This paper treats the uncertainties in practical train operations as disturbances in train dynamics and proposes a robust optimization method for multi-train operations. First, the indeterministic problem is transformed into a deterministic problem, by linearizing the train dynamics, analyzing the propagation of disturbances, and introducing new state variables. Then, a nonlinear program (NLP) is developed to solve the deterministic problem. The speed profiles of each train are simultaneously optimized to minimize the total traction energy while ensuring safe-separation among adjacent trains. Our results show that operation constraints and absolute safe time headway can always be guaranteed, even in the worst-case scenarios caused by disturbances.

This paper studies the optimization of ride comfort during the maneuver of bus docking at a stop station. We propose an analytical comfort model that considers the coupled and nonlinear effect of acceleration and jerk levels on the comfort perceived by standing bus passengers. This is studied through offline path planning by formulating the docking problem as a Nonlinear Program while implementing the comfort model to minimize discomfort. Geometry constraints are imposed on several points on the vehicle contour to ensure that the bus stays within the road bounds and docking is performed safely. The offline solution is then used as a reference in a real-time control event using a Volvo 7900 autonomous bus. To gain perspective, the measurements from the field test were compared to those of a human-driven trajectory. The results indicate that only around$\mathbf{\SI{1.7}{\%}}$of bus occupants will experience discomfort with the proposed model, in comparison to$\mathbf{\SI{60}{\%}}$in a human-driven bus, while respecting road and vehicle constraints and accurately docking within an acceptable predefined distance from the curb. We also show through simulations that in comparison to our proposed model, the traditional method of quadratic penalties for comfort modeling produces higher discomfort levels and prevents some trajectories characterized by high acceleration and jerk. Such trajectories can be permitted and comfortable using our approach.

This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across various types of collision avoidance missions. Utilizing numerical optimal control techniques, this study proposes a unified optimization-based planning framework to meet these demands. We focus on handling two collision avoidance problems, i.e., the object not colliding with obstacles and not colliding with boundaries of the constrained region. The object or obstacle is denoted as a union of convex polytopes and ellipsoids, and the constrained region is denoted as an intersection of such convex sets. Using these representations, collision avoidance can be approached by formulating explicit constraints that separate two convex sets, or ensure that a convex set is contained in another convex set, referred to as separating constraints and containing constraints, respectively. We propose to use the hyperplane separation theorem to formulate differentiable separating constraints, and utilize the S-procedure and geometrical methods to formulate smooth containing constraints. We state that compared to the state of the art, the proposed formulations allow a considerable reduction in nonlinear program size and geometry-based initialization in auxiliary variables used to formulate collision avoidance constraints. Finally, the efficacy of the proposed unified planning framework is evaluated in two contexts, autonomous parking in tractor-trailer vehicles and overtaking on curved lanes. The results in both cases exhibit an improved computational performance compared to existing methods.

This research investigates optimization-based schemes aimed at achieving effective collision avoidance in autonomous vehicles. The study introduces three explicit formulations of collision constraints that can be applied universally to both general vehicles and obstacles regardless of whether they are represented by convex or nonconvex polygons. These formulations are devised by reformulating implicit vertex-edge constraints, exclusively designed to prevent collisions between any vertex and any edge, as explicit constraints through analytically characterizing modified signed distance functions (MSDFs), equilibrium functions, and binary variables, respectively. The proposed schemes can formulate the optimization-based planning problem involving collision avoidance as a nonlinear program (NLP), a mathematical program with equilibrium constraints, and a mixed-integer NLP, which are readily addressed using off-the-shelf solvers. Furthermore, the research examines the sensitivity of the MSDFs, indicating that the formulation can exhibit numerical sensitivity to the sign. Finally, the efficacy of the proposed schemes is demonstrated in the context of an autonomous bus parallel parking in a confined bus stop with multiple corridors. The results illustrate that all the three schemes perform equally well in terms of identifying feasible solutions, while the scheme using MSDFs avoids adding dual variables to be optimized, exhibiting the added benefit of requiring lower computational resources compared to the state of the art.

This paper presents numerical strategies for a computationally efficient energy management system that co-optimizes the power split and gear selection of a hybrid electric vehicle (HEV). We formulate a mixed-integer optimal control problem (MIOCP) that is transcribed using multiple-shooting into a mixed-integer nonlinear program (MINLP) and then solved by nonlinear model predictive control. We present two different numerical strategies, a Selective Relaxation Approach (SRA), which decomposes the MINLP into several subproblems, and a Round-n-Search Approach (RSA), which is an enhancement of the known ‘relax-n-round’ strategy. Subsequently, the resulting algorithmic performance and optimality of the solution of the proposed strategies are analyzed against two benchmark strategies; one using rule-based gear selection, which is typically used in production vehicles, and the other using dynamic programming (DP), which provides a global optimum of a quantized version of the MINLP. The results show that both SRA and RSA enable about 3.6% cost reduction compared to the rule-based strategy, while still being within 1% of the DP solution. Moreover, for the case studied RSA takes about 35% less mean computation time compared to SRA, while both SRA and RSA being about 99 times faster than DP. Furthermore, both SRA and RSA were able to overcome the infeasibilities encountered by a typical rounding strategy under different drive cycles. The results show the computational benefit of the proposed strategies, as well as the energy saving possibility of co-optimization strategies in which actuator dynamics are explicitly included.

This paper presents a distributed optimization procedure for the cooperative eco-driving control problem of a platoon of electric vehicles subject to safety and travel time constraints. Individual optimal trajectories are generated for each platoon member to account for heterogeneous vehicles and for the road slope. By rearranging the problem variables, the Riccati recursion can be applied along the chain-like structure of the platoon and be used to solve the problem by repeatedly transmitting information up and down the platoon. Since each vehicle is only responsible for its own part of the computations, the proposed control strategy is privacy-preserving and could therefore be deployed by any group of vehicles to form a platoon spontaneously while driving. The energy efficiency of this control strategy is evaluated in numerical experiments for platoons of electric trucks with different masses and rated motor powers.

Abstract Trip destination prediction is an area of increasing importance in many applications such as trip planning, autonomous driving and electric vehicles. Even though this problem could be naturally addressed in an online learning paradigm where data is arriving in a sequential fashion, the majority of research has rather considered the offline setting. In this paper, we present a unified framework for trip destination prediction in an online setting, which is suitable for both online training and online prediction. For this purpose, we develop two clustering algorithms and integrate them within two online prediction models for this problem. We investigate the different configurations of clustering algorithms and prediction models on a real-world dataset. We demonstrate that both the clustering and the entire framework yield consistent results compared to the offline setting. Finally, we propose a novel regret metric for evaluating the entire online framework in comparison to its offline counterpart. This metric makes it possible to relate the source of erroneous predictions to either the clustering or the prediction model. Using this metric, we show that the proposed methods converge to a probability distribution resembling the true underlying distribution with a lower regret than all of the baselines.

This paper presents a computationally efficient algorithm for eco-driving along horizons of over 100 km. The eco-driving problem is formulated as a bi-level program, where the bottom level is solved offline, pre-optimising gear as a function of longitudinal velocity (kinetic energy) and acceleration. The top level is solved online, optimising a nonlinear dynamic program with travel time, kinetic energy and acceleration as state variables. To further reduce computational effort, the travel time is adjoined to the objective by applying necessary Pontryagin’s Maximum Principle conditions, and the nonlinear program is solved using real-time iteration sequential quadratic programming scheme in a model predictive control framework. Compared to average driver’s driving cycle, the energy savings of using the proposed algorithm is up to 11.60%.

The problems of bus bunching mitigation and the energy management of groups of vehicles have traditionally been treated separately in the literature and been formulated in two different frameworks. The present work bridges this gap by formulating the optimal control problem of the bus line eco-driving and regularity control as a smooth, multi-objectivenonlinear program. Since this nonlinear program has only a few coupling variables, it is shown how it can be solved in parallel aboard each bus, such that only a marginal amount of computations need to be carried out centrally. This procedure leverages the structure of the bus line by enabling parallel computations and reducing the communication loads between the buses, which makes the problem resolution scalable in terms of the number of buses. Closed-loop control is then achieved by embedding this procedure in amodel predictive control. Stochastic simulations based on real passengers and travel times data are realized for several scenarios with different levels of bunching for a line of electric buses. Our method achieves fast recoveries to regular headways as well as energy savings of up to 9.3% when compared with traditional holding or speed control baselines.

This paper proposes a stochastic observer for estimating power capability of a preceding heavy-duty vehicle, using its speed measurement and road slope information. A chance-constrained optimisation problem is formulated to take into consideration the uncertainties associated with measurement error in the speed and imperfect knowledge of the road slope. An online learning approach is proposed to solve the chance-constrained optimisation problem, which learns probability distribution of the measurements along the travelled distance. The effectiveness of the proposed observer is analysed in two case studies on real road topographies and compared with an existing deterministic leading vehicle observer. The results show that the proposed leading vehicle observer is robust against uncertainties.

We propose an eco-driving technique for a heavy-duty ego vehicle that drives behind a leading heavy-duty vehicle. By observing a decrease in speed of the leading vehicle when driving uphill, its power capability is estimated and its future speed is predicted within a look-ahead horizon. The predicted speed is utilised in a model predictive controller (MPC) to plan the optimal speed of the ego vehicle such that its fuel consumption is minimised, while keeping a safe distance to the leading vehicle and reducing the need for braking. The effectiveness of the proposed technique is analysed in two case studies on real road topographies. By using the leading vehicle observer, fuel savings are achieved up to 8% compared to the case where the preceding vehicle is assumed to have a constant speed within the look-ahead horizon.

This paper studies the problem of optimal overtaking of a slow-moving leading vehicle in the presence of oncoming and/or adjacent vehicles with varying but known longitudinal speeds. A computationally efficient modeling approach is introduced, in which the overtaking problem is formulated by sampling in relative distance to the leading vehicle, replacing velocity state with its inverse and utilizing a nonlinear change of control variables. These three steps achieve a computationally efficient nonlinear control problem that can be solved using the sequential quadratic programming. Measures have been taken to ensure the feasibility of the nonlinear problem, even when the sequential quadratic programming iterates are stopped prematurely. A case study is presented, where this new formulation is compared with the previously published formulations in terms of solution quality and computation time.

This paper presents an energy-efficient velocity control technique for a truck driving behind a slow moving truck. An observer is designed to estimate the acceleration capability of the leading vehicle, which is then used to predict the velocity and time trajectory of the leading vehicle. This information, together with information of road topography, is used by the ego vehicle to optimally plan its velocity along a look-ahead horizon. The optimal planning is achieved by nonlinear model predictive control, where constraints are set to keep a safe distance to the leading vehicle and arrive at the destination within a given time. The designed controller is tested on various driving cycles. The proposed technique is also tested on a traffic light scenario, where information about the position of the traffic light and timing of its signals is considered to be known. The simulations results show that the proposed technique can save a significant amount of fuel.

This paper comparatively examines three different electrochemical energy storage systems (ESSs), i.e., a Li-ion battery pack, a supercapacitor pack, and a dual buffer, for a hybrid bus powertrain operated in Gothenburg, Sweden. Existing studies focus on comparing these ESSs, in terms of either general attributes (e.g., energy density and power density) or their implications to the fuel economy of hybrid vehicles with a heuristic/nonoptimal ESS size and power management strategy. This paper adds four original contributions to the related literature. First, the three ESSs are compared in a framework of simultaneous optimal ESS sizing and energy management, where the ESSs can serve the powertrain in the most cost-effective manner. Second, convex optimization is used to implement the framework, which allows the hybrid powertrain designers/integrators to rapidly and optimally perform integrated ESS selection, sizing, and power management. Third, both hybrid electric vehicle (HEV) and plug-in HEV (PHEV) scenarios for the powertrain are considered, in order to systematically examine how different the ESS requirements are for HEV and PHEV applications. Finally, a sensitivity analysis is carried out to evaluate how price variations of the onboard energy carriers affect the results and conclusions.