Minimization of Fuel Consumption for Vehicle Trajectories Typaldos, Panagiotis; Papamichail, Ioannis; Papageorgiou, Markos
IEEE transactions on intelligent transportation systems,
2020-April, 2020-4-00, Letnik:
21, Številka:
4
Journal Article
Recenzirano
Eco-driving, a timely and well-known subject, aims at reducing fuel consumption by appropriately maneuvering a vehicle with a human or automated driver. In this work, the eco-driving problem is cast ...in an optimal control framework. State equations reflect the simple vehicle kinematics for position and speed, with the acceleration acting as a control input. Initial and final states (position and speed) are fixed. For the fuel consumption estimation, a number of alternatives are employed. To start with, a realistic, but nonlinear and non-smooth formula from the literature is considered. Simple smoothing procedures are then applied to enable the application of powerful numerical algorithms for the efficient solution of the resulting nonlinear optimal control problem. Furthermore, simpler quadratic approximations of the nonlinear formula are also considered, which enable analytical problem solutions. A comprehensive comparison on the basis of various driving scenarios demonstrates that the often utilized, but sometimes strongly questioned, square-of-acceleration term delivers excellent approximations for fuel minimizing trajectories in the present setting. A GLOSA (Green Light Optimal Speed Advisory) approach, based on the analytical solution of an optimal control problem is also presented.
A path-planning algorithm for connected and non-connected automated road vehicles on multilane motorways is derived from the opportune formulation of an optimal control problem. In this framework, ...the objective function to be minimized contains appropriate respective terms to reflect: the goals of vehicle advancement; passenger comfort; and avoidance of collisions with other vehicles and of road departures. Connectivity implies, within the present work, that connected vehicles can exchange with each other (V2V) real-time information about their last generated short-term path. For the numerical solution of the optimal control problem, an efficient feasible direction algorithm (FDA) is used. To ensure high-quality local minima, a simplified Dynamic Programming (DP) algorithm is also conceived to deliver the initial guess trajectory for the start of the FDA iterations. Thanks to very low computation times, the approach is readily executable within a model predictive control (MPC) framework. The proposed MPC-based approach is embedded within the Aimsun microsimulation platform, which enables the evaluation of a plethora of realistic vehicle driving and advancement scenarios under different vehicles mixes. Results obtained on a multilane motorway stretch indicate higher efficiency of the optimally controlled vehicles in driving closer to their desired speed, compared to ordinary manually driven vehicles. Increased penetration rates of automated vehicles are found to increase the efficiency of the overall traffic flow, benefiting manual vehicles as well. Moreover, connected controlled vehicles appear to be more efficient in achieving their desired speed, compared also to the corresponding non-connected controlled vehicles, due to the improved real-time information and short-term prediction achieved via V2V communication.
The main purpose of this work is to generate optimal trajectories for vehicles crossing a signalized junction, with traffic signals operated in either fixed-time or real-time (adaptive) mode. In the ...latter case, the next switching time is decided in real time based on the prevailing traffic conditions and is therefore uncertain in advance. The GLOSA (Green Light Optimal Speed Advisory) problem is addressed by using traffic lights information and calculating a trajectory and velocity profile for the vehicle based on the vehicle’s initial state (position and speed) and a fixed final destination state. At first, an appropriate optimal control problem is formulated and solved analytically via Pontryagin’s minimum principle (PMP) for the case of known switching times. Subsequently, for the case of real-time signals, availability of a time-window of possible signal switching times, along with the corresponding probability distribution, is assumed, and the problem is cast in the format of a stochastic optimal control problem and is solved numerically using stochastic dynamic programming (SDP) techniques. Application results, for various driving scenarios, of the deterministic approach, which considers the case of known switching times, and a comprehensive comparison of the stochastic GLOSA approach with a sub-optimal approach are presented. In particular, it is demonstrated that the proposed SDP approach achieves better average performance compared with the sub-optimal approach because of the better (probabilistic) information on the traffic light switching time.
The paper presents a movement strategy for Connected and Automated Vehicles (CAVs) in a lane-free traffic environment with vehicle nudging by use of an optimal control approach. State-dependent ...constraints on control inputs are considered to ensure that the vehicle moves within the road boundaries and to prevent collisions. An objective function, comprising various weighted sub-objectives, is designed, whose minimization leads to vehicle advancement at the desired speed, when possible, while avoiding obstacles. A nonlinear optimal control problem (OCP) is formulated for the minimization of the objective function subject to constraints for each vehicle. A computationally efficient Feasible Direction Algorithm (FDA) is called, on event-triggered basis, to compute in real-time the numerical solution for finite time-horizons within a Model Predictive Control (MPC) framework. The approach is applied to each vehicle on the road, while running simulations on a lane-free ring-road, for a wide range of vehicle densities and different types of vehicles. From the simulations, which create myriads of driving episodes for each involved vehicle, it is observed that the proposed approach is highly efficient in delivering safe, comfortable and efficient vehicle trajectories, as well as high traffic flow outcomes. The approach is under investigation for further use in various lane-free road infrastructures for CAV traffic.
A discrete-time stochastic optimal control problem was recently proposed to address the GLOSA (Green Light Optimal Speed Advisory) problem in cases where the next signal switching time is decided in ...real time and is therefore uncertain in advance. The corresponding numerical solution via SDP (Stochastic Dynamic Programming) calls for substantial computation time, which excludes problem solution in the vehicle's on-board computer in real time. To overcome the computation time bottleneck, as a first attempt, a modified version of Dynamic Programming, known as Discrete Differential Dynamic Programming (DDDP) was recently employed for the numerical solution of the stochastic optimal control problem. The DDDP algorithm was demonstrated to achieve results equivalent to those obtained with the ordinary SDP algorithm, albeit with significantly reduced computation times. The present work considers a different modified version of Dynamic Programming, known as Differential Dynamic Programming (DDP). For the stochastic GLOSA problem, it is demonstrated that DDP achieves quasi-instantaneous (extremely fast) solutions in terms of CPU times, which allows for the proposed approach to be readily executable online, in an MPC (Model Predictive Control) framework, in the vehicle's on-board computer. The approach is demonstrated by use of realistic examples. It should be noted that DDP does not require discretization of variables, hence the obtained solutions may be slightly superior to the standard SDP solutions.
This article presents a joint trajectory optimization algorithm for connected and automated vehicles forming 1-D snake-like interruptible platoons or 2-D deformable and interruptible flocks in a ...lane-free traffic environment on highways. A double double-integrator model is employed for the longitudinal and lateral movements of each vehicle. An appropriately defined Euclidian distance to track the front vehicle is utilized to establish and operate a 1-D platoon of vehicles, at selectable distance from each other. The Euclidian distance is used as a soft constraint, which allows for platoons to divide, if required to avoid obstacles, and reunite eventually. Moreover, the distance from a selectable frame (e.g. a triangle) are employed as soft constraints to form and maintain a 2-D deformable and interruptible flock of vehicles. The flock may feature a leader vehicle, e.g. at the front corner of a triangle. A collision avoidance function considering constant time-gaps or space-gaps, is used based on the elliptical distance between each two vehicles or external obstacles. A joint multi-objective function is formulated and minimized using an efficient feasible direction algorithm with respect to constant and state-dependent bounds on control inputs, including road boundary constraints. This leads to creating a flexible platoon or deformable flock accounting for low fuel consumption, passenger convenience, collision avoidance, achievement of desired speed and prevention of infeasible maneuvers. Challenging scenarios are examined on a lane-free straight motorway stretch, producing promising results for further exploration of the proposed concepts within an MPC (model predictive control) framework.
A path-planning algorithm for connected and non-connected automated road vehicles on multilane motorways is derived from the opportune formulation of an optimal control problem. In this framework, ...the objective function to be minimized contains appropriate respective terms to reflect: the goals of vehicle advancement; passenger comfort; and avoidance of collisions with other vehicles, of road departures and of negative speeds. Connectivity implies that connected vehicles are able to exchange with each other (V2V) or the infrastructure (V2I), real-time information about their last generated path. For the numerical solution of the optimal control problem, an efficient feasible direction algorithm is used. To ensure high-quality local minima, a simplified Dynamic Programming algorithm is also conceived to deliver the initial guess trajectory for the feasible direction algorithm. Thanks to low computation times, the approach is readily executable within a model predictive control (MPC) framework. The proposed MPC-based approach is embedded within the Aimsun microsimulation platform, which enables the evaluation of a plethora of realistic vehicle driving and advancement scenarios. Results obtained on a multilane motorway stretch indicate higher efficiency of the optimally controlled vehicles in driving closer to their desired speed, compared to ordinary Aimsun vehicles. Increased penetration rates of automated vehicles are found to increase the efficiency of the overall traffic flow, benefiting manual vehicles as well. Moreover, connected controlled vehicles appear to be more efficient compared to the corresponding non-connected controlled vehicles, due to the improved real-time information and short-term prediction.
The paper presents a movement strategy for Connected and Automated Vehicles (CAVs) in a lane-free traffic environment with vehicle nudging by use of an optimal control approach. State-dependent ...constraints on control inputs are considered to ensure that the vehicle moves within the road boundaries and to prevent collisions. An objective function, comprising various weighted sub-objectives, is designed, whose minimization leads to vehicle advancement at the desired speed, when possible, while avoiding obstacles. A nonlinear optimal control problem (OCP) is formulated for the minimization of the objective function subject to constraints for each vehicle. A computationally efficient Feasible Direction Algorithm (FDA) is called, on event-triggered basis, to compute in real-time the numerical solution for finite time-horizons within a Model Predictive Control (MPC) framework. The approach is applied to each vehicle on the road, while running simulations on a lane-free ring-road, for a wide range of vehicle densities and different types of vehicles. From the simulations, which create myriads of driving episodes for each involved vehicle, it is observed that the proposed approach is highly efficient in delivering safe, comfortable and efficient vehicle trajectories, as well as high traffic flow outcomes. The approach is under investigation for further use in various lane-free road infrastructures for CAV traffic.
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