Optimal H∞ Control for Lateral Dynamics of Autonomous Vehicles

Abstract

This paper presents the design and validation of a model-based H∞ vehicle lateral controller for autonomous vehicles in a simulation environment. The controller was designed so that the position and orientation tracking errors are minimized and so that the vehicle is able to follow a trajectory computed in real-time by exploiting proper video-processing and lane-detection algorithms. From a computational point of view, the controller is obtained by solving a suitable LMI optimization problem and ensures that the closed-loop system is robust with respect to variations in the vehicle’s longitudinal speed. In order to show the effectiveness of the proposed control strategy, simulations have been undertaken by taking advantage of a co-simulation environment jointly developed in Matlab/Simulink © and Carsim 8 ©. The simulation activity shows that the proposed control approach allows for good control performance to be achieved.

Combined longitudinal and lateral dynamics regulation of autonomous vehicles via induced ℒ2$$ {\mathcal{L}}_2 $$‐gain linear parameter varying control strategies based on parameter‐dependent Lyapunov functions

“… Sensors & Algorithm –By taking advantage of the ADT functionalities, the vehicle is equipped with sensors and algorithms useful for simulating autonomous vehicle behaviors. In particular, a virtual camera has been used in the simulations to detect the lane's strips, various algorithms of the toolbox have been used to compute the current curvature radius ($$$ R $$$) on the basis of the detected lane strips 41 and a virtual radar was used to measure the relative distance and the relative velocity from the preceding car. Feed‐Forward Controller –This module implements the feed‐forward controller described in Section 5.3. Feedback Controller –This module implements the combined longitudinal and lateral $$$ {\mathcal{L}}_2 $$$ optimal gain‐scheduling state‐feedback controller described in Section 5.2. Lower Level Controller –This module is in charge to convert the desired acceleration ($$$ {a}_{des} $$$), determined by the longitudinal controller, into torque at the wheels ($$$ {T}_{11} $$$ and $$$ {T}_{12} $$$). In particular, by considering the equations describing the rolling tires (36) and the longitudinal vehicle dynamic $$$$ m{a}_x={F}_{x11}+{F}_{x12}+{F}_{x21}+{F}_{x22} $$$$ after some mathematical operation, it is possible to determine …”

“…• the radius of curvature can be computed as the inverse of the absolute value of the curvature k at a point: R c = 1∕|k|, 41 it can be defined as 82…”

“…Sensors & Algorithm-By taking advantage of the ADT functionalities, the vehicle is equipped with sensors and algorithms useful for simulating autonomous vehicle behaviors. In particular, a virtual camera has been used in the simulations to detect the lane's strips, various algorithms of the toolbox have been used to compute the current curvature radius (R) on the basis of the detected lane strips 41 and a virtual radar was used to measure the relative distance and the relative velocity from the preceding car. 3.…”

“…$$ where $$$ {\dot{\psi}}_{des} $$$ is the rate of change in the reference orientation of the vehicle. Moreover, by considering that the vehicle rides at longitudinal velocity $$$ {v}_x $$$ on a curved road of radius $$$ {R}_c $$$, $$$ R $$$ is sufficiently large so that the small angle assumption holds true, the radius of curvature can be computed as the inverse of the absolute value of the curvature $$$ k $$$ at a point: $$$ {R}_c=1/\mid k\mid $$$, 41 it can be defined as 82 $$$$ {\dot{\psi}}_{des}=\frac{v_x}{R_c}. $$$$ Finally, by integrating the latter expressions, it is possible to compute the reference yaw angle (desired orientation) $$$ {\psi}_{des} $$$.…”

“…Linear parameter varying (LPV) control techniques have also gained interest and have been successfully applied in the context of autonomous vehicles: these are a class of model‐based control approaches that allow one to globally approximate the dynamics of a nonlinear system subject to transitions among different working points and conditions with a single model, well suited for the control synthesis 32–36 . Successful applications of LPV control strategies applied to path following control and lateral tracking control problems for autonomous vehicles are reported in References 37–41, whilst a comprehensive review of polytopic LPV approaches for IAVs can be found in Reference 42. Finally, recent advances in the design of path control strategies for autonomous vehicles have been presented in Amer et al 43 and Yao et al 44 …”