Vehicle Trajectory Optimization Research Articles

Trajectory optimization and stability control for a novel unmanned intelligent wheel-legged vehicles on unstructured terrains

The trend of intelligent vehicles is currently expanding, and a new class of unmanned intelligent vehicles known as wheel-legged vehicles (WLVs) is emerging. WLVs excel in transportation on unstructured terrain by offering a unique combination of the efficiency of wheels on flat ground and the versatility of legs to tackle obstacles. To enhance the locomotion performance of WLVs on unstructured terrains, this paper presents a novel framework for improving their locomotion through nonlinear programming-based (NLP) trajectory optimization and stability control. The framework optimizes the vehicle’s body and wheel positioning while incorporating terrain information and employs a linear rigid body dynamic model for efficient motion planning. The stability control framework combines feedforward control using ground reaction forces with feedback control through joint PD control and utilizes model predictive control (MPC) to adjust the wheel slip ratio to prevent slip on steep slopes. Experimental validation on the real vehicle with torque-controlled wheels demonstrated the capability of driving over a 1 m height with a 30°slope at an average speed of 0.7 m/s and a maximum speed of 1.03 m/s. Our approach also enables the WLV to overcome obstacles, such as inclines, while dynamically negotiating these challenging terrains.

A trajectory optimization method for CAVs at intersections considering energy-efficiency balance

With the development of vehicle-to-everything (V2X) technology, connected automated vehicles (CAVs) will be an important part of urban road transportation. However, frequent acceleration, deceleration, and rapid stopping within intersections lead to increased energy consumption, reduced driving efficiency and balanced benefits. The study proposes an optimal control method for vehicle trajectories that considers energy-efficiency balance (OCM-EEB) based on the characteristics of V2X technology. The method first develops a vehicle trajectory control model based on the Intelligent Driver Model (IDM) by accounting for the features of V2X technology, and further, introduces the idea of balanced optimization, considering energy-efficiency balance, a vehicle trajectory optimal control model (OCM) is proposed. The proposed model was solved by design algorithms based on the non-dominated sorting genetic algorithm-II (NSGA-II). The experimental results showed that the vehicle trajectory optimization control method could increase the balanced driving efficiency of the vehicle within intersection, which is conducive to improving the robustness of the vehicle’s trajectory state, and then prove the effectiveness of the method proposed in this study. The method also provides an important technical basis for the vehicle trajectory optimization experiments under a real V2X environment in the future.

Wireless sensor fusion localization method for target vehicles in a collaborative environment of vehicle road trajectory information

Abstract Vehicle positioning technology is the foundation for achieving traffic management. Vehicle positioning errors are significant in complex environments, making it challenging to ensure positioning accuracy. To reduce positioning errors, this paper explores a wireless sensor fusion localization method for target vehicles in a collaborative environment of vehicle road trajectory information. Based on wireless sensor data, we achieve collaborative environmental perception of vehicle and road trajectory information and construct a target vehicle trajectory optimization model. Through a fuzzy neural network, data from different sensors are integrated to overcome the problem of limited positioning accuracy of a single sensor in a complex environment. The experimental results show that both the heading angle and rolling angle errors float between −0.1° and 0.1°, and the positioning error is less than 0.1 m, which proves that the method has high positioning accuracy and good application value.

Space-time graph path planner for unsignalized intersection management with a V2V agent coordination architecture

Reducing traffic congestion and increasing passenger safety are important objectives for emerging automated transportation systems. Autonomous intersection management systems (AIMS) enable large scale optimization of vehicle trajectories with connected and autonomous vehicles (CAVs). We propose a novel approach for computing the fastest waypoint trajectory in intersections using graph search in a discretized space-time graph that produces collision-free paths with variable vehicle speeds that comply with traffic rules and vehicle dynamical constraints. To assist our planner algorithm in decentralized scenarios, we also propose a multi-agent protocol architecture for vehicle coordination for trajectory planning using a vehicle-to-vehicle (V2V) network. The trajectories generated allow a much higher evacuation rate and congestion threshold, with lower O(N) algorithm runtime compared to the state of the art conflict detection graph platoon path planning method, even for large scenarios with vehicle arrival rate of 1/s and thousands of vehicles.

Edge-Intelligence-Powered Joint Computation Offloading and Unmanned Aerial Vehicle Trajectory Optimization Strategy

UAV-based air-ground integrated networks offer a significant benefit in terms of providing ubiquitous communications and computing services for Internet of Things (IoT) devices. With the empowerment of edge intelligence (EI) technology, they can efficiently deploy various intelligent IoT applications. However, the trajectory of UAVs can significantly affect the quality of service (QoS) and resource optimization decisions. Joint computation offloading and UAV trajectory optimization bring many challenges, including coupled decision variables, information uncertainty, and long-term queue delay constraints. Therefore, this paper introduces an air-ground integrated architecture with EI and proposes a TD3-based joint computation offloading and UAV trajectory optimization (TCOTO) algorithm. Specifically, we use the principle of the TD3 algorithm to transform the original problem into a cumulative reward maximization problem in deep reinforcement learning (DRL) to obtain the UAV trajectory and offloading strategy. Additionally, the Lyapunov framework is used to convert the original long-term optimization problem into a deterministic short-term time-slot problem to ensure the long-term stability of the UAV queue. Based on the simulation results, it can be concluded that our novel TD3-based algorithm effectively solves the joint computation offloading and UAV trajectory optimization problems. The proposed algorithm improves the performance of the system energy efficiency by 3.77%, 22.90%, and 67.62%, respectively, compared to the other three benchmark schemes.

Joint Trajectory and Communication Optimization for Heterogeneous Vehicles in Maritime SAR: Multi-Agent Reinforcement Learning

Joint Trajectory and Communication Optimization for Heterogeneous Vehicles in Maritime SAR: Multi-Agent Reinforcement Learning

Convex Approach to Real-Time Multiphase Trajectory Optimization for Urban Air Mobility

Electric vertical takeoff and landing technology has emerged as a promising solution to alleviate ground transportation congestion. However, the limited capacity of onboard batteries enforces hard time constraints for vehicle operations in a complex urban environment. Therefore, a constrained, real-time trajectory optimization method is necessary to enable safe and energy-efficient vehicle flight. Unfortunately, most existing trajectory optimization methods suffer from low computational efficiency, unpredictable convergence processes, and strong dependence on a good initial trajectory. In this paper, we employ a successive convex programming approach to solve the multiphase minimum-energy-cost electric vertical takeoff and landing vehicle trajectory optimization problem for urban air mobility applications. The main contribution is the development and validation of two novel convexification methods that find approximate optimal solutions to the multiphase nonlinear trajectory optimization problem in real time by solving a sequence of convex subproblems. Specifically, the first method transforms the original nonlinear problem into a sequence of second-order cone programming problems through a convenient change of variables and lossless convexification, while the second approach achieves a similar goal without the need for control convexification. The resulting convex subproblems can be solved reliably in real time by advanced interior point methods. The proposed methods are demonstrated through numerical simulations of two different urban air mobility scenarios and compared with the solution obtained from GPOPS-II, a state-of-the-art general-purpose optimal control solver. Our proposed sequential convex programming methods can obtain near-optimal solutions with faster computational speed than GPOPS-II.

An adaptive coupled control method based on vehicles platooning for intersection controller and vehicle trajectories in mixed traffic

AbstractConnected and autonomous driving technologies offer a novel solution for intersection control optimization. Connected and autonomous vehicles (CAVs) can access signal plans and optimize trajectories to minimize delays and reduce fuel consumption. However, optimizing trajectories for individual vehicles significantly increases complexity, especially for joint optimization of traffic signals and vehicle trajectories. Given the current technical, regulatory, and policy constraints, a superior intersection management approach is necessary before fully automated driving is achieved. This paper introduces an adaptive coupling control (ACC) method based on vehicle platooning to optimize signal timings and vehicle trajectories in mixed traffic. Initially, vehicle platoon segmentation is conducted, led by CAVs. The study then proposes a single‐layer coupled optimization model based on vehicle platoons, simplifying the joint optimization model. To address logistic constraint difficulties, a linearization of the coupled model (LCM) method is developed. Numerical experiments demonstrate that the ACC method significantly reduces vehicle delay and fuel consumption. At high CAV penetration rates (0.8 < R <1) and high traffic volumes (over 900 pcu/h), vehicle platoon control delivers excellent performance, with delays and fuel consumption even lower than in a fully automated environment (R = 1). This surprising result suggests that the mixed platoon system (ACC method) positively impacts mixed traffic.

Progressive virtual risk-based vehicle trajectory optimization in mixed traffic flow

Ramp-merging zones have perennially served as bottlenecks for both safety and efficiency within road traffic. Addressing the inherent uncertainties and anomalous behaviors potentially exhibited by human-driven vehicles (HDVs) in mixed traffic flow, this study introduced a distributed merging control algorithm based on virtual risk assessment. Initially, we proposed a progressive vehicle projection method based on matching degree, formulated to engender smooth longitudinal accelerations. Building upon this foundation, a virtual risk-based longitudinal planning model named V-RQM was established, furnishing longitudinal accelerations with robust stability and safety to Connected and Autonomous Vehicles (CAVs). Results from four diverse simulation experiments corroborate that V-RQM is aptly versatile, suited for conventional one-dimensional car-following environments as well as pre-merging control in heterogeneous traffic flow. The model not only mitigates oscillatory amplitudes while sustaining high traffic efficiency but also exhibits commendable resilience against uncertainties and anomalies indigenous to mixed traffic flow. This research pioneers a novel model-driven approach to ramp-merging control, setting the stage for the full exploitation of CAV capabilities.

Trajectory optimization of unmanned aerial vehicles in the electromagnetic environment

AbstractWe consider a type of routing problems common in defence and security, in which we control a fleet of unmanned aerial vehicles (UAVs) that have to reach one or more target locations without being detected by an adversary. Detection can be carried out by a variety of sensors (radio receivers, cameras, personnel, etc) placed by the adversary around the target sites. We model the act of detecting a UAV from first principles by noting that sensors work by monitoring frequencies in the electromagnetic spectrum for signals or noise emitted. By this, we are able to provide a flexible and versatile nonlinear optimisation framework in which the problem is modeled as a novel trajectory optimisation problem with paths of the UAVs as continuous arcs in an Euclidean space. The flexibility of our approach is exhibited by the fact that we can easily consider various relevant objectives, among them minimising the overall probability of detection and maximising the location error that the adversary experiences when trying to locate our UAVs. Our model is also versatile enough to consider the act of jamming, in which one or more of our UAVs intentionally send out signals to interfere with the operations of the adversary’s sensors. Numerical results show the flexibility of our framework, and that we can solve realistic instances of this problem type.

Bidirectional neural network for trajectory planning: An application to medical emergency vehicle

This paper focuses on the autonomous trajectory optimization of in-hospital emergency vehicles, aiming to plan a fast, safe, and comfortable trajectory for real time navigation to reach the emergency room. This has direct and significant practical implications for saving patients’ time and reducing the burden on medical staff. To address it, we propose a novel real-time trajectory planning algorithm and introduce a training framework that contributes to planner’s transferability. In the dataset preparation phase, we employ an optimization-based method to solve the in-hospital trajectory planning problem, generating substantial trajectories. In the training phase, we design a neural network-based planner to establish logical connections between states and control commands. To enhance interaction with the vehicle itself, we design a novel network training framework that incorporates a neural network-based vehicle simulator to learn the vehicle’s self-information, facilitating training the planner. During the inference phase, our planner can plan a collision-free, time-efficient, and comfortable trajectory. Furthermore, our algorithm demonstrates ease of transferability to different vehicle models. Finally, extensive simulations experiments are conducted to validate the safety, speed, and comfortability of the algorithm’s trajectory planning, as well as its excellent transferability.

Integrated optimization of traffic signal timings and vehicle trajectories considering mandatory lane-changing at isolated intersections

Intersections are the predominant bottlenecks in urban areas due to the intricate conflicts among vehicles with different movements. With the advent of connected and automated vehicles (CAVs), it is more effective to reorganize urban traffic in a coordinated manner, and integrate the planning of both the traffic signal timings and vehicle trajectories. Most existing studies in this field assume that all vehicles are in their intended lanes initially, and only optimize the trajectories in the longitudinal dimension for simplicity, which is ideal and unrealistic. Therefore, this paper considers mandatory lane-changing for the integrated optimization of traffic signal timings and vehicle trajectories at isolated intersections. The entire planning horizon is segmented into a series of time-slots, based on which we select phases and plan the trajectories. First, a single-layer mixed integer programming (MIP) model is formulated to obtain global optimal solutions. Nevertheless, for large-scale cases, the MIP model is not applicable due to its computational complexities. Thus, we regulate vehicles into multi-lane platoons that correspond to green phases to reduce the solution space, and propose a beam-search-based platoon formation planning (BPFP) framework for efficient optimization. A beam search procedure is proposed to select phases for each time-slot, which incorporates a vehicle assignment algorithm to design the platoon formation as a subroutine. The two-dimensional vehicle trajectories are subsequently planned according to the platoon formation profiles. Numerical experiments illustrate that BPFP is capable of acquiring near-optimal solutions and considerably outperforms the baselines, while the computation time is within seconds even in over-saturated scenarios.

Optimization of isolated intersection signal timing and trajectory planning under mixed traffic environment: The flexible catalysis of connected and automated vehicles

With the development of connected and automated vehicles (CAVs) enables real-time interaction between intersection signals and vehicle trajectories. The full use of this technological breakthrough will help traffic managers improve the performance of intersections. Most previous research focuses on the 100% CAV environment and the single lateral or longitudinal optimization of CAVs. Based on the flexible characteristics of CAVs, this paper proposes that CAV is regarded as the catalyst of vehicle platoon in mixed traffic environment and considers the uncertainty of CAVs and CHVs’ interaction in the real-world, which can promote the generation of controllable platoon through the “catalytic” mode of cooperative, accelerated, or direct lane-changing, and cooperative or direct overtaking. Simultaneously, a two-stage optimization model of mixed traffic trajectory and signal timing is proposed. Stage I: Based on the predicted vehicle platoon information, a dynamic NEMA signal timing scheme without duplicate structures is generated to minimize vehicle delays. Stage II: Based on the timing scheme, the generation of controllable and stable platoon and vehicle trajectory optimization model are established to minimize vehicle emissions. Dynamic programming with NEMA signal groups as sub-states is designed to solve the proposed model. The performance of the proposed model under different scenarios is investigated through numerical experiments and compared with benchmark models. Results show that the proposed model will outperform the benchmark models regarding average vehicle delay and emission under more realistic traffic demands. The average vehicle delay can be reduced by 54.32% and 7.33%, and the average vehicle emissions can be reduced by 19.1% and 0.8%, respectively. Meanwhile, the sensitivity analysis of CAV market penetration shows that the proposed model can perform satisfactorily at 20% CAV market penetration. Notedly, with increased market penetration, the proposed model will obtain better performance.

Investigation of Surface-Catalycity Effects on Hypersonic Glide Vehicle Trajectory Optimization

The optimization of a hypersonic glide vehicle’s reachable domain is studied using different models to constrain the stagnation-point heat transfer. The vehicle is modeled as a high-lift common aero vehicle that uses bank-angle modulation for crossrange maneuvering with a leading-edge thermal protection system made of an ultra-high-temperature ceramic. A constrained nonlinear optimization problem is formulated to determine the range of feasible trajectories that satisfy aerodynamic heating and loading constraints. The optimal control profile is determined using a modified particle swarm optimization routine that employs a penalty function approach to handle path and terminal constraints. Baseline trajectories are determined using an existing convective heat-flux correlation, and the effect of surface catalycity on the optimized trajectories is investigated by applying a correction factor, derived from high-fidelity computational fluid dynamics simulations, to the heat-flux correlation. Results demonstrate a high sensitivity of the optimized trajectories to the underlying aerothermodynamics model such that accounting for surface catalycity expands the reachability by an order of magnitude.

Optimization of multi-target continuous dynamic trajectory for unmanned aerial vehicles

In the problem of trajectory optimization for unmanned aerial vehicles (UAVs) passing through multiple target points, continuous velocity and acceleration in the process of optimization are essential for maintaining a feasible trajectory. This paper proposes a multi-segment holistic Bezier shaping method (MHBSM) for dynamic trajectory optimization. The MHBSM not only achieves holistic optimization of UAVs passing through a multi-target trajectory but also ensures high-order continuity at the junctions of trajectory segments. Unlike methods that generate non-dynamic trajectories by connecting arcs and straight lines (such as Dubins curves) without considering speed changes, MHBSM optimizes the trajectory while taking into account the dynamics of UAVs. The method optimizes the differential flat output space of a fixed-wing UAV dynamic model and transforms the dynamic optimization problem into a three-dimensional position optimization problem. The problem is then further transformed into an optimization of control points using the Bezier curve. The resulting trajectory satisfies the dynamic constraints. In comparison to the Gaussian pseudospectral method (GPM), MHBSM achieves similar optimization results with only a 2.58% difference, while requiring approximately 1.36% of the computational time on average. The MHBSM demonstrates excellent convergence performance while satisfying the constraints of continuous acceleration and obstacle avoidance.

Integrated Back of Queue Estimation and Vehicle Trajectory Optimization Considering Uncertainty in Traffic Signal Timings

Integrated Back of Queue Estimation and Vehicle Trajectory Optimization Considering Uncertainty in Traffic Signal Timings

Auxiliary Steering Control of Vehicle Driving with Force/Haptic Guidance

The rapid development of the automobile industry has resulted in the development of many vehicles, increased traffic, and frequent accidents. The complexity of road conditions is a major contributor to the occurrence of traffic accidents. Drivers are distracted and hence unable to fully observe all road information and make optimal and timely driving decisions. This study proposes an auxiliary steering control system with force/tactile guidance (ASCFT) and its corresponding control strategy to address this problem. We combined vehicle autonomous path planning based on road condition information and the human–machine sharing control strategy, which integrated the manipulative force of the driver and a virtual guidance force on the steering wheel. Consequently, the ASCFT eliminated the mechanical connection between the steering wheel and the steering wheels in favor of a force/tactile-assisted steering structure, providing the driver with a sense of steering force based on road information. Additionally, we proposed a smooth vehicle trajectory optimization method based on the improved RRT algorithm and a path-following controller based on the forecast information to achieve auxiliary safety driving. The ASCFT’s performance was confirmed through constructing a fixed-base simulator experimental platform with the ASCFT. The results revealed that at the vehicle speed of 60 km/h and a handwheel rotation of 60°, the steering wheel was instantly released and turned back in about 3.5 s. Furthermore, predictive haptic feedback warned the driver of an upcoming obstacle.

Optimization of Vehicle Trajectories Considering Uncertainty in Actuated Traffic Signal Timings

This paper introduces a robust green light optimal speed advisory (GLOSA) system for fixed and actuated traffic signals considering a probability distribution. These distributions represent the domain of possible switching times from the signal phasing and timing (SPaT) messages. The system finds the least-cost (minimum fuel consumption) vehicle trajectory using a computationally efficient A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^\ast$</tex-math> </inline-formula> algorithm incorporated within a dynamic programming (DP) procedure to minimize the vehicle’s total fuel consumption. Constraints are introduced to ensure that vehicles do not collide with other vehicles, run red indications, or exceed a maximum vehicular jerk for passenger comfort. Results of simulation scenarios are evaluated against empirical comparable trajectories of uninformed drivers to compute fuel consumption savings. The proposed approach produced significant fuel savings compared to an uninformed driver behavior amounting to 37% on average for deterministic SPaT and 30% for stochastic SPaT data. A sensitivity analysis was performed to understand how the degree of uncertainty in SPaT predictions affects the optimal trajectory’s fuel consumption. The results present the required levels of confidence in these predictions to achieve savings in fuel consumption. Specifically, the study demonstrates that the proposed system can be within 85% of the maximum savings if the timing error is ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 3.3 seconds) at a 95% confidence level. Results also emphasize the importance of more reliable SPaT predictions as the time to green decreases relative to the time the vehicle is expected to reach the intersection given its current speed.

Multiple UAVs Trajectory Optimization in Multicell Networks With Adjustable Overlapping Coverage

Trajectory optimization of Unmanned Aerial Vehicles (UAVs) operating as flying base stations (FBSs) evolved as a novel integration component in beyond 5G (B5G) networks and has recently received significant research attention. Notably, the vast majority of previous research has mainly concentrated on the case of a single terrestrial macro base station (BS) which is used as a depot for multiple FBSs. In this paper, we focus on the more general use case where multiple FBSs located at different macro-BSs used as a depot serve ground users (GUs) at cluster points (CPs). To this end, we formulate the FBSs trajectory optimization problem using a mixed integer linear programming (MILP) formulation with the aim to minimize total travel time (TTT) of the FBSs in a multi-cell network in which their cell coverage or boundary is adjustable for the FBSs deployment; creating in that sense virtual cells for the FBSs. Furthermore, heuristic algorithms are proposed to provide competitive solutions and reduce the computational time in view of the curse of dimensionality of the original problem. Numerical investigations reveal that the proposed FBSs path planning optimization solutions decrease the TTT and increase the efficiency of offloading collected data for the FBSs deployment with gains up to approximately 23% and 19% respectively compared to nominal schemes that consider the pre-defined coverage range of the cells or no cell boundaries. Aside from the above, compared to previously proposed nominal strategies, the proposed schemes achieve an almost 27% improvement in terms of fairness (Jain’s index) on the FBS traveling time.

Entry trajectory optimization for hypersonic vehicles based on convex programming and neural network

Trajectory optimization is important in achieving long-range atmospheric entry hypersonic vehicles. However, the trajectory optimization problem for atmospheric entry of hypersonic vehicles is characterized by strong nonlinearity, parameter uncertainties and multiple constraints. This study proposes a novel online trajectory optimization method for hypersonic vehicles based on convex programming and a feedforward neural network. A sequential second-order cone programming (SOCP) method is obtained to describe the trajectory optimization problem after the Gauss pseudo-spectral discretization. Subsequently, multiple optimal trajectories under aerodynamic uncertainties are generated offline and classified as the training and validation datasets. Then, a multilayer feedforward neural network is trained using these datasets and to output the optimal control command online. This method yields approximately 95% shorter computation time compared with the offline SOCP method. Considering the existence of the aerodynamic uncertainties, three terminal states calculated by this method are all smaller than 4.1%. In conclusion, the proposed trajectory optimization method can provide a high-precision, robust entry trajectory for hypersonic vehicles efficiently.