Achieving high-level autonomous driving poses significant challenges, primarily due to the extensive and time-consuming testing required for low-probability abnormal behavior scenarios. Existing simulation platforms are limited by microscopic traffic flow models based on car-following and lane-changing theories (focused on the behavior of individual vehi-cles), which limits the implementation of complex and diverse abnormal behaviors such as road deviation and cutting in. This paper proposes an Abnormal behavior Generation model based on Event Probability triggers and Static paths (AGEPS model), which is capable of continuously and automatically generating abnormal behaviors without disrupting normal traffic flow. The AGEPS model is computationally efficient and scalable, as it decouples path optimization and trajectory tracking from obstacle avoidance, using explicit control law for both tracking and avoidance. The paper demonstrates three typical abnormal behaviors: Overtaking on the Right (OOR), Driving on the Lane Line (DOL), and Sudden Braking (SUB), indicating that the AGEPS model effectively generates these behaviors by selecting and tracking target static paths while adjusting lateral offsets and desired speeds. Experimental results validate the AGEPS model's effectiveness and its ability to generate abnormal behaviors continuously. Simulation results indicate that the AGEPS model reduces single-step computation time (including decision-making and control) by over 92.8 % compared to the MPC controller, with a single-step execution time of just 4 ms.

Reinforcement learning (RL) has shown remarkable success in solving complex decision-making and control tasks. However, many model-free RL algorithms experience performance degradation due to inaccurate value estimation, particularly the overestimation of Q-values, which can lead to suboptimal policies. To address this issue, we previously proposed the Distributional Soft Actor-Critic (DSAC or DSACv1), an off-policy RL algorithm that enhances value estimation accuracy by learning a continuous Gaussian value distribution. Despite its effectiveness, DSACv1 faces challenges such as training instability and sensitivity to reward scaling, caused by high variance in critic gradients due to return randomness. In this paper, we introduce three key refinements to DSACv1 to overcome these limitations and further improve Q-value estimation accuracy: expected value substitution, twin value distribution learning, and variance-based critic gradient adjustment. The enhanced algorithm, termed DSAC with Three refinements (DSAC-T or DSACv2), is systematically evaluated across a diverse set of benchmark tasks. Without the need for task-specific hyperparameter tuning, DSAC-T consistently matches or outperforms leading model-free RL algorithms, including SAC, TD3, DDPG, TRPO, and PPO, in all tested environments. Additionally, DSAC-T ensures a stable learning process and maintains robust performance across varying reward scales. Its effectiveness is further demonstrated through real-world application in controlling a wheeled robot, highlighting its potential for deployment in practical robotic tasks.

Reinforcement learning (RL) has gained significant interest for its potential to improve decision and control in autonomous driving. However, current approaches have yet to demonstrate sufficient scenario generality and observation generality, hindering their wider utilization. To address these limitations, we propose a unified benchmark simulator for RL algorithms (called IDSim) to facilitate decision and control for high-level autonomous driving, with emphasis on diverse scenarios and a unified observation interface. IDSim is composed of a scenario library and a simulation engine, and is designed with execution efficiency and determinism in mind. The scenario library covers common urban scenarios, with automated random generation of road structure and traffic flow, and the simulation engine operates on the generated scenarios with dynamic interaction support. We conduct four groups of benchmark experiments with five common RL algorithms and focus on challenging signalized intersection scenarios with varying conditions. The results showcase the reliability of the simulator and reveal its potential to improve the generality of RL algorithms. Our analysis suggests that multi-task learning and observation design are potential areas for further algorithm improvement.

Deep reinforcement learning (RL) is a powerful approach for solving optimal control problems. However, RL-trained policies often suffer from the action fluctuation problem, where the consecutive actions significantly differ despite only slight state variations. This problem results in mechanical components' wear and tear and poses safety hazards. The action fluctuation is caused by the high Lipschitz constant of actor networks. To address this problem, we propose a neural network named LipsNet. We propose the Multi-dimensional Gradient Normalization (MGN) method, to constrain the Lipschitz constant of networks with multi-dimensional input and output. Benefiting from MGN, LipsNet achieves Lipschitz continuity, allowing smooth actions while preserving control performance by adjusting Lipschitz constant. LipsNet addresses the action fluctuation problem at network level rather than algorithm level, which can serve as actor networks in most RL algorithms, making it more flexible and user-friendly than previous works. Experiments demonstrate that LipsNet has good landscape smoothness and noise robustness, resulting in significantly smoother action compared to the Multilayer Perceptron.

In-vehicle human-machine interface (HMI) plays a significant role in accomplishing effective interactions between driving automation systems and drivers, especially during the transition of control. For this reason, different in-vehicle HMIs have been designed to convey additional semantic information from the driving automation systems to the drivers to realize safer, smoother, and better control transitions. This review summarizes and analyses 86 previously published studies that researched the effects of additional semantic information delivered through in-vehicle HMIs just before, during and right after takeover request (TOR). The additional semantic information mentioned in this review refer to the information beyond simple alerts to not only gain drivers’ attention but also additionally communicate contextual content and explanation to the drivers regarding its own purpose. In this review, the additional semantic information are categorized according to their purposes and effects into three aspects: mode awareness enhancement, situation awareness enhancement, and takeover maneuver assistance. The specificities and the corresponding concerns when applying additional semantic information to in-vehicle HMIs have been detailed analyzed throughout the entire article. Further suggestions are proposed for what should be carefully considered when adding additional information for better takeover. Prospects into future in-vehicle HMI possibilities are also raised that could be applied in both academic research and industry.

Decision and control are core functionalities of high-level automated vehicles. Current mainstream methods, such as functional decomposition and end-to-end reinforcement learning (RL), suffer high time complexity or poor interpretability and adaptability on real-world autonomous driving tasks. In this article, we present an interpretable and computationally efficient framework called integrated decision and control (IDC) for automated vehicles, which decomposes the driving task into static path planning and dynamic optimal tracking that are structured hierarchically. First, the static path planning generates several candidate paths only considering static traffic elements. Then, the dynamic optimal tracking is designed to track the optimal path while considering the dynamic obstacles. To that end, we formulate a constrained optimal control problem (OCP) for each candidate path, optimize them separately, and follow the one with the best tracking performance. To unload the heavy online computation, we propose a model-based RL algorithm that can be served as an approximate-constrained OCP solver. Specifically, the OCPs for all paths are considered together to construct a single complete RL problem and then solved offline in the form of value and policy networks for real-time online path selecting and tracking, respectively. We verify our framework in both simulations and the real world. Results show that compared with baseline methods, IDC has an order of magnitude higher online computing efficiency, as well as better driving performance, including traffic efficiency and safety. In addition, it yields great interpretability and adaptability among different driving scenarios and tasks.

Although latent hazard notification for highly automated driving is expected to enhance traffic safety, its practical effects have yet to be verified. This study systemically investigated the expected safety benefits and driver behavioral adaptation based on structural equation modeling. First, we developed a notification system to inform drivers of latent hazards with auditory alerts and conducted a driving simulation experiment involving eyes-off-road situations. To test the system, we adopted two types of events (i.e., the collision avoidance function working or failure) in which latent hazards transform into immediate risks. Then, a measurement model was developed to evaluate driver trust, driver attention, and traffic safety. Subsequently, we examined the corresponding causal relationships. On the one hand, latent hazard notification significantly improves driver attention (i.e., more fixations on latent hazards, less engagement in non-driving-related tasks, and faster notice of immediate risks), which significantly enhances traffic safety. On the other hand, latent hazard notification significantly increases driver trust, which lowers driver attention and consequently impairs traffic safety. This causality reveals driver behavioral adaptation, although driver trust does not directly affect traffic safety. Overall, we find that latent hazard notification for highly automated driving can improve traffic safety, but the consequent driver behavioral adaptation impairs 15.12% of the expected safety benefits.

For highly automated vehicles, effective take-over performance measures are essential for establishing quantitative take-over models and exploring approaches to improve take-over performance. However, there is a lack of comprehensive take-over performance measures that suitably combine multiple objective metrics based on an average evaluation from human drivers. In this study, we proposed a human-centered comprehensive measure of take-over performance (HCMTP). There are four main building blocks for the HCMTP. First, we adopted sparse principal component analysis to identify the main aspects of take-over performance based on multiple original objective take-over performance metrics. Second, we developed a scale of take-over performance assessment to obtain drivers’ original subjective self-assessments of take-over performance. Third, we established nonlinear individual mapping functions to acquire different drivers’ evaluation criteria for take-over performance. Fourth, we proposed a relabeling algorithm to obtain drivers’ average evaluation of take-over performance. To verify the effectiveness of the HCMTP, we conducted a verification experiment involving 68 participants. The results indicate that the HCMTP is effective and able to reduce the interference of individual differences, stochasticity, and data imbalance. This study contributes to identifying the main aspects of take-over performance, systematically understanding how human drivers subjectively evaluate take-over performance, and evaluating drivers’ take-over performance comprehensively.

In the area of autonomous driving, it typically brings great difficulty in solving the motion planning problem since the vehicle model is nonlinear and the driving scenarios are complex. Particularly, most of the existing methods cannot be generalized to dynamically changing scenarios with varying surrounding vehicles. To address this problem, this development here investigates the framework of integrated decision and control. As part of the modules, static path planning determines the reference candidates ahead, and then the optimal path-tracking controller realizes the specific autonomous driving task. An innovative and effective constrained finite-horizon approximate dynamic programming (ADP) algorithm is herein presented to generate the desired control policy for effective path tracking. With the generalized policy neural network that maps from the state to the control input, the proposed algorithm preserves the high effectiveness for the motion planning problem towards changing driving environments with varying surrounding vehicles. Moreover, the algorithm attains the noteworthy advantage of alleviating the typically heavy computational loads with the mode of offline training and online execution. As a result of the utilization of multi-layer neural networks in conjunction with the actor-critic framework, the constrained ADP method is capable of handling complex and multidimensional scenarios. Finally, various simulations have been carried out to show that the constrained ADP algorithm is effective.

The Hamilton-Jacobi-Bellman (HJB) equation serves as the necessary and sufficient condition for the optimal solution to the continuous-time (CT) optimal control problem (OCP). Compared with the infinite-horizon HJB equation, the solving of the finite-horizon (FH) HJB equation has been a long-standing challenge, because the partial time derivative of the value function is involved as an additional unknown term. To address this problem, this study first-time bridges the link between the partial time derivative and the terminal-time utility function, and thus it facilitates the use of the policy iteration (PI) technique to solve the CT FH OCPs. Based on this key finding, the FH approximate dynamic programming (ADP) algorithm is proposed leveraging an actor-critic framework. It is shown that the algorithm exhibits important properties in terms of convergence and optimality. Rather importantly, with the use of multilayer neural networks (NNs) in the actor-critic architecture, the algorithm is suitable for CT FH OCPs toward more general nonlinear and complex systems. Finally, the effectiveness of the proposed algorithm is demonstrated by conducting a series of simulations on both a linear quadratic regulator (LQR) problem and a nonlinear vehicle tracking problem.

As human-machine collaborative driving systems, highly automated driving vehicles require human drivers to take over when take-over requests are triggered. Extensive studies have shown that drivers’ take-over performance is affected by their fatigue state, traffic conditions, and the take-over time budget (TB). However, there is still a paucity of a systematic understanding of how these factors affect take-over performance, which prevents the implementation of adaptive take-over systems. This study establishes a highly accurate take-over performance prediction model to systematically explore the effects of these factors on take-over performance and to propose an adaptive TB adjustment strategy for highly automated driving vehicles. First, we propose metrics to evaluate drivers’ fatigue states and the relative positions of surrounding traffic. Second, a generalized additive model is established to predict take-over performance and accurately evaluate the influence of the aforementioned factors on take-over performance. Based on the model, we propose an adaptive adjustment strategy of the TB for take-over systems and demonstrate its effectiveness by a verification experiment. This study contributes to understanding the influence of drivers’ passive fatigue states, the relative positions of surrounding traffic, and the TB on drivers’ take-over performance as well as to the development of adaptive take-over systems for highly automated vehicles.

Due to the growing interest in automated driving, a deep understanding on the characteristics of human driving behavior is critical for human-like autonomous vehicles. Among various driving behaviors, lane change is the most important one for vehicle lateral driving safety. This study proposes an unsupervised method to extract and discover the behavioral patterns of lane change maneuvers for the purpose of exploring the composed behavioral patterns during lane change. This method involves two phases: Firstly, the lane change sequences will be segmented into blocks using time-series segmentation algorithms. Three segmentation algorithms were utilized in this study. In the second phase, the segments will be clustered to find the corresponding behavioral pattern of each segment. Two extended latent Dirichlet allocation (LDA) models were adopted to cluster the segments. The combination of different segmentation and clustering algorithms were evaluated and compared by employing entropy and perplexity as the evaluation criteria. Collected lane change data from naturalistic driving were applied to examine its effectiveness. The results show that this method could effectively mine descriptive behavioral patterns from lane change data. This study provides a promising data mining solution to facilitating deep and comprehensive understanding on driver lane change behaviors, which will promote the development of human-like autonomous vehicles.

In this paper, we propose a new state representation method, called encoding sum and concatenation (ESC), to describe the environment observation for decision-making in autonomous driving. Unlike existing state representation methods, ESC is applicable to the situation where the number of surrounding vehicles is variable and eliminates the need for manually pre-designed sorting rules, leading to higher representation ability and generality. The proposed ESC method introduces a feature neural network (NN) to encode the real-valued feature of each surrounding vehicle into an encoding vector, and then adds these vectors up to obtain the representation vector of the set of surrounding vehicles. Then, a fixed-dimensional and permutation-invariance state representation can be obtained by concatenating the set representation with other variables, such as indicators of the ego vehicle and road. By introducing the sum-of-power mapping, this paper has further proved that the injectivity of the ESC state representation can be guaranteed if the output dimension of the feature NN is greater than the number of variables of all surrounding vehicles. This means that the ESC representation can be used to describe the environment and taken as the inputs of learning-based policy functions. Experiments demonstrate that compared with the fixed-permutation representation method, the policy learning accuracy based on ESC representation is improved by 62.2%.

In reinforcement learning (RL), function approximation errors are known to easily lead to the Q -value overestimations, thus greatly reducing policy performance. This article presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q -value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q -value overestimations because it is capable of adaptively adjusting the update step size of the Q -value function. Then, a distributional soft policy iteration (DSPI) framework is developed by embedding the return distribution function into maximum entropy RL. Finally, we present a deep off-policy actor-critic variant of DSPI, called DSAC, which directly learns a continuous return distribution by keeping the variance of the state-action returns within a reasonable range to address exploding and vanishing gradient problems. We evaluate DSAC on the suite of MuJoCo continuous control tasks, achieving the state-of-the-art performance.

Cover Caption: The cover image is based on the Research Article Direct and indirect reinforcement learning by Yang Guan et al., https://doi.org/10.1002/int.22466.

Reinforcement learning (RL) algorithms have been successfully applied to a range of challenging sequential decision-making and control tasks. In this paper, we classify RL into direct and indirect RL according to how they seek the optimal policy of the Markov decision process problem. The former solves the optimal policy by directly maximizing an objective function using gradient descent methods, in which the objective function is usually the expectation of accumulative future rewards. The latter indirectly finds the optimal policy by solving the Bellman equation, which is the sufficient and necessary condition from Bellman's principle of optimality. We study policy gradient (PG) forms of direct and indirect RL and show that both of them can derive the actor–critic architecture and can be unified into a PG with the approximate value function and the stationary state distribution, revealing the equivalence of direct and indirect RL. We employ a Gridworld task to verify the influence of different forms of PG, suggesting their differences and relationships experimentally. Finally, we classify current mainstream RL algorithms using the direct and indirect taxonomy, together with other ones, including value-based and policy-based, model-based and model-free.

It is widely acknowledged that drivers should remain in the control loop before automated vehicles completely meet real-world operational conditions. This paper presents an “indirect shared control” framework for steer-by-wire vehicles, which allows the control authority to be continuously shared between the driver and automation through an weighted-input-summation method. A “best-response” driver steering model based on model predictive control (MPC) for indirect shared control is proposed. Unlike any conventional driver model for manual driving, this model assumes that drivers can learn and incorporate the controller strategy into their internal model for predictive path following. The analytic solution to the driver model is provided to enable off-line simulations. A driving-simulator experiment was conducted to demonstrate the advantages of the indirect shared control system in a highway lane-keeping task. The result showed that the proposed indirect shared control method was effective to improve the subjects’ lane-keeping performance and reduce steering control effort. The proposed driver steering model was also validated by the experiment data, which produced a smaller prediction error than the conventional MPC driver model.

The splitting strategy over prediction horizon of model predictive control (MPC) has the potential to compute optimal action in a parallel way. However, such time-splitting algorithms often lead to very slow convergence speed because the state consensus only happens in each pair of adjacent nodes, i.e. a point-to-point topology. This paper proposes a generic cross-node consensus method to extend the shortcoming of limiting to point-to-point topology for the purpose of accelerating the convergence of time-splitting MPC. The cross-node consensus is realized by predicting the state transition from one node to another using plant prediction model, which can increase the information exchange efficiency in the prediction horizon. The time-splitting optimization algorithm is implemented by combing with alternating directions method of multipliers (ADMM). Simulations with autonomous driving show that this new algorithm significantly reduces the number of iterations in time-splitting MPC, averagely about 81% compared with classic time-splitting technique.

Accurate trajectory prediction of surrounding road users is critical to autonomous driving systems. In mixed traffic flows, road users with different kinds of behaviors and styles bring complexity to the environment, which requires considering interactions among road users when anticipating their future trajectories. This paper presents a long-term interactive trajectory prediction method for surrounding vehicles using a hierarchical multi-sequence learning network. In contrast to non-interactive method which assumes that road users are independent of each other, this method can automatically learn high-level dependencies among multiple interacting vehicles through the proposed structural-LSTM (long short-term memory) network. Specifically, structural-LSTM first assigns one LSTM for each interacting vehicle. Then these LSTMs share their cell states and hidden states with their spatial-neighboring LSTMs by a radial connection, and recurrently analyze the output state of itself as well as the other LSTMs in a deeper layer. Finally based on all output states, the network predicts trajectories for surrounding vehicles. The proposed method is evaluated on the NGSIM dataset, and its results show that satisfyingly accurate prediction performance of long-term trajectories of surrounding vehicles is accessible, e.g., longitudinal and lateral RMS error can be reduced to less than 1.93m and 0.31m over 5s time horizon, respectively.

This paper presents an object classification method for vision and light detection and ranging (LIDAR) fusion of autonomous vehicles in the environment. This method is based on convolutional neural network (CNN) and image upsampling theory. By creating a point cloud of LIDAR data upsampling and converting into pixel-level depth information, depth information is connected with Red Green Blue data and fed into a deep CNN. The proposed method can obtain informative feature representation for object classification in autonomous vehicle environment using the integrated vision and LIDAR data. This method is also adopted to guarantee both object classification accuracy and minimal loss. Experimental results are presented and show the effectiveness and efficiency of object classification strategies.

Shared control is an important approach to avoid the driver-out-of-the-loop problems brought by imperfect autonomous driving. Steer-by-wire technology allows the mechanical decoupling between the steering wheel and the road wheels. On steer-by-wire vehicles, the automation can join the control loop by correcting the driver steering input, which forms a new paradigm of shared control. The new framework, under which the driver indirectly controls the vehicle through the automation's input transformation, is called indirect shared control. This paper presents an indirect shared control system, which realizes the dynamic control authority allocation with respect to the driver's authority intention. The simulation results demonstrate the effectiveness and benefits of the proposed control authority adaptation method.

This paper presents two fuel-prioritized feedback controllers, which are called the estimated minimum principle (EMP) and kinetic energy conversion (KEC), to realize eco-cruising on varying slopes for vehicles with conventional powertrains. The former is derived from the minimum principle with an estimated Hamiltonian, and the latter is designed based on the equivalent conversion between the kinetic-energy change of vehicle body and the fuel consumption of the engine. They are implemented with analytical control laws and rely on current road slope information only without look-ahead prediction. This feature results in a very light computing load, with the average computing time of each step less than one millisecond. Their fuel-saving performances are quantitatively studied and compared with a model predictive control and a constant speed control. As an expansion, the control rule for avoiding rear-end collision is also designed by using a safety-guaranteed car-following model to constrain the high-risk behaviors.

Detection of driver cognitive distraction is critical for active safety systems of road vehicles. Compared with visual distraction, cognitive distraction is more challenging for detection due to the lack of apparent exterior features. This paper presents a novel real-time detection algorithm for driver cognitive distraction by using support vector machine (SVM). Data are collected from 26 subjects, driving in typical urban and highway scenarios in a simulator. The chosen urban scenario is the stop-controlled intersection and the highway scenario is the speed-limited highway. Driver cognitive distraction while driving is induced by clock tasks which compete with the main driving tasks for visuospatial short working memory. For each subject, distracted driving instances and the equal number of non-distracted driving instances were collected (24 for urban scenario and 20 for highway scenario in total). Features concerning both driving performance and eye movement are used for training and validation. The proposed algorithm have correct rate of 93.0% and 98.5% for highway and urban scenarios respectively. Results also show that driver distraction can be recognized 6.5 s to 9.0 s after its happening, indicating good performance of the detection algorithm.

Accurate detection and tracking of traffic participants are crucial to advanced driver assistance systems. This paper presents a centralized object tracking approach for surrounding objects in road traffic environments by using multiple linearly arrayed ultrasonic sensors. An ultrasonic sensor model is specifically developed for traffic environment, which consists of detection scope, chance of detection and ranging error, incorporating factors of object shapes, materials, distances and orientations. A centralized filter is designed to selectively fuse new measurements that are obtained using the Extended Kalman Filter (EKF) from certain sensors to conduct object tracking at each step. The effectiveness of proposed method is validated by simulations, which is found to have superior tracking performance compared to traditional triangle localization method, with more stable and smaller tracking error, especially when the object is entering or leaving the detection area.

Driver distraction has been identified as one major cause of unsafe driving. The existing studies on cognitive distraction detection mainly focused on high-speed driving situations, but less on low-speed traffic in urban driving. This paper presents a method for the detection of driver cognitive distraction at stop-controlled intersections and compares its feature subsets and classification accuracy with that on a speed-limited highway. In the simulator study, 27 subjects were recruited to participate. Driver cognitive distraction is induced by the clock task that taxes visuospatial working memory. The support vector machine (SVM) recursive feature elimination algorithm is used to extract an optimal feature subset out of features constructed from driving performance and eye movement. After feature extraction, the SVM classifier is trained and cross-validated within subjects. On average, the classifier based on the fusion of driving performance and eye movement yields the best correct rate and F-measure (correctrate = 95.8 ± 4.4%; for stop-controlled intersections and correct rate = 93.7 ± 5.0%; for a speed-limited highway) among four types of the SVM model based on different candidate features. The comparisons of extracted optimal feature subsets and the SVM performance between two typical driving scenarios are presented.

Lane change maneuver recognition is critical in driver characteristics analysis and driver behavior modeling for active safety systems. This paper presents an enhanced classification method to recognize lane change maneuver by using optimized features exclusively extracted from vehicle state and driver operation signals. The sequential forward floating selection (SFFS) algorithm was adopted to select the optimized feature set to maximize the k-nearest-neighbor classifier performance. The hidden Markov models (HMMs), based on the optimized feature set, were developed to classify driver lane change and lane keeping maneuvers. Fifteen drivers participated in the road test for validation with an accumulation of 2,200 km naturalistic driving data, from which 372 lane changes were extracted. Results show that the recognition rate of lane change maneuver achieves 88.2%. The numbers are 87.6% and 88.8% for left and right lane change maneuvers, respectively, superior to the results from conventional classifiers.

Driver distraction has been identified as an important driving safety issue. However, existed studies focused less on low-speed condition, especially at intersections. This paper aims to find the impact of driver cognitive distraction on vehicle performance at stop-controlled intersections. Eight subjects (young adult: 4, older adult: 4) participated in this study and each of them drove through 40 stop-controlled intersections. The intersections were presented randomly at two levels of FOV (field of view). Driver cognitive distraction was induced by a one-back task and a clock task. Results showed that the cognitive tasks led to more abrupt steering in both age groups while significant influence on lane-keeping capability was only observed in the young group. Steering smoothness was mainly influenced by the cognitive tasks at brake on-restart phase in the young group while at after-restart phase in the older group. Impaired longitudinal control (stop for watching) was observed in the older adult group. These findings can be applied to automatically recognize driver distraction at stop-controlled intersections in future.

The recent progress of advanced vehicle control systems presents a great opportunity for the application of model predictive control (MPC) in the automotive industry. However, high computational complexity inherently associated with the receding horizon optimization must be addressed to achieve real-time implementation. This paper presents a generic scale reduction framework to reduce the online computational burden of MPC controllers. A lower dimensional MPC algorithm is formulated by combining an existing “move blocking ” strategy with a “constraint-set compression” strategy, which is proposed to further reduce the problem scale by partially relaxing inequality constraints in the prediction horizon. The closed-loop stability is guaranteed by adding terminal zero-state constraint. The tradeoff between control optimality and computational intensity is achieved by proper design of the blocking and compression matrices. The fast algorithm has been applied on intelligent vehicular longitudinal automation, implemented as a fuel economy-oriented adaptive cruise controller and experimentally evaluated by a series of real-time simulations and field tests. These results indicate that the proposed method significantly improves the computational speed while maintaining satisfactory control optimality without sacrificing the desired performance.

This paper studies the principles and mechanism of a fuel-optimal strategy in cruising scenarios, i.e., the pulse and glide (PnG) operation, for road vehicles equipped with a step-gear transmission. In the PnG strategy, the control of the engine and the transmission determines the fuel-saving performance, and it is obtained by solving an optimal control problem (OCP). Due to a discrete gear ratio, strong nonlinear engine fuel characteristics, and different dynamics in the pulse/glide mode, the OCP is a switching nonlinear mixed-integer problem. This challenging problem is converted by a knotting technique and the Legendre pseudospectral method to a nonlinear programming problem, which then solves the optimal engine torque and transmission gear position. The optimization results show the significant fuel saving of the PnG operation as compared with the constant-speed cruising strategy. The underlying fuel-saving mechanism of the PnG strategy is explained graphically. For a real-time implementation, a near-optimal practical rule that enables a driver and/or an automatic control system to fast select gear positions and engine torque profile is proposed with only slightly deteriorated fuel saving.

Eco-driving technologies are able to largely reduce the fuel consumption of ground vehicles. This paper presents how to determine the fuel-optimized operating strategies of passenger cars under cruising process. The design naturally casts into an optimal control problem with the S-shaped engine fueling rate as the integrand of cost function. The solutions are numerically solved by the Legendre pseudospectral method, of which many are found to demonstrate periodic behaviors. In the periodic operation, the engine switches between the minimum brake specific fuel consumption (BSFC) point and the idling point, while the vehicle speed oscillates between its upper and lower bounds. The formation of periodic operation are analyzed and explained by the π-test theory and steady state analysis method.

This paper presents a computational framework to solve optimal control problems (OCPs) using Legendre Pseudospectral (PS) method and its application to obtain eco-driving strategies for ground vehicles. Both control and state variables of OCPs are approximated by Lagrange interpolating polynomials at the Legendre-Gauss-Lobatto (LGL) collocation points. The OCP is converted into a nonlinear programming (NLP) problem, and numerically solved by matured optimization algorithms. To implement the PS method, we developed a computational package, called Pseudospectral Optimal control Problem Solver (POPS) in Matlab environment. Further, the POPS is applied to obtain fuel-optimized driving strategies for automated vehicles in hilly road conditions.