Design of a Path-Tracking Steering Controller for Autonomous Vehicles

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

Human drivers have rich and diverse driving characteristics on curved roads. Finding the characteristic quantities of the experienced drivers during curve driving and applying them to the steering control of autonomous vehicles is the research goal of this article. We first recruited 10 taxi drivers, 5 bus drivers, and 5 driving instructors as the representatives of experienced drivers and conducted a real car field experiment on six curves with different lengths and curvatures. After processing the collected driving data in the Frenet frame and considering the free play of a real car’s steering system, it was interesting to observe that the shape enclosed by steering wheel angles and the coordinate axis was a trapezoid. Then, we defined four feature points, four feature distances, and one feature steering wheel angle, and the trapezoidal steering wheel angle (TSWA) model was developed by backpropagation neural network with the inputs were vehicle speeds at four feature points, and road curvature and the outputs were feature distances and feature steering wheel angle. The comparisons between TSWA model and experienced drivers, model predictive control, and preview-based driver model showed that the proposed TSWA model can best reflect the steering features of experienced drivers. What is more, the concise expression and human-like characteristic of TSWA model make it easy to realize human-like steering control for autonomous vehicles. Lastly, an autonomous vehicle composed of a nonlinear vehicle model and electric power steering (EPS) system was established in Simulink, the steering wheel angles generated by TSWA model were tracked by EPS motor directly, and the results showed that the EPS system can track the steering angles with high accuracy at different vehicle speeds.

This paper presents a novel function of energy-optimal adaptive cruise control (EACC) for electric vehicles based on model predictive control (MPC), which optimally plans the host car's speed trajectory for higher energy efficiency through taking the surrounding traffic information and the road conditions ahead into account. To cope with the nonlinearity of the system dynamics, nonlinear MPC (NMPC) is designed in this paper. Afterwards, the nonlinear equality constraints are relaxed so that the optimization problem has a convex feasible set. Moreover, it is proven that the nonlinear problem can be recast as a second-order cone programming (SOCP) problem. The performance of NMPC is evaluated in the real driving condition and compared to both linear MPC and receding horizon dynamic programming (RH-DP). In order to enable real-time control, the interior point method is used to solve both linear and nonlinear MPC problems and the computation time is investigated in this paper.

This paper presents a model predictive control-based obstacle avoidance algorithm for autonomous ground vehicles at high speed in unstructured environments. The novelty of the algorithm is its capability to control the vehicle to avoid obstacles at high speed taking into account dynamical safety constraints through a simultaneous optimization of reference speed and steering angle without a priori knowledge about the environment and without a reference trajectory to follow. Previous work in this specific context optimized only the steering command. In this paper, obstacles are detected using a planar light detection and ranging sensor. A multi-phase optimal control problem is then formulated to simultaneously optimize the reference speed and steering angle within the detection range. Vehicle acceleration capability as a function of speed, as well as stability and handling concerns such as preventing wheel lift-off, are included as constraints in the optimization problem, whereas the cost function is formulated to navigate the vehicle as quickly as possible with smooth control commands. Simulation results show that the proposed algorithm is capable of safely exploiting the dynamic limits of the vehicle while navigating the vehicle through sensed obstacles of different sizes and numbers. It is also shown that the proposed variable speed formulation can significantly improve performance by allowing navigation of obstacle fields that would otherwise not be cleared with steering control alone.

We propose a steering control algorithm for autonomous backward driving in a narrow corridor. Passable spaces are detected using a stereo camera, and the steering angle is controlled by a model predictive controller (MPC). For passable space detection, an UV-disparity map is calculated from the original disparity map. Information regarding passable spaces collected by the stereo camera is used in steering control. Backward driving requires the driver’s preemptive actions, which can be learned by experience because of the non-intuitive responses (the initial motion of the vehicle is opposite to the driver’s steering angle input). This occurs because a backward-driving vehicle is a non-minimum phase system. One of the most popular steering control algorithms is Stanley method, which is based on the feedback of lateral displacement error and heading angle error. The method is very intuitive and works well for forward driving, but it exhibits significant undershoot for backward driving cases. Furthermore, the method does not explicitly consider any constraints on control inputs and states. We designed a steering controller based on the MPC technique that requires future information but can handle constraints explicitly. Because we have near-future information from the stereo camera under limited passable spaces, MPC can be effectively implemented. We performed several simulations and experiments to show the performance and superiority of the suggested method over a simple feedback-based control algorithm.

Integrated Driver and Active Steering Control for Vision-Based Lane Keeping

An important feature of linear model predictive control (MPC) is the ability to provide offset-free control through integral action. Linear MPC can utilize a steady-state target optimizer (SSTO) in conjunction with a dynamic optimization in order to manage systems that are non-square, have integrating modes, or encounter infeasible setpoints. Integral action does not ensure that the feasible steady-state target is closest to the true optimum when the desired setpoint is infeasible. This paper describes the modifications necessary to linear state-space MPC algorithms in order to address this problem (assuming systems with no integrating modes). The solution employs features of the integrated system optimization and parameter estimation (ISOPE) algorithm: the SSTO cost is modified by a term that results in matching of the true plant and model conditions necessary for optimality. This work combines well with prior work which has determined the situations where the modification is actually necessary.

Multi-axle vehicles are commonly used for heavy-duty special operations, which easily leads to high driving torque demands when adopting distributed electric drive configurations. This study achieves the objective of reducing the driving torque of each in-wheel motor while controlling the stability of multi-axle vehicles. Taking a five-axle distributed drive test vehicle as the research object, a hierarchical control strategy integrating active all-wheel steering and direct yaw moment control is proposed. The upper layer is implemented based on model predictive control, with fuzzy control introduced to dynamically adjust control weights; the lower layer accomplishes the allocation of targets calculated by the upper layer through minimizing the objective function of tire load ratio. A linear parameter varying (LPV) tire model is introduced into the vehicle model to improve the calculation accuracy of tire lateral forces, and a neural network method is employed to solve the real-time performance issue of the model predictive control (MPC) controller. The proposed strategy is verified through a combination of simulation and real vehicle tests. High-speed condition simulations demonstrate that the AWS/DYC strategy significantly outperforms the ARS/DYC approach: compared to the active rear-wheel steering strategy, while the sideslip angle is reduced by 90.98%, the peak driving torque is reduced by 30.78%. Notably, tire slip angle analysis reveals that AWS/DYC maintains relatively uniform slip angle distribution across axles with a maximum of 4.7°, entirely within the linear working region, optimally balancing tire performance utilization with lateral stability while preserving safety margin, whereas ARS/DYC causes slip angles to exceed 11.9° at the rear axle, entering saturation. Low-speed real vehicle tests further confirm the engineering applicability of the strategy. The proposed method is of significant importance for the application of distributed drive configurations in the field of special vehicles.

Roller compaction is the major process of dry granulation which is attractive to heat or moisture-sensitive pharmaceutical products. Currently, the product quality of roller compaction is analyzed off-line in the quality control lab. In this work, we demonstrate how online process control can be applied on roller compaction using the simulator built in Part I of this paper. Different control strategies are discussed: multi-loop proportional–integral–derivative, linear model predictive control (MPC), and nonlinear MPC. The MPC strategy provides a systematic approach to design the multivariable control system. The simulation results show that the linear MPC can serve as a high-performance control strategy for roller compaction with the trade-off between the control performance and computational complexity. Such enhanced process control facilitates the FDA’s process analysis technology initiative.

<div class="section abstract"><div class="htmlview paragraph">Due to the recent advancements in autonomous vehicle technology, future vehicle velocity predictions are becoming more robust, which allows fuel economy (FE) improvements in hybrid electric vehicles (HEVs) through optimal energy management strategies (EMS). Velocity predictions generated between 5 and 30 s predictions could be implemented using model predictive control (MPC), but the performance of MPC must be well understood. Also, the vulnerability of predictive optimal EMS to velocity prediction accuracy should be addressed. Before an optimal EMS can be implemented, its overall performance must be evaluated and benchmarked against relevant velocity prediction metrics. A real-world highway drive cycle (DC) in the high-fidelity, controls-oriented 2017 Toyota Prius Prime model operating in charge-sustaining mode was utilized to observe FE realization. We propose three important metrics for comparison to no velocity prediction control: (1) perfect full DC prediction using dynamic programming (DP), (2) 10 s prediction horizon MPC, (3) 10 s constant velocity prediction. The very first optimal EMS requires the whole DC prediction in advance, whereas the rest of the two strategies only require limited horizon velocity prediction. These different velocity predictions are input into an optimal EMS derivation algorithm to derive optimal engine torque and engine speed. Our results show that the constant velocity prediction algorithm outperformed the baseline control strategy, but underperformed the MPC strategy. We also show that using a 10 s prediction window, MPC strategy provided FE improvement results very close to the full DC prediction case. So with the advancement in perception systems, MPC could be implementable in real vehicles. Also, constant velocity prediction results are good enough that optimization should be implemented in vehicle controllers with MPC type of framework. In future work, we seek to combine these models with velocity prediction models to demonstrate FE improvements on a physical vehicle.</div></div>

Most controllers concerning lateral stability and rollover prevention for autonomous vehicles are designed separately and used simultaneously. However, roll motion influences lateral stability in cornering maneuvers, especially at high speed. Typical rollover prevention control stabilizes the vehicle with differential braking to create an understeering condition. Although this method can prevent rollover, it can also lead to deviation from a reference path specified for an autonomous vehicle. This contribution proposes and implements a coupled longitudinal and lateral controller for path tracking via model predictive control (MPC) to simultaneously enforce constraints on control input, state output, lateral stability, and rollover prevention. To demonstrate the approach in simulation, an 8 degrees of freedom (DOF) vehicle model is used as the MPC prediction model, and a high-fidelity 14-DOF model as the plant. The MPC-based lateral control generates a sequence of optimal steering angles, while a PID speed controller adjusts the driving or braking torque. The lateral stability envelope is determined by the phase plane of yaw rate and lateral velocity, while the roll angle threshold is derived from the load transfer ratio (LTR) and tire vertical force under the condition of quasi-steady-state rollover. To track the desired trajectory as fast as possible, a minimum-time velocity profile is determined using a forward-backward integration approach, subject to tire friction limit constraints. We demonstrate the approach in simulation, by having the vehicle track an arbitrary course of continuously varying curvature thus highlighting the accuracy of the controller and its ability to satisfy lateral and roll stability requirements. The MATLAB® code for the 8-DOF and 14-DOF vehicle models, along with the implementation of the proposed controller are available as open source in the public domain.

SUMMARYA four wheel steering (4WS) control strategy is derived and evaluated using a nonlinear vehicle model along with a nonlinear tire model. The vehicle model used is a.three degree-of-freedom model. Yaw rate, lateral velocity and longitudinal velocity are considered with the roll effects included in the calculation of the normal loads for each of the four wheels. These normal forces are used in the tire model to calculate the tire forces and moments for each wheel. The results of simulation indicate the potential benefits gained by using 4WS. These benefits include stability and performance at high speeds and maneuverability at low speeds.

Modeling and model predictive control of the BioPower combined heat and power (CHP) plant

In this article, multi-input multi-output (MIMO) linear model predictive controller (LMPC) based on state space model and nonlinear model predictive controller based on neural network (NNMPC) are applied on a continuous stirred tank reactor (CSTR). The idea is to have a good control system that will be able to give optimal performance, reject high load disturbance, and track set point change. In order to study the performance of the two model predictive controllers, MIMO Proportional-Integral-Derivative controller (PID) strategy is used as benchmark. The LMPC, NNMPC, and PID strategies are used for controlling the residual concentration (CA) and reactor temperature (T). NNMPC control shows a superior performance over the LMPC and PID controllers by presenting a smaller overshoot and shorter settling time.

Autonomous vehicle control based on receding horizon method