charging and rest decisions during the entire trip. This problem is formulated as a mixed integer program with bilinear constraints, resulting in a high computational load when applying exact solution approaches. To obtain real-time solutions, we develop a rollout-based approximate scheme, which scales linearly with the number of stations while offering solid performance guarantees. We perform simulation studies over the Swedish road network based on realistic truck data. The results show that our rollout-based approach provides near-optimal solutions to the problem in various conditions while cutting the computational time drastically.
Freight transportation is of outmost importance in our society and is continuously increasing. At the same time, transporting goods on roads accounts for about 26% of the total energy consumption and 18% of all greenhouse gas emissions in the European Union. Despite the influence the transportation system has on our energy consumption and the environment, road transportation is mainly done by individual long-haulage trucks with no real-time coordination or global optimization. In this paper, we review how modern information and communication technology supports a cyber-physical transportation system architecture with an integrated logistic system coordinating fleets of trucks traveling together in vehicle platoons. From the reduced air drag, platooning trucks traveling close together can save about 10% of their fuel consumption. Utilizing road grade information and vehicle-to-vehicle communication, a safe and fuel-optimized cooperative look-ahead control strategy is implemented on top of the existing cruise controller. By optimizing the interaction between vehicles and platoons of vehicles, it is shown that significant improvements can be achieved. An integrated transport planning and vehicle routing in the fleet management system allows both small and large fleet owners to benefit from the collaboration. A realistic case study with 200 heavy-duty vehicles performing transportation tasks in Sweden is described. Simulations show overall fuel savings at more than 5% thanks to coordinated platoon planning. It is also illustrated how well the proposed cooperative look-ahead controller for heavy-duty vehicle platoons manages to optimize the velocity profiles of the vehicles over a hilly segment of the considered road network.
In this paper, we propose an integrated framework for safe intersection coordination of connected and automated vehicles (CAVs) in mixed traffic. An intelligent intersection is introduced as a central node to orchestrate state data sharing among connected agents and enable CAV to acknowledge the presence of human-driven vehicles (HDVs) beyond the line of sight of onboard sensors. Since state data shared between agents might be uncertain or delayed, we design the intelligent intersection to safely compensate for these uncertainties and delays using robust set estimation and forward reachability analysis. When the intersection receives state data from an agent, it first generates a zonotope to capture the possible measurement noise in the state estimate. Then, to compensate for communication and processing delays, it uses forward reachability analysis to enlarge the set to capture all the possible states the agent could have occupied throughout the delays. Finally, using the resulting set as the initial condition, a distributed model predictive control onboard the CAV will plan an invariant safe motion by considering the worst-case behavior of human drivers. As a result, the vehicle is guaranteed to be safe while driving through the intersection. A prototype of our proposed framework is implemented using.
This paper considers the heterogeneous traffic intersection where both Human Driven Vehicles (HDVs) and Connected and Automated Vehicles (CAVs) exist. In such a dynamic environment, CAVs must act in a way such that safety is guaranteed at all times, which is challenging due to the unpredictable nature of human behavior. To guarantee safety, in this paper we consider the worst-case behavior of HDVs by constructing the forward reachable set and ensuring collision avoidance against the forward reachable set within the CAV's planning horizon. To ensure safety at all times, a maximal invariant safe set is designed and used as a terminal constraint such that within this set there is always admissible control for CAVs to react against all possible future behavior of other vehicles safely. Finally, we propose to solve the intersection coordination problem within a Distributed Model Predictive Control (DMPC) framework where all pairwise safety constraints among CAVs are decoupled by prioritization. As a result, each CAVs solves a Mixed Integer Quadratic Programming (MIQP) problem considering collision avoidance with all CAVs of higher priority and with all HDVs. We give theoretical proof of the recursive feasibility of our proposed DMPC formulation and practical invariant safety guarantees. The resulting solution is evaluated in simulation and shows that our coordination framework can provide invariant safe coordination in a heterogeneous traffic intersection.
This paper addresses the coordination challenge at intersections of mixed traffic involving both Human-Driven Vehicles (HDVs) and Connected and Autonomous Vehicles (CAVs). To strike a balance between coordination performance and safety guarantees, we propose an invariant safe Contingency Model Predictive Control (CMPC) framework. The CMPC framework incorporates two parallel horizons for the ego vehicle: a nominal horizon optimized for performance based on the most likely prediction of the opponent HDV, and a contingency horizon designed to maintain an invariant safe backup plan for emergencies. In the contingency horizon, we consider the worst-case behavior of the human driver and formulate safety constraints using the forward reachable sets of the HDV within the planning horizon. These safety constraints are complemented by maximal invariant safe sets as terminal constraints. The two horizons are tied together by enforcing equality of the feedback inputs at the beginning of the horizons. We provide theoretical evidence supporting the recursive feasibility and persistent performance improvement of the invariant safe CMPC compared to our previously proposed nominal invariant safe Model Predictive Control (MPC). Through simulation studies, we evaluate the proposed method. The simulation results demonstrate that the CMPC approach achieves enhanced performance by reducing conservatism while simultaneously preserving the invariant safety property.
Vehicle platooning is an emerging and promising technology with the benefit of fuel-saving and traffic capacity improvement, but the presence of long platoons near merging roads could act as a long barrier for merging traffic. This can lead to merging failure and traffic performance degradation without proper treatment. This paper addresses the merging coordination problem for Connected and Automated Vehicles (CAVs) and Platoons of CAVs to achieve an efficient traffic flow at the merging zone without collisions. We present a bilevel framework where we decouple traffic coordination from vehicle motion control. At the traffic coordination level, a centralized coordinator schedules a merging time and speed for each approaching CAV passing through the merging point with Mixed Integer Linear Programming (MILP). The goal of the coordinator is to optimize traffic performance while considering the presence of platoons. At the vehicle control level, each vehicle plans its motion with the assigned schedule as terminal constraints. The individual motion plan is then followed by the vehicle while keeping a minimum safety distance to its neighbor. The resulting solution is evaluated in simulation and it is shown that our coordination framework can adequately manage traffic for the on-ramp merging scenario with CAVs and platoons.
This paper presents a robust model predictive controller for discrete-time nonlinear systems, subject to state and input constraints and unknown but bounded input disturbances. The prediction model uses a linearized time-varying version of the original discrete-time system. The proposed optimization problem includes the initial state of the current nominal model of the system as an optimization variable, which allows to guarantee robust exponential stability of a disturbance invariant set for the discrete-time nonlinear system. From simulations, it is possible to verify the proposed algorithm is real-time capable, since the problem is convex and posed as a quadratic program.
The objective of the EU project COMPANION is to develop co-operative mobility technologies for supervised vehicle platooning, in order to improve fuel efficiency and safety for goods transport. The potential social and environmental benefits inducted by heavy-duty vehicle platoons have been largely proven. However, until now, the creation, coordination, and operation of such platoons have been mostly neglected. In addition, the regulation and standardization of coordinated platooning, together with its acceptance by the end-users and the society need further attention and research. In this paper we give an overview over the project and present the architecture of the off-board and onboard platforms of the COMPANION cooperative platoon management system. Furthermore, the consortium reports on the first results of the human factors for platooning, legislative analysis of platooning aspects, clustering and optimization of platooning plans and prediction of congestion due to planned special events. Finally, we present the method of validation of the system via simulation and trials.
The paper presents the problem of distributing potential games over communication graphs. Suppose a potential game can be designed for a group of agents (players) where each has access to all others' actions (strategies). The paper shows how to design a corresponding potential game for these agents if the full information assumption is replaced with communication over a network depicted by undirected graphs with certain properties. A state-based formulation for potential games is utilized. This provides degrees of freedom to handle the previous information limitation. Notions of Nash's equilibria for the developed game (called here distributed potential game) are presented, and relations between these equilibria and those of the full information game are studied. In part II of the paper learning Nash equilibria for the newly developed game is studied. The development focuses on providing a way to utilize available algorithms of the full information game. The motivation for the results comes from a platoon matching problem for heavy duty vehicles. Utilizing the newly developed distributed game, recent results based on potential games can be extended, providing a basis for an on-the-go strategy where platoon matching on road networks can be solved locally.
In part I of the paper the problem of distributing potential games over undirected graphs was formulated. A restricted information potential game was designed using state-based formulation. Here, learning Nash equilibria for this game is studied. An algorithm is developed with mainly two phases, an estimation phase and a learning phase. The setting allows for available learning methods of the full information game to be directly incorporated in the learning phase. The result matches the outcome (i.e. converges to the same equilibria) of the full information game. In addition, the design takes into account considerations of convergence time, and synchrony of actions update. The developed distributed game and learning algorithm are used to solve a platoon matching problem for heavy duty vehicles. This serves two objectives. First, it provides a motivation for the presented gaming results. Second, the problem addressed can facilitate platoon matching where it provides a basis for an on-the-go strategy.
Efficiently solving path planning problems for a large number of robots is critical to the successful operation of modern warehouses. The existing approaches adopt classical shortest path algorithms to plan in environments whose cells are associated with both space and time in order to avoid collision between robots. In this work, we achieve the same goal by means of simulation in a smaller static environment. Built upon the new framework introduced in (Bertsekas, 2021a), we propose multiagent rollout with reshuffling algorithm, and apply it to address the warehouse robots path planning problem. The proposed scheme has a solid theoretical guarantee and exhibits consistent performance in our numerical studies. Moreover, it inherits from the generic rollout methods the ability to adapt to a changing environment by online replanning, which we demonstrate through examples where some robots malfunction.
In recent years, the main goal of the automative industry has been to reduce fuel consumption. Downsizing is a promising way to achieve this, which has shown success. Downsized, turbocharged engines suffer from slow transient torque response. This slow response is due to the slow dynamics of the turbocharger. This paper investigates the torque response of a spark ignited engine with variable geometry turbine (VGT) and variable valve timing. Optimal open-loop trajectories for the overlap and the VGT position for a fast transient response are found. This optimization is based on a 1-D simulation model. Based on this optimization, a generic feedback strategy for controlling the VGT is found. This strategy is implemented and evaluated on an engine and shows good performance.
In recent years, the aim to reduce fuel consumption has been the main goal forthe automotive industry. Downsizing is a promising way to achieve this whichhas shown success. Downsized, turbocharged engines do however suffer from slowtransient torque response. This slow response is due to the slow dynamics of theturbocharger. This paper investigates the torque response of an si engine with vvtand vvt. Optimal open-loop trajectories for the overlap and the vgt position for afast transient response are found. This optimization is based on a one-dimensionalsimulation model. Based on this optimization, a generic feedback strategy forcontrolling the vgt is found. This strategy is implemented and evaluated on anengine and shows good performance.
The aim to reduce fuel consumption and emissions has been targeted by several approaches. One of them is downsizing, where a small engine is equipped with a turbocharger in order to give the same power as a larger engine, but with less fuel consumption. This in turn requires advanced control systems to take full benefit from the downsizing. Recent hardware advancements have enabled the use of variable geometry turbochargers also on SI engines, pushing the control demands further. This paper investigates possible extensions to control oriented mean value engine models for turbocharged SI-engines, focusing on the turbine. Mean value models do not take the pulsating phenomena in the exhaust manifold into account. This is assumed to cause large model errors, especially for the turbine efficiency and turbine power. The main contribution of this paper is to present an investigation of the effects of incorporating pressure pulses in the mean value model, together with an analysis of the effects of the pulsation on the turbine performance maps. An evaluation of the extended mean value model using measurements on a four cylinder SI engine with a variable geometry turbocharger is also presented. The evaluation show little difference between using pressure pulses and mean values. An analysis of the expression for turbine power shows that, when treating the maps quasi-steady, the calculated turbine power is almost the same when using pressure pulsations as when using just the mean pressure ratio. The analysis also indicates that this is due to the fact that the turbine power is an approximately linear function of the turbine pressure ratio.
For a turbocharged si engine, the exhaust pressure is of high importance for the gas exchange process as well as for the turbine power. It is therefore important to control the exhaust pressure accurately during load transients. This paper presents and evaluates a nonlinear controller for the exhaust pressure in an si engine equipped with a variable geometry turbine. A mapping from the states, inputs, and disturbances to future outputs is formed, and inverting the input/output relation in this mapping gives a control law. The controller, which can be tuned as a pi controller, utilizes a model for the turbine mass flow capturing the flow characteristics over the operating range. This controller is compared to a linear pi controller and a feedback linearization controller. Evaluation is performed using both simulations and measurements on a real engine, showing the superior behavior of the nonlinear controllers over the linear controller for this problem. Moreover, the presented controller achieves almost as good performance as a feedback linearization controller, but with easier tuning and implementation.
An important target for car manufacturerswhen developing new cars is to reduce fuelconsumption. One approach to this problem is to usea downsized turbocharged engine. To fully utilize thebenefits of the new hardware introduced, good controlsystems are needed. This paper presents a nonlinearcontroller for controlling the exhaust pressure in aSI engine equipped with VGT. A mapping from thestates, inputs and disturbances to future outputs isformed, and inverting the input-output relation inthis mapping gives a control law. An analysis showsthat the controller adapts its gain to the input-outputsensitivity. The controller is evaluated using both simulationsand measurements on a real engine, showingthe benefit of using the nonlinear controller over acorresponding linear controller.
A key problem in optimal input design is that the solution depends on system parameters to be identified. In this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved exactly using the present parameter estimate and one sample of this input is applied to the system. The results apply to stable ARX systems with the input restricted to be generated by white noise filtered through a finite impulse response filter, or a binary signal obtained from the latter by a static nonlinearity.
A key problem in optimal input design is that the solution depends on system parameters to be identified. In this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved using the present parameter estimate and one sample of this input is applied to the system. The results apply to stable ARX systems with the input restricted to be generated by white noise filtered through an FIR filter, or a binary signal obtained from the latter by a static nonlinearity.
Controlling the longitudinal movement of heavy-duty vehicles based on optimal control can be a cost-efficient way of reducing their fuel consumption. Such controllers today mainly exist for highway driving, in which the velocity is allowed to deviate from a constant set-speed. For vehicles with varying velocity demands, for instance vehicles in distribution and mining applications, such controllers do not exist to the same extent. This paper describes an implementation of, and experiments with, an optimal controller in a real heavy-duty vehicle. The velocity profile of the driving cycle varies due to curvature and varying legal speed limits. These limitations are used together with road slope, actuator limitations, and driveability considerations as constraints in the optimal control problem. The problem is solved offline as a mixed integer quadratic program, which generates trajectories for the velocity and for freewheeling. These are used as reference for the existing cruise control functions in experiments in a Scania truck. Results in terms of fuel consumption and trip time are compared with a benchmark controller that mainly follows a fixed fraction of the maximum possible velocity. Solving the optimal control problem results in 18% reduction of the fuel consumption and 1% reduction of the trip time. Experiments with fuel measurements results in 16% reduction of the fuel consumption and 1% reduction of the trip time.
Fuel efficient driving patterns are well investigated for highway driving, but less so for applications with varying speed requirements, such as urban driving. In this paper, the driving mission of a heavy-duty vehicle in urban driving is formulated as an optimal control problem. The velocity of the vehicle is restricted to be within upper and lower constraints referred to as the driving corridor. The driving corridor is constructed from a test cycle with large variations in the speed profile, together with statistics from vehicles in real operation. The optimal control problem is first solved off-line using Pontryagin's maximum principle. A sensitivity analysis is performed in order to investigate how variations in the driving corridor influence the energy consumption of the optimal solution. The same problem is also solved using a model predictive controller with a receding horizon approach. Simulations are performed in order to investigate how the length of the control horizon influences the potential energy savings. Simulations on a test cycle with varying speed profile show that 7% energy can be saved without increasing the trip time or deviating from a normal driving pattern. A horizon length of 1000 m is sufficient to realize these savings by the model predictive controller. The vehicle model used in these simulations is extended to include regenerative braking in order to investigate its influence on the optimal control policy and the results.
The fuel consumption of heavy-duty vehicles in urban driving is strongly dependent on the acceleration and braking of the vehicles. In intersections with traffic lights, large amount of fuel can be saved by adapting the velocity to the phases of the lights. In this paper, a heavy-duty vehicle obtains information about the future signals of traffic lights within a specific horizon. In order to minimize the fuel consumption, the driving scenario is formulated as an optimal control problem. The optimal control is found by applying a model predictive controller, solving at each iteration a quadratic program. In such problem formulation, the constraints imposed by the traffic lights are formulated using a linear approximation of time. Since the fuel-optimal velocity can deviate strongly from how vehicles normally drive, constraints on the allowed velocity are imposed. Simulations are performed in order to investigate how the horizon length of the information from the traffic lights influences the fuel consumption. Compared to a benchmark vehicle without knowledge of future light signals, the proposed controller using a control horizon of 1000m saves 26% of energy with similar trip time. Increasing the control horizon further does not improve the results.
Improving the powertrain control of heavy-duty vehicles can be an efficient way to reduce the fuel consumption and thereby reduce both the operating cost and the environmental impact. One way of doing so is by using information about the upcoming driving conditions, known as look-ahead information, in order to coast in gear or to use freewheeling. Controllers using such techniques today mainly exist for vehicles in highway driving. This paper therefore targets how such control can be applied to vehicles with more variations in their velocity. The driving mission of such a vehicle is here formulated as an optimal control problem. The control variables are the tractive force, the braking force, and a Boolean variable representing closed or open powertrain. The problem is solved by a model predictive controller, which at each iteration solves a mixed integer quadratic program. The fuel consumption is compared for four different control policies: a benchmark following the reference of the driving cycle, look-ahead control without freewheeling, freewheeling with the engine idling, and freewheeling with the engine turned off. Simulations on a driving cycle with a varying velocity profile show the potential of saving 11 %, 19 %, and 23% respectively for the control policies compared with the benchmark, in all cases without increasing the trip time. Copyright
Reducing the fuel consumption is a major issue in the vehicle industry. In this paper, it is done by formulatinga driving mission of a heavy-duty truck as an optimal control problem and solving it using dynamic programming.The vehicle model includes an engine and a gearbox with parameters based on measurements in test cells. The dynamic programming algorithm is solved by considering four specifictypes of transitions: transitions between the same gear, coastingin neutral gear, coasting with a gear engaged with no fuel injection and transitions involving gear changes. Simulations are performed on a driving cycle commonly used for testing distribution type of driving. In order to make sure that the truck does not deviate too much from a normal way of driving, restrictions on maximum and minimum allowed velocities are imposed based on statistics from real traffic data. The simulations show that 12.7% fuel can be saved without increasing the trip time by allowing the truck to engage neutral gear and make small deviations from the reference trajectory.
The optimal speed trajectory for a heavy-duty truck is calculated using the Pontryagin's maximum principle. The truck motion depends on controllable tractive and braking forces and external forces such as air and rolling resistance and road slope. The velocity of the vehicle is restricted to be within a driving corridor which consists of an upper and a lower boundary. Simulations are performed on data from a test cycle commonly used for testing distribution driving. The data include road slope and a speed reference, from which the driving corridor is created automatically. The simulations include a sensitivity analysis on how changes in the parameters for the driving corridor influence the energy consumption and trip time. For the widest driving corridor tested, 15.8% energy was saved compared to the most narrow corridor without increasing the trip time. Most energy was saved by reducing the losses due to braking and small amounts of energy were saved by reducing the losses due to air resistance. Finally, optimal trajectories with the same trip time derived from different settings on the driving corridor are compared in order to analyse energy efficient driving patterns.
The optimal speed trajectory for a heavy duty truck is calculated by using the Pontryagin’s maximum principle. The truck motion depends on controllable tractive and braking forces and external forces such as air and rolling resistance and road slope. The solution is subject to restrictions such as maximum power and position dependent speed restrictions. The intended application is driving in environments with varying requirements on the velocity due to e.g. legal limits and traffic. In order to limit the vehicle to a speed trajectory that follows the normal traffic flow, data from real truck operation have been analysed and used for setting upper and lower boundaries for the decelerations. To evaluate the solution, simulations have been performed on a segment of a road normally used as a distribution test cycle. Three different policies were compared where the solution adopts to free optimization, optimization following traffic flow and finally cruise control using look-ahead control. Results from the simulations show that fuel consumption and trip time can be reduced simultaneously while following the traffic flow.
Controlling the longitudinal movement of heavy-duty vehicles based on optimal control can be a cost-efficient way of reducing their fuel consumption. Such controllers today mainly exist for vehicles in haulage applications, in which the velocity is allowed to deviate from a constant set-speed. For distribution vehicles, which is the focus of this paper, the desired and required velocity has large variations, which makes the situation more complex. This paper describes the implementation of an optimal controller in a real heavy-duty distribution vehicle. The optimal control problem is solved offline as a Mixed Integer Quadratic Program, which yields reference trajectories that are tracked online in the vehicle. Some important steps in the procedure of the implementation are, except for designing the controller: developing a positioning system for the test track where the experiments are performed, estimating the parameters of the resistive forces, and setting the velocity constraints. Simulations show a potential of 10% reduction in fuel consumption without increasing the trip time. Experiments are then performed in a Scania truck, with the optimal solution as reference for the existing cruise control functions in the vehicle. It is concluded that in order to verify the fuel savings experimentally, the low-level controllers in the vehicle must be modified such that the tracking error is decreased.
This paper addresses the problem of quantifying the model error ("variance-error") in estimates of dynamic systems. It is shown that, under very general conditions, the asymptotic ( in data length) covariance of an estimated system property ( represented by a smooth function of estimated system parameters) can be interpreted in terms of an orthogonal projection of a certain function, associated with the property of interest, onto a subspace determined by the model structure and experimental conditions. The presented geometric approach simplifies structural analysis of the model variance and this is illustrated by analyzing the influence of inputs and sensors on the model accuracy.
This paper addresses the problem of quantifying the model error ("variance-error") in estimates of dynamic systems. It is shown that, under very general conditions, the asymptotic (in data length) covariance of an estimated system property (represented by a smooth function of estimated system parameters) can be interpreted in terms of an orthogonal projection of a certain function gamma, associated with the property of interest, onto a subspace determined by the model structure and experimental conditions. An explicit method to construct a suitable gamma, in such a way that the individual impacts of model structure, model order and experimental conditions become visible, is presented. The technique is used to derive asymptotic variance expressions for a Hammerstein model and a nonlinear regression problem.
Hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems. A static input nonlinearity followed by a linear dynamical part is an adequate way to model many real-life systems. This paper investigates the asymptotic (in terms of sample size) variance of Hammerstein model estimates. The work extends earlier results by Ninness and Gibson (2002) in the following ways. Not only frequency function estimation but estimation of general quantities is considered. The expressions are not restricted to be valid asymptotically in the model order. In addition, the results cover model structures having noise models and allow for data generated under feedback. The increase in variance due to the estimation of the input nonlinearity is characterized. In particular, under open loop operation, white additive noise and the assumption of a separable process, it is shown that the variance increase is exactly a term that was observed in Ninness and Gibson (2002) to result in good agreement with simulations. This term vanishes in the formal asymptotic in model order analysis in Ninness and Gibson (2002).
For linear time-invariant systems, the input influences the accuracy of identified parameters only through its second order properties and its cross-correlation with the noise. A wide range of input design problems for such systems can be recast as semi-definite problems in the auto-correlation coefficients of the input or similar design variables. This allows for efficient numerical solutions of such problems. When the system is non-linear the situation is radically different. Nonlinearities can make the parameter accuracy depend on all moments of the input so that the accuracy may depend on the complete distribution of the input sequence. In this contribution we discuss some emerging ways to cope with this situation. In particular we illustrate how to formulate some input design problems as polynomial matrix inequalities for which relaxation methods exist which can generate a sequence of LMI problems with optimal values that under-bound the optimal solution and that converge to a global optimum of the original problem. Both deterministic and stochastic input models are considered. In the stochastic case we discuss how to delineate optimization of the statistical properties from the subsequent signal generation.
Errors-in-variables estimation problems for single-inputsingle-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.
It is commonly believed that solutions to optimal input design problems for identification of dynamical systems often are sensitive to the underlying assumptions. For example, a wide class of problems can be solved with sinusoidal inputs with the same number of excitation frequencies (over the frequency range (-\p,\p]) as number of estimated parameters. With such an input it is not possible to check whether the true system is of higher order or not since then the input is not persistently exciting enough. In this contribution we argue that the optimal solution is often not unique and that there are alternatives to sinusoidal inputs which are more robust. For simplicity, we restrict attention to finite impulse-response models. For such a model of order n, it is only the n first auto-correlation coefficients of the input which determine the accuracy of the parameter estimate. Thus, the remaining coefficients can be used to make the solution more robust. For the problem of estimating some scalar system quantity J with a prescribed accuracy using minimum input energy, there is, under certain assumptions, an input spectrum that is optimal regardless of the model order. Furthermore, we show that using this input allows J to be estimated consistently even when the model order is lower than the true system order.
In this paper, we present a hardware and software testbed designed for evaluating vehicle-to-everything (V2X) usecases. From platooning to remote driving, there are many proposals to use V2X communication to solve sustainability or safety issues in transport networks. However, researchers mostly evaluate their proposals in only simulation studies, since setting up real, full-scale field tests can often be prohibitively expensive or time-consuming. The open-sourced Small Vehicles for Autonomy (SVEA) testbed is built around a communication software stack and a 1/10th-scale automated vehicle platform suitable for both cost-effective and time-efficient experimentation with V2X use-cases. The testbed is designed to support evaluation in a wide range of conditions, such as heterogeneous networks or vehicle fleets. To illustrate the suitability of the SVEA testbed for studying V2X use-cases, we detail and implement three use-cases: platooning, adaptive speed regulation from a road-side infrastructure camera, and remote-driving by a human operator sitting in a control tower. Finally, we conclude the paper with a discussion on the use of the platform so far and future development plans.
In this chapter, we discuss teleoperation systems for connected and automated vehicles and overview the research around making these systems safe and human-centric. In recent years, teleoperation by human operators has become an important modality of supervision for connected and automated vehicles. While automated driving systems continue to mature and handle a rich variety of scenarios, we are continually reminded that unplanned exceptions and deviations from the driving systems' operational design domain – be it unpredictable human behavior or unmodeled kangaroo mechanics – can create potentially unsafe situations for automated vehicles. From decades of research in human factors in air traffic control, we know that we can robustify against automation failure by closely integrating human operators into our automation systems. To this end, teleoperation systems have become of great interest to the connected and automated vehicle research community. By establishing teleoperation systems, we can ensure that when a vehicle experiences automation failure, we have a fallback system where a human operator is able to handle the failure. Moreover, due to the recent introduction of ultra-reliable and low latency communication in 5G networks, we know that wireless communication channels are reliable enough to safely deploy such fallback systems. Since the human operator is remote, we can potentially set up “control towers” for vehicles where a few operators can manage many vehicles. However, to reach this potential, there are several safety and cyber–physical–human system design challenges that need to be addressed. In this chapter, we will introduce these challenges and discuss the recent research that has been conducted to solve these challenges. Furthermore, we will discuss the future research directions that will further enhance the safety of teleoperation systems.
We study the strategic interaction among vehicles in a non-cooperative platoon coordination game. Vehicles have predefined routes in a transportation network with a set of hubs where vehicles can wait for other vehicles to form platoons. Vehicles decide on their waiting times at hubs and the utility function of each vehicle includes both the benefit from platooning and the cost of waiting. We show that the platoon coordination game is a potential game when the travel times are either deterministic or stochastic, and the vehicles decide on their waiting times at the beginning of their journeys. We also propose two feedback solutions for the coordination problem when the travel times are stochastic and vehicles are allowed to update their strategies along their routes. The solutions are evaluated in a simulation study over the Swedish road network. It is shown that uncertainty in travel times affects the total benefit of platooning drastically and the benefit from platooning in the system increases significantly when utilizing feedback solutions.
Truck platooning is a well-studied technology that has the potential to reduce both the environmental impact and operational costs of trucks. The technology has matured over the last 20 years, and the commercial rollout of platooning is approaching. Cooperation across carriers is essential for the viability of platooning; otherwise, many platooning opportunities are lost. We first present a cross-carrier platooning system architecture in which many carriers cooperate in forming platoons through a platoon-hailing service. Then, we present a cross-carrier platoon coordination approach in which each carrier optimizes its platooning plans according to the predicted plans of other carriers. A profit-sharing mechanism to even out the platooning profit in each platoon is embedded in the platoon coordination approach. Finally, a simulation study over the Swedish road network is performed to evaluate the potential of platooning under realistic conditions. The simulation study shows that the energy consumption of trucks in Sweden can be reduced by 5.4% due to platooning and that cooperation across carriers is essential to achieve significant platooning benefits.
Profit-sharing is needed within platoons in order for competing transportation companies to collaborate in forming platoons. In this paper, we propose distribution models of the profit designed for vehicles that are located at the same origin and are operated by competing transportation companies. The vehicles have default departure times, but can decide to depart at other times in order to benefit from platooning. We model the strategic interaction among vehicles with game theory and consider pure Nash equilibria as the solution concept. In a numerical evaluation we compare the outcomes of the games associated with different distribution models of the profit.
This paper studies a multi-fleet platoon coordination system in transport networks that deploy hubs to form trucks into platoons. The trucks belong to different fleets that are interested in increasing their profits by platooning across fleets. The profit of each fleet incorporates platooning rewards and costs for waiting at hubs. Each truck has a fixed route and a waiting time budget to spend at the hubs along its route. To ensure that all fleets are willing to participate in the system, we develop a cross-fleet Pareto-improving coordination strategy that guarantees higher fleet profits than a coordination strategy without cross-fleet platoons. By leveraging multiple hubs for platoon formation, the coordination strategy can be implemented in a real-time and distributed fashion while largely reducing the amount of travel information to be shared for system-wide coordination. We evaluate the proposed strategy in a simulation study over the Swedish transportation network. The cross-fleet platooning strategy significantly improves fleets' profits compared with single-fleet platooning, especially the profits from smaller fleets. The cross-fleet platooning strategy also shows strong competitiveness in terms of the system-wide profit compared to the case when a system planner optimizes all fleets' total profit.
The emerging commercial rollout of heavy-duty vehicle platooning necessitates the development of efficient platoon coordination solutions. The commercial vehicle fleet consists of vehicles owned by different transportation companies with different objectives. To capture their strategic behavior, we study platoon coordination that aims to maximize profits for individual vehicles. The interaction among vehicles is modeled as a non-cooperative game. In our cyber-physical system, we consider a large number of vehicles with fixed routes in a transportation network that can wait at hubs along their routes to form platoons. Each vehicle aims to maximize its utility function, which includes a reward for platooning and a cost for waiting. We propose open-loop coordination solutions when the vehicles decide on their waiting times at the beginning of their trips and do not update their decisions during their trips. It is shown that the corresponding game admits at least one Nash equilibrium. We also propose feedback solutions in which the vehicles are allowed to update their decisions along their routes. In a simulation study over the Swedish road network, we compare the proposed platoon coordination solutions and evaluate the benefits of non-cooperative platooning at a societal scale.
We consider the platoon matching problem for a set of trucks with the same origin, but different destinations. It is assumed that the vehicles benefit from traveling in a platoon for instance through reduced fuel consumption. The vehicles belong to different fleet owners and their strategic interaction is modeled as a non-cooperative game where the vehicle actions are their departure times. Each truck has a preferred departure time and its utility function is defined as the difference between its benefit from platooning and the cost of deviating from its preferred departure time. We show that the platoon matching game is an exact potential game. An algorithm based on best response dynamics is proposed for finding a Nash equilibrium of the game. At a Nash equilibrium, vehicles with the same departure time are matched to form a platoon. Finally, the total fuel reduction at the Nash equilibrium is studied and compared with that of a cooperative matching solution where a common utility function for all vehicles is optimized.
We consider a hub-based platoon coordination problem in which vehicles arrive at a hub according to an independent and identically distributed stochastic arrival process. The vehicles wait at the hub, and a platoon coordinator, at each time-step, decides whether to release the vehicles from the hub in the form of a platoon or wait for more vehicles to arrive. The platoon release time problem is modeled as a stopping rule problem wherein the objective is to maximize the average platooning benefit of the vehicles located at the hub and there is a cost of having vehicles waiting at the hub. We show that the stopping rule problem is monotone and the optimal platoon release time policy will therefore be in the form of a one time-step look-ahead rule. The performance of the optimal release rule is numerically compared with (i) a periodic release time rule and (ii) a non-causal release time rule where the coordinator knows all the future realizations of the arrival process. Our numerical results show that the optimal release time rule achieves a close performance to that of the non-causal rule and outperforms the periodic rule, especially when the arrival rate is low.