Formulation and interpretation of optimal braking and steering patterns towards autonomous safety-critical manoeuvres

ABSTRACT

Stability control of a vehicle in autonomous safety-critical at-the-limit manoeuvres is analysed from the perspective of lane keeping or lane changing, rather than that of yaw control as in traditional ESC systems. An optimal control formulation is developed, where the optimisation criterion is a linear combination of the initial and final velocity of the manoeuvre. Varying the interpolation parameter in this formulation turns out to result in an interesting family of optimal braking and steering patterns in stabilising manoeuvres. The two different strategies of optimal lane-keeping control and optimal yaw control are shown to be embedded in the formulation and result from the boundary values of the parameter. The results provide new insights and have the potential to be used for future safety systems that adapt the level of braking to the situation at hand, which is demonstrated through examples of how to exploit theresults.     

A study on single lane-change manoeuvres for determining rearward amplification of multi-trailer articulated heavy vehicles with active trailer steering systems

The Society of Automotive Engineers issued a test procedure, SAE-J2179, to determine the rearward amplification (RA) of multi-trailer articulated heavy vehicles (MTAHVs). Built upon the procedure, the International Organization for Standardization released the test manoeuvres, ISO-14791, for evaluating directional performance of MTAHVs. For the RA measures, ISO-14791 recommends two single lane-change manoeuvres: (1) an open-loop procedure with a single sine-wave steering input; and (2) a closed-loop manoeuvre with a single sine-wave lateral acceleration input. For an articulated vehicle with active trailer steering (ATS), the RA measure in lateral acceleration under the open-loop manoeuvre was not in good agreement with that under the closed-loop manoeuvre. This observation motivates the research on the applicability of the two manoeuvres for the RA measures of MTAHVs with ATS. It is reported that transient response under the open-loop manoeuvre often leads to asymmetric curve of tractor lateral acceleration [Winkler CB, Fancher PS, Bareket Z, Bogard S, Johnson G, Karamihas S, Mink C. Heavy vehicle size and weight – test procedures for minimum safety performance standards. Final technical report, NHTSA, US DOT, contract DTNH22-87-D-17174, University of Michigan Transportation Research Institute, Report No. UMTRI-92-13; 1992]. To explore the effect of the transient response, a multiple cycle sine-wave steering input (MCSSI) manoeuvre is proposed. Simulation demonstrates that the steady-state RA measures of an MTAHV with and without ATS under the MCSSI manoeuvre are in excellent agreement with those under the closed-loop manoeuvre. It is indicated that between the two manoeuvres by ISO-14791, the closed-loop manoeuvre is more applicable for determining the RA measures of MTAHVs with ATS.     

Disturbance compensation with a torque controllable steering system

Via a conventional steering system the driver perceives desired and disturbing effects such as road feedback and resonance effects, respectively. They appear with overlapping frequency spectra within the driver's steering torque. This paper introduces a control algorithm that is suppressing periodic disturbances without affecting useful steering road feedback attributes as well as regular power assistance characteristic. This is realised by an integrated torque actuator within the steering column in conjunction with a conventional Hydraulic-assisted Power Steering (HPS) system.     

Disturbance compensation with a torque controllable steering system

Via a conventional steering system the driver perceives desired and disturbing effects such as road feedback and resonance effects, respectively. They appear with overlapping frequency spectra within the driver's steering torque. This paper introduces a control algorithm that is suppressing periodic disturbances without affecting useful steering road feedback attributes as well as regular power assistance characteristic. This is realised by an integrated torque actuator within the steering column in conjunction with a conventional Hydraulic-assisted Power Steering (HPS) system.     

Vehicle steering returnability with maximum steering wheel angle at low speeds

In this paper, an analytical model with suitable vehicle parameters, together with a multi-body model is proposed to predict steering returnability in low-speed cornering with what is expected to be adequate precision as the steering wheel moves from lock to lock. This model shows how the steering response can be interpreted in terms of vertical force, lateral force with aligning moment, and longitudinal force. The simulation results show that vertical steering rack forces increase in the restoring direction according to steering rack displacement for both the inner and outer wheels. As lateral forces due to side-slip angle are directed toward the medial plane of the vehicle in both wheels, the outer wheel pushes the steering wheel in the returning direction while the inner wheel does not. In order to improve steering returnability, it is possible to increase the total steering rack force in both road wheels through adjustments to the kingpin axis and steering angle. This approach is useful for setting up a proper suspension geometry during conceptual chassis design.     

Model predictive control with constraints for a nonlinear adaptive cruise control vehicle model in transition manoeuvres

A vehicle following control law, based on the model predictive control method, to perform transition manoeuvres (TMs) for a nonlinear adaptive cruise control (ACC) vehicle is presented in this paper. The TM controller ultimately establishes a steady-state following distance behind a preceding vehicle to avoid collision, keeping account of acceleration limits, safe distance, and state constraints. The vehicle dynamics model is for continuous-time domain and captures the real dynamics of the sub-vehicle models for steady-state and transient operations. The ACC vehicle can execute the TM successfully and achieves a steady-state in the presence of complex dynamics within the constraint boundaries.     

Steady-state steering of a tilting three-wheeled vehicle

The design of a narrow-track enclosed vehicle for urban transport was the subject of the CLEVER project. Due to its narrow track and requirement for car-like controls, an actively controlled tilting system was integrated into the chassis to allow for high lateral accelerations without rolling over. The cornering behaviour of this unique vehicle concept is investigated and compared with the ideal Ackermann response. The steer kinematics of this 1F1T (one front wheel, one wheel tilting) configuration are assessed through the use of a steady-state steering model, with attention focused on how steer parameters such as tilt axis height and inclination can be tuned to provide the required response. A prototype vehicle was designed and built and the results of experimental testing are presented to illustrate the real balancing performance of the combined steering and tilting approach used for the CLEVER vehicle. The experimental results follow the trends demonstrated in the model.     

Lateral dynamics emulation via a four-wheel steering vehicle

In this paper, we examine the lateral dynamics emulation capabilities of an automotive vehicle equipped with four-wheel steering. We first demonstrate that the lateral dynamics of a wide range of vehicles can be emulated, either with little or with no modification on the test vehicle. Then we discuss a sliding mode controller for active front and rear wheel steering, in order to track some given yaw rate and side-slip angle. Analytically, it is shown that the proposed controller is robust to plant parameter variations by±10%, and is invariant to unmeasurable wind disturbance. The performance of the sliding mode controller is evaluated via computer simulations to verify its robustness to vehicle parameter variations and delay in the loop, and its insensitivity to wind disturbance. Finally, the emulation of a bus, a van, and two commercially available passenger vehicles is demonstrated in an advanced nonlinear simulator.     

重型车双前轴转向梯形及杆系的设计与计算

转向梯形机构的几何参数决定汽车转向时内、外转向轮转角的几何关系,在汽车转向时,各车轮的转向必须保证纯滚动而无滑动,使各车轮的转角必须保证有统一的瞬时转向中心。本文主要概述了重型车双前轴转向梯形及杆系的设计与计算。     

High-speed optimal steering of a tractor–semitrailer

A high-speed optimal trailer steering controller for a tractor–semitrailer is discussed. A linear model of a tractor–semitrailer with steered trailer axles is described, and an optimal trailer steering controller is introduced. A path-following controller is derived to minimise the path-tracking error in steady-state manoeuvres using active trailer steering. A roll stability controller is introduced by adding the lateral acceleration of trailer centre of gravity as another objective in the steering controller, so as to improve roll stability in transient manoeuvres. A strategy to switch between these two control modes is demonstrated. Simulation results show that the steering controller can ensure good path tracking of articulated vehicles in steady-state manoeuvres and improve roll stability significantly in transient manoeuvres, while maintaining the path-tracking deviation within an acceptable range. Tests with an experimental tractor–semitrailer equipped with a high-bandwidth active steering system validate the controller design and simulation results. The roll stability controller reduces the measured rearward amplification by 27%.     

Automatic path-tracking controller of a four-wheel steering vehicle

The present paper proposes an automatic path-tracking controller of a four-wheel steering (4WS) vehicle based on the sliding mode control theory. The controller has an advantage in that the front- and rear-wheel steering can be decoupled at the front and rear control points, which are defined as centres of percussion with respect to the rear and front wheels, respectively. Numerical simulations using a 27-degree-of-freedom vehicle model demonstrated the following characteristics: (1) the automatic 4WS controller has a more stable and more precise path-tracking capability than the 2WS controller, and (2) the automatic 4WS controller has robust stability against system uncertainties such as cornering power perturbation, path radius fluctuation, and cross-wind disturbance.     

Driver steering and muscle activity during a lane-change manoeuvre

The article reports an experimental study of driver steering control behaviour in a lane-change manoeuvre. Eight test subjects were instrumented with electromyography to measure muscle activation and co-contraction. Each subject completed 30 lane-change manoeuvres with one vehicle on a fixed-base driving simulator. For each driver, the steering torque feedback characteristic was changed after every ten manoeuvres; the response of the vehicle to steering angle inputs was not changed. Drivers' control strategies were found to be robust to changes in steering torque feedback. Path-following errors, muscle activity and muscle co-contraction all reduce with the number of lane-changes performed by the driver, suggesting the existence of a learning process. Comparing the test subjects, there was some evidence that high levels of co-contraction were used to allow high-frequency steering inputs to be generated. The results contribute to the understanding of vehicle-driver (and more generally, human-machine) dynamic interaction.     

Modelling and control of a new differential steering concept

This paper presents a new steer-by-wire concept using an all-wheel drive vehicle layout with in-wheel motors while completely omitting the application of any dedicated steering device. Steering is based on the so-called differential steering principle which generates the necessary steering moment about the kingpins by a traction force difference between left and right sides of the vehicle. In order to investigate the behaviour of the vehicle and to design the underlying control algorithms, a planar vehicle model is presented, where the vehicle is described as constrained non-holonomic system requiring a special treatment. A state feedback linear controller for controlling of the lateral dynamics of the vehicle at higher speeds and a simple PI angle controller for low-speed manoeuvring are developed. The resulting behaviour of the system is investigated by various simulation experiments demonstrating a comparable steering performance of the new steering concept as that of conventional passenger cars.     

Driver steering and muscle activity during a lane-change manoeuvre

The article reports an experimental study of driver steering control behaviour in a lane-change manoeuvre. Eight test subjects were instrumented with electromyography to measure muscle activation and co-contraction. Each subject completed 30 lane-change manoeuvres with one vehicle on a fixed-base driving simulator. For each driver, the steering torque feedback characteristic was changed after every ten manoeuvres; the response of the vehicle to steering angle inputs was not changed. Drivers' control strategies were found to be robust to changes in steering torque feedback. Path-following errors, muscle activity and muscle co-contraction all reduce with the number of lane-changes performed by the driver, suggesting the existence of a learning process. Comparing the test subjects, there was some evidence that high levels of co-contraction were used to allow high-frequency steering inputs to be generated. The results contribute to the understanding of vehicle–driver (and more generally, human–machine) dynamic interaction.     

基于ADAMS的某车型转向特性分析

用ADAMS软件建立了某车型转向传动机构的虚拟样机模型,分析了转向机构中的关键点改变对阿克曼转向特性的影响,为新车型开发过程中转向梯形的选择提供了最佳方向。     

Automotive steering system preferences evaluated using a driving simulator

The automotive steering system is the primary channel through which road and vehicle behavior feedback is transmitted to the driver. While the driver provides directional platform control through the steering wheel, perceptions of the vehicle’s handling responsiveness are simultaneously transmitted back to the driver allowing for correction of any instabilities the vehicle may encounter. Based on these factors, drivers often pay special attention to the steering system when deciding what vehicle to purchase. Therefore, a significant amount of effort and time is invested in attempting to determine the optimal design of steering system components and configurations. In this study, the determination of an optimal steering configuration was attempted based on responses obtained from questionnaires that subjects answered. The questions were designed to evaluate the degree of satisfaction regarding the “control”, “ease of operation”, and “fun” participants experienced after each driving run. During the study, human subjects drove a driving simulator for 15 combinations of 3 different roadway environments and 5 different steering configurations, filling out a questionnaire after each scenario. The subjects were also classified as a type of driver (“utility”, “enthusiast”, and/or “performance”). The study attempted to determine if the mean values of questionnaire responses for “control”, “ease”, and “fun” type of questions changed as the scenario and/or driver type changed. Analysis of Variance (ANOVA) was used to determine if the mean values of the three types of questions were statistically different. The overall results suggest that the average responses for vehicle “control”, “ease”, and the “fun” type of questions were dependent on the type of roadway environment; however, only the responses for “fun” type of questions were influenced by the given steering configurations. Indeed, the steering system can impact the driver’s perceptions of the vehicle’s operational experience.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

镁合金方向盘疲劳试验的计算机模拟

通过利用有限元技术对镁合金方向盘疲劳试验的主要过程加以模拟,分析产品的几种主要受力状态。作为模拟分析的重要技术,CAE可以进行高效、快速的分析,便于对试验结果做出预先判定、优化产品设计。