Optimal Steering Angle Research Articles

Fuel-Optimal Trajectory Planning for Lunar Vertical Landing

In this paper we consider a trajectory planning problem arising from a lunar vertical landing with minimum fuel consumption. The vertical landing requirement is written as a final steering angle constraint, and a nonnegative regularization term is proposed to modify the cost functional. In this way, the final steering angle constraint will be inherently satisfied according to Pontryagin’s Minimum Principle. As a result, the modified optimal steering angle has to be determined by solving a transcendental equation. To this end, a transforming procedure is employed, which allows for finding the desired optimal steering angle by a simple bisection method. Consequently, the vertical landing trajectory can be found offline by the indirect shooting method. Finally, some numerical examples are presented to demonstrate and verify the developments of the paper.

Model Predictive Controller Approach for Automated Vehicle's Path Tracking.

In this paper, a model predictive control (MPC) approach for controlling automated vehicle steering during path tracking is presented. A (linear parameter-varying) LPV vehicle plant model including steering dynamics is proposed to determine the system evolution matrices. The steering dynamics are modeled in two different ways by using first-order lag and a second-order lag; the application of the first-order system resulted in a slightly more accurate path-following. Additionally, a cascade MPC structure is applied in which two MPCs are used; the second-order steering dynamics are separated from the path-following controller in a second MPC. Both steering system models and the cascade MPC are evaluated in simulation and on a test vehicle. The reference trajectory is calculated based on a fixed predefined path by transforming the necessary path segment to the vehicle ego coordinate system, thereby describing the reference for the path-following task in a novel way. The MPC method computes the optimal steering angle vector at each time step for following the path. The longitudinal dynamics is controlled separately by a PI controller. After simulation evaluation, experimental tests were conducted on a test vehicle on an asphalt surface. Both simulation and experimental results prove the effectiveness of the proposed reference definition method. The effect of the applied steering system models is evaluated. The inclusion of the steering dynamics in the prediction model resulted in a significant increase in controller performance. Finally, the computational requirements of the proposed control and modeling methods are also discussed.

Collision Avoidance Method for Autonomous Ships Based on Modified Velocity Obstacle and Collision Risk Index

A novel real-time collision avoidance method for autonomous ships based on modified velocity obstacle (VO) algorithm and grey cloud model is proposed. A typical VO algorithm is used to judge whether there is a collision risk for ships in the potential collision area (PCA). Then, in order to quantify the collision risk of ships in different encounter situations within the PCA and trigger a prompt warning of danger of collision, this study sets up a novel collision risk assessment method based on asymmetric grey cloud model (AGC). It can effectively consider the randomness, ambiguity, and incompleteness of the information in the ship collision risk evaluation process. Moreover, reachable collision-free velocity sets under different encounter situations and optimal steering angle model are constructed. A real-time collision avoidance method based on modified VO algorithm and manoeuvring motion characteristics of vessels is put forward. In this model, various constraints are considered including the International Regulations for Preventing Collisions at Sea (COLREGs), ship manoeuvrability, and ordinary practice of seaman. Finally, several case studies are carried out to verify the performance and reliability of the collision avoidance model. The results show that the proposed method can not only effectively identify and quantify the collision risk in real-time but also offer proper collision-free solutions for autonomous ships.

Prediction of the Equivalent Steering Angle of a Front-Wheel, High-Clearance Paddy Field Management Machine

To solve the problem of poor steering consistency for each steering wheel of a four-wheel, independent-steering, high-clearance paddy field management machine, given that the true steering angle of the front wheel cannot be directly obtained through the left and right front wheels steering angle value, a BP (Back Propagation) neural network equivalent steering angle prediction method based on signal feature extraction is proposed in this paper, which can be used to obtain the equivalent steering angle of the front wheel. First, the kinematics model of the paddy field management machine was constructed with the prediction of the steering angle of the management machine as the object. The body was set up in two application environments of cement ground and paddy field, two moving speeds (25 cm/s, 50 cm/s) and three preset steering angles (0°, ±10°) to form six motion modes. The steering angle of the front wheel of the body, the three-axis acceleration of the body, and the angular velocity of the z-axis under twelve conditions were collected. Combining the collected data with the actual trajectory data of the differential BeiDou, the feasibility analysis of the equivalent steering angle prediction was carried out. With the aim of determining an appropriate combination of input factors for optimal equivalent steering angle prediction by the BP neural network, we used FFT (Fast Fourier Transform) and power spectrum conversion to extract and analyze the signal features of the airframe attitude data and obtain the frequency characteristics of the peak power point of the power spectrum, respectively. Through a factor combination test, the optimal BP neural network training factors were determined and, finally, we confirmed that the rotation angles of the front wheels and the z-axis angular velocity may be used as effective training factors. In our investigation on the test set, the mean square error of the equivalent steering angle was found to be less than 0.66°, demonstrating that our approach is effective for obtaining the true steering angle of the front wheel.

The Braking-Pressure and Driving-Direction Determination System (BDDS) Using Road Roughness and Passenger Conditions of Surrounding Vehicles

A fully autonomous vehicle must ensure not only fully autonomous driving but also the safety and comfort of its passengers. However, the self-driving technology that is currently completed focuses only on perfect driving and does not guarantee the safety and comfort of passengers. This paper proposes a braking-pressure and driving-direction determination system (BDDS), which computes the brake pressure and steering angle optimized for passenger safety by utilizing more diverse information than existing autonomous vehicles. The BDDS proposed in this paper consists of two modules. The road roughness classification module (RRCM) classifies the roughness of the road by using the pressure data applied to the suspension and the K-NN algorithm and computes the optimal brake pressure. The passenger recognition and sharing module (PRSM) identifies the current occupant status of the vehicle by using a body pressure sensor and CNN, shares the information with surrounding vehicles, and computes the optimal steering angle using passenger information and road information. As a result of the simulations described in this paper, the parameters of AI models were optimized. In addition, the RRCS was about 7% more accurate than the K-means clustering algorithm, and PRS was about 9% more accurate than the existing seat recognition system.

A Novel Decision Support Methodology for Autonomous Collision Avoidance Based on Deduction of Manoeuvring Process

In the last few years, autonomous ships have attracted increasing attention in the maritime industry. Autonomous ships with an autonomous collision avoidance capability are the development trend for future ships. In this study, a ship manoeuvring process deduction-based dynamic adaptive autonomous collision avoidance decision support method for autonomous ships is presented. Firstly, the dynamic motion parameters of the own ship relative to the target ship are calculated by using the dynamic mathematical model. Then the fuzzy set theory is adopted to construct collision risk models, which combine the spatial collision risk index (SCRI) and time collision risk index (TCRI) in different encountered situations. After that, the ship movement model and fuzzy adaptive PID method are used to derive the ships’ manoeuvre motion process. On this basis, the feasible avoidance range and the optimal steering angle for ship collision avoidance are calculated by deducting the manoeuvring process and the modified velocity obstacle (VO) method. Moreover, to address the issue of resuming sailing after the ship collision avoidance is completed, the Line of Sight (LOS) guidance system is adopted to resume normal navigation for the own ship in this study. Finally, the dynamic adaptive autonomous collision avoidance model is developed by combining the ship movement model, the fuzzy adaptive PID control model, the modified VO method and the resume-sailing model. The results of the simulation show that the proposed methodology can effectively avoid collisions between the own ship and the moving TSs for situations involving two or multiple ships, and the own ship can resume its original route after collision avoidance is completed. Additionally, it is also proved that this method can be applied to complex situations with various encountered ships, and it exhibits excellent adaptability and effectiveness when encountering multiple objects and complex situations.

Path tracking control strategy for the intelligent vehicle considering tire nonlinear cornering characteristics in the PWA form

To improve the path tracking control performance of the intelligent vehicle under critical maneuvers, a novel control strategy is introduced in this work. Considering that the tire cornering characteristics show high nonlinearities and uncertainties under those special driving conditions, a three-dimensional piecewise affine (PWA) identification method is proposed to realize the nonlinear modeling of the tire cornering characteristics for the first time. On this basis, the PWA model of the vehicle lateral dynamics is established. To obtain the vehicle target yaw rate for path tracking, a driver direction control model with adaptive preview time is put forward. Then, the linear quadratic optimal control method is further adopted to design multiple path tracking controllers for different working areas of the affine subsystems, thus the optimal steering angles of the front wheels can be generated to guarantee the path tracking performance for the intelligent vehicle under a wide range of driving conditions. Finally, to evaluate the performance of the proposed path tracking control strategy which considers the tire nonlinear cornering characteristics in the PWA form, the CarSim-Simulink co-simulation work is conducted. The co-simulation results show that the proposed control strategy presents significant performance advantages over the other two methodologies and demonstrates satisfactory path tracking control performance.

Human–Machine Cooperative Control of Intelligent Vehicles for Lane Keeping—Considering Safety of the Intended Functionality

Reasonably foreseeable misuse by persons, as a primary aspect of safety of the intended functionality (SOTIF), has a significant effect on cooperation performance for lane keeping. This paper presents a novel human–machine cooperative control scheme with consideration of SOTIF issues caused by driver error. It is challenging to balance lane keeping performance and driving freedom when driver error occurs. A safety evaluation strategy is proposed for safety supervision, containing assessments of driver error and lane departure risk caused by driver error. A dynamic evaluation model of driver error is designed based on a typical driver model in the loop to deal with the uncertainty and variability of driver behavior. Additionally, an extension model is established for determining the cooperation domain. Then, an authority allocation strategy is proposed to generate a dynamic shared authority and achieve an adequate balance between lane keeping performance and driving freedom. Finally, a model predictive control (MPC)-based controller is designed for calculating optimal steering angle, and a steer-by-wheel (SBW) system is employed as an actuator. Numerical simulation tests are conducted on driver error scenarios based on the CarSim and MATLAB/Simulink software platforms. The simulation results demonstrate the effectiveness of the proposed method.

Influence of Steering Angle Profiles on the Orbit Transfer Trajectory

This paper considers a planar orbit transfer trajectory design problem using finite thrust modeling. In this problem, the steering angles associated with the thrust direction are calculated from the predetermined profile format, and the unknown parameters in the profile are directly optimized. Three profile formats that were implemented in previous lunar exploration missions are considered. In addition, a steering angle profile defined in the rotating frame and the optimal steering angle profile are newly studied to compare the performances. To this end, the direct parameter optimization problem and the indirect optimization problem are formulated, and the characteristics of the steering angle profile and its influence on the transfer trajectory are analyzed.

A Decision-Making Method for Ship Collision Avoidance Based on Improved Cultural Particle Swarm

In the process of ship collision avoidance decision making, steering collision avoidance is the most frequently adopted collision avoidance method. In order to obtain an effective and reasonable steering angle, this paper proposes a decision-making method for ship collision avoidance based on improved cultural particle swarm. Firstly, the ship steering angle direction is to be determined. In this stage, the Kalman filter is used to predict the ship’s trajectory. According to the prediction parameters, the collision risk index of the ship is calculated and the situation with the most dangerous ship is judged. Then, the steering angle direction of the ship is determined by considering the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs). Secondly, the ship steering angle is to be calculated. In this stage, the cultural particle swarm optimization algorithm is improved by introducing the index of population premature convergence degree to adaptively adjust the inertia weight of the cultural particle swarm so as to avoid the algorithm falling into premature convergence state. The improved cultural particle swarm optimization algorithm is used to find the optimal steering angle within the range of the steering angle direction. Compared with other evolutionary algorithms, the improved cultural particle swarm optimization algorithm has better global convergence. The convergence speed and stability are also significantly improved. Thirdly, the ship steering angle direction decision method in the first stage and the ship steering angle decision method in the second stage are integrated into the electronic chart platform to verify the effectiveness of the decision-making method of ship collision avoidance presented in this paper. Results show that the proposed approach can automatically realize collision avoidance from all other ships and it has an important practical application value.

MPC-based path tracking with PID speed control for high-speed autonomous vehicles considering time-optimal travel

In order to track the desired path as fast as possible, a novel autonomous vehicle path tracking based on model predictive control (MPC) and PID speed control was proposed for high-speed automated vehicles considering the constraints of vehicle physical limits, in which a forward-backward integration scheme was introduced to generate a time-optimal speed profile subject to the tire-road friction limit. Moreover, this scheme was further extended along one moving prediction window. In the MPC controller, the prediction model was an 8-degree-of-freedom (DOF) vehicle model, while the plant was a 14-DOF vehicle model. For lateral control, a sequence of optimal wheel steering angles was generated from the MPC controller; for longitudinal control, the total wheel torque was generated from the PID speed controller embedded in the MPC framework. The proposed controller was implemented in MATLAB considering arbitrary curves of continuously varying curvature as the reference trajectory. The simulation test results show that the tracking errors are small for vehicle lateral and longitudinal positions and the tracking performances for trajectory and speed are good using the proposed controller. Additionally, the case of extended implementation in one moving prediction window requires shorter travel time than the case implemented along the entire path.

Vehicle Path Tracking Maneuver Based on Model Predictive Control Theory

Vehicle path tracking problem has been a hot research topic in the field of automotive safety. Therefore, combined with a 3-DOF vehicle model is established. The basic idea behind the work was to identify the optimal steering angle input during a vehicle travels along a prescribed path. Based on Model Predictive Control (MPC), the steering angle input was determined as the control variable, tracking the desired path was determined as control object. By using the Model Predictive Control, the optimal control problem was converted into a secondary plan problem which was then solved by the active set method. The results show that the minimum error of lateral position for the generated path-tracking trajectory can be good indicators of successful solving of the path-tracking problem in vehicle handling inverse dynamics for MPC. The study can help drivers identify safe lane-keeping trajectories and area easily as well as evaluating performance of emergency collision-avoidance for a vehicle.

A comparison between a centralised multilayer LPV/ℋ∞ and a decentralised multilayer sliding mode control architectures for vehicle's global chassis control

This paper investigates new achievements in global chassis control, involving Active Front steering (AFS) and Direct Yaw Control (DYC), to improve the overall vehicle performance, i.e. the vehicle manoeuvrability, lateral stability and rollover avoidance. Two multilayer control architectures, each formed by three hierarchical layers, are developed, validated and compared. The lower layer represents the actuators implemented into the vehicle which generate their control inputs based on the orders sent from the middle layer. The middle layer is the control layer which is responsible to generate the control inputs that minimise the errors between the desired and actual vehicle yaw rate, side-slip angle and roll angle, regardless of the driving situation. The control layer is the main difference of the proposed architectures, where a centralised and a decentralised controllers are developed. In the centralised architecture, the novelty is that one single Multi-Input-Multi-Output MIMO optimal controller generates the optimal additive steering angle provided by the AFS and the optimal differential braking provided by the DYC to minimise -at once- all the vehicle state errors . The optimal control technique based on offline Linear Matrix Inequality optimal solutions, in the framework of Linear-Parameter-Varying systems, is applied to synthesise the controller. In the decentralised architecture, a heuristic solution is proposed by decoupling the control problem where the Super-Twisting Sliding Mode (STSM) technique is applied to derive the AFS control input which minimises only the errors on the yaw rate, and the roll angle. Similarly, the DYC control input is privileged to minimise only the error on the side-slip angle. The higher layer of both architectures is the decision making layer which instantly monitors two criteria laying on lateral stability and rollover risks. Then, it generates two weighted parameters which adapt the controller(s) performance(s) according to the driving conditions in order to improve the vehicle's manoeuvrability, lateral stability and rollover avoidance. Both control architectures are tested and validated on the professional simulator ‘SCANeR Studio’. Simulation shows that both architectures are relevant to the global chassis control. The centralised one is optimal, complex and overall closed-loop stability is guaranteed, while the decentralised one does not guarantee the overall closed-loop stability, but it is intuitive, simple and robust.

MPC-based path tracking with PID speed control for autonomous vehicles

In this paper, a new coupled lateral and longitudinal controller based on model predictive control (MPC) framework was proposed for an autonomous vehicle to track the desired trajectory and speed. Considering the constraints of control input limit and state output admissible, we used a spatial-based 8 degrees of freedom (DOF) vehicle model as the prediction model and used a high-fidelity model, i.e., a 14-DOF vehicle model as the plant model in the formulation of MPC algorithm. For the lateral control, the MPC controller generates the optimal road-wheel steering angle; for the longitudinal control, the PID controller embedded in the optimization solution generates the total driving or braking wheel torque. All these control inputs were passed to the plant simultaneously. The developed vehicle models were simulated with step steering input and compared with the simulation result of CarSim vehicle model for validation. We implemented the proposed controller for path tracking and speed control with MATLAB considering an 8-shaped curved trajectory as the reference. The simulation results showed that the path tracking and speed tracking performance were good using the combined lateral and longitudinal control strategy.

Optimal Array Steering for High Spatial Resolution Over Time Varying UAV Communication Channels

The Doppler spread in a highly dynamic environment leads to a large-scale channel variation over time for unmanned aerial vehicles (UAVs). In this letter, we adopt the high spatial resolution of massive multi-input multi-output (MIMO) technology to reduce the influence of Doppler spread. An algorithm is proposed for the asymptotically-optimal steering angle to achieve the longest virtual coherence time for large antenna arrays. We first design a matrix to detect array steering vectors of separated propagation paths. A closed-form expression of virtual coherence time over virtual channel for large antenna arrays is therefore derived for the optimal steering angle. Simulation results show that our proposed algorithm can improve the average virtual coherence time by about 13.65 to 27.35 times as compared to benchmarks.

Model Predictive Trajectory Tracking for a Ground Vehicle in a Heterogeneous Rendezvous with a Fixed-Wing Aircraft

Abstract The maneuver of landing a fixed-wing unmanned aerial vehicle (UAV) autonomously on a moving ground platform requires precise spatial synchronization of both agents. Depending on the desired control strategy for the maneuver, the unmanned ground vehicle (UGV) must be capable to track the UAV’s trajectory robustly with respect to the ground plane even in the presence of disturbances such as wind gusts. In this paper, a linear model predictive trajectory tracking controller for a UGV based on a kinematic bicycle model is presented, assuming that the UAV aims at following a straight flight path with a given velocity. The vehicle model is discretized and linearized in each sampling step, resulting in a quadratic optimization problem which yields the optimal steering angle and motor current demand of the UGV. In the optimization problem, actuator constraints as well as hardware-related dead-times are taken into account. By constraining the yaw rate of the UGV, sideslip of the UGV is prevented, preserving the consistency of the kinematic model. Main requirements for the controller are the ability to allow sufficiently precise trajectory tracking with a longitudinal and lateral deviation of less than 0.5 m, i.e., within the dimensions of the landing platform in the given hardware setup, and real-time capability. Hardware-in-the-loop simulations and experimental results with a model-scale ground vehicle are presented that indicate the validity of the proposed control scheme.

An Improved Fuzzy Logic Control Method for Path Tracking of an Autonomous Vehicle

Highlights This study focused on the path tracking accuracy of a two-wheel steering, two-wheel drive autonomous vehicle. An improved fuzzy logic control method (IFM) was designed to control the steering angle of the front wheels. The IFM was better than traditional pure pursuit and fuzzy logic control methods for automatic path tracking. Abstract. This article presents a path-tracking algorithm based on an improved fuzzy logic control method (IFM) that generates optimal steering angles for an autonomous wheeled vehicle to track a sequence of waypoints. The path-tracking algorithm was designed to focus on the vehicle performance, including tracking accuracy, stability, and convergence speed. A prototype vehicle with two-wheel steering and two-wheel drive (2WS-2WD) was developed as a test platform and equipped with a series of sensors for evaluating the IFM. In this study, we considered two variables, i.e., lateral deviation (d) and heading deviation (θ), as inputs for the control system. The output (δ) was the steering angle of the front wheels as controlled by an electric linear actuator. A maximum steering angle strategy was adopted for rapid convergence when the vehicle was far from the desired path or when the heading deviation was large. An update-line distance algorithm was used for finding the best turning time as the vehicle moved closer to the next waypoint. To validate the proposed algorithm, testing was performed to compare traditional pure pursuit (TPP), traditional fuzzy logic control method (TFM), and the IFM in tracking two types of paths (straight and rectangular). Traveling at 0.5 m s-1 and with a signal sampling period of 0.5 s, the prototype converged to the desired straight path from different initial states. When the vehicle reached a stable state, the steady-state error was between 5.0 and 6.5 cm with a mean of ≤6.0 cm. The settling distance in the straight path test was between 125.0 and 422.3 cm, and the convergence time was in the range of 11.5 to 16.0 s; the greater the initial deviation of the vehicle was, the greater the settling distance and settling time were. In the 15 m x 14 m rectangular path test, the overall mean error of the IFM was 14.4 cm when the initial lateral and heading deviations were 0, and the maximum deviation was 67.4 cm, which occurred at the corners. The test results show that the proposed IFM had better accuracy, stability, and convergence speed for path tracking when compared to the TPP and TFM algorithms.

Hierarchical Control for Trajectory Generation and Tracking Via Active Front Steering

Abstract A new hierarchical model predictive controller (HMPC) for autonomous vehicle steering control is presented. The controller generates a path of shortest distance by determining lateral coordinates on a longitudinal grid, while respecting road bounds. This path is then parameterized by arc length before being optimized to restrict the normal acceleration values along the trajectory's arc length. The optimized trajectory is then tracked using a nonlinear MPC scheme using a bicycle plant model to calculate an optimal steering angle for the tires. The proposed controller is evaluated in simulation during a double-lane-change maneuver, where it generates and tracks a reference trajectory while observing the road boundaries and acceleration limits. Its performance is compared to a controller without path optimization, along with another that uses a smooth, predetermined, reference path instead of creating its own initial reference. It is shown that the proposed controller improves the tracking compared to a controller without path optimization, with a four-times reduction in average lateral tracking error. The average lateral acceleration is also reduced by 6%. The controller also maintains the tracking performance of a controller that uses a smooth reference path, while showing a much greater flexibility due to its ability to create its own initial reference path rather than having to follow a predetermined trajectory.

Active steering control for autonomous vehicles based on a driver-in-the-loop platform: A case study of collision avoidance

Leveraging the advancements in sensor and mapping technologies, the collision-free autonomous vehicle becomes possible in the future. In this article, a case study of collision avoidance by active steering control is presented and verified by a driver-in-the-loop platform. The proposed control system integrates a risk assessment algorithm and a hierarchical model predictive control approach to ensure a safe driving. First, a fuzzy logic is used to estimate the potential conflict. Besides, a nonlinear model predictive control is introduced in the upper layer of the model predictive controller to generate a collision-free trajectory. Furthermore, the lower layer determines the optimal steering angle based on the linear time-variant model predictive control to follow the replanning path. The performance of the controller has been evaluated in the real-time driver-in-the-loop test. The results show that the autonomous vehicle is able to avoid the collision with the surrounding vehicle that is operated by a real driver, and the performance of collision avoidance is improved by means of the risk assessment.

Mixed local motion planning and tracking control framework for autonomous vehicles based on model predictive control

This study proposes a novel mixed motion planning and tracking (MPT) control framework for autonomous vehicles (AVs) based on model predictive control (MPC), which is made up of an MPC-based longitudinal motion planning module, a feed-forward longitudinal motion tracking module, and an MPC-based integrated lateral motion planning and tracking module. First, given the global reference path and the surroundings information obtained from onboard devices and V2X network, the longitudinal motion planning based on a vehicle kinematics model is applied to determine the local target path, the desired longitudinal acceleration, and velocity considering the longitudinal safety priority. Then, based on the planned target path and longitudinal velocity, the integrated lateral MPT module based on a 2 degree-of-freedom vehicle model is developed to determine the optimal steering angle while satisfying the multiple kinematics and dynamics constraints. Finally, based on the desired longitudinal acceleration and the steering angle, the longitudinal forces of tires are determined. More importantly, co-simulations under several typical scenarios between MATLAB/Simulink and CarSim are conducted, and the results demonstrate excellent performance of the proposed mixed framework in both planning and tracking and also its real-time implementation.