Keywords

1 Introduction

In the past few years, the persistent expansion of global trade volume has resulted in a shortage of truck drivers in both domestic and foreign logistics and transportation industries. This shortage is evident in nations such as the United States, the United Kingdom, Germany, China, Japan, India, and Brazil [1]. The deficit of truck drivers in the United States has intensified during the recent years, despite the truck transportation industry's efforts to meet the growing demand. Consequently, the utilization of driverless truck technology has surfaced as a substantial remedy to tackle the shortage of truck drivers in numerous countries. As a fundamental and critical component of autonomous driving, the main aim of path tracking control is to make the actual route of the vehicle as close as possible to the pre-planned route, minimizing lateral and heading errors. As a result, improving the precision and firmness of the trajectory tracking regulator becomes imperative and urgent.

The development of unmanned driving path tracking control began early, and currently the main methods for tracking control include Proportional–Integral–Differential (PID) control [2], Sliding Mode control [3], Fuzzy logic control [4], Model Predictive control (MPC) [5], and LQR control [6]. Among them, LQR control is a feedback control method designed based on optimization principles [7, 8]. The primary principle is to establish a linearized model for the path tracking error of the vehicle system and solve the optimal feedback control parameters through quadratic optimization within the cyclic control cycle [9]. The LQR regulator is widely utilized in unmanned vehicles to accurately follow paths due to its exact performance, easy-to-follow algorithm, suitability for non-linear systems, and ability to take into account dynamic limitations. Currently, numerous scholars have conducted research on this topic and proposed various solutions. Hu et al. [10] introduced a fuzzy LQR with preview PID angle compensation that exhibits high tracking accuracy while maintaining stability across varying vehicle speeds. Xu et al. [11] developed a multi-point preview lateral controller based on the monorail dynamics model, implementing a LQR approach. They utilized the system's disturbance term as a state vector to construct an augmented LQR problem, resulting in enhanced path tracking accuracy. Wang et al. [12] presented an enhanced lateral path control strategy for vehicle navigation. The foundation of this strategy is constructed using an LQR algorithm while integrating a fuzzy control approach to actively adapt the weighting coefficients of LQR in real-time. This, in turn, enhances the precision of tracking, stability of steering, and effectiveness of computation. Although the aforementioned enhancements to the LQR have yielded favorable outcomes, there exists potential for additional advances in both control accuracy and stability.

This paper proposes the utilization of an improved genetic algorithm to optimize a LQR controller, aiming to enhance the tracking precision and stability of the controller. Firstly, a classic LQR controller was designed using the Two-Degree-of-Freedom vehicle dynamics lateral tracking error model. In order to eradicate the persistent deviation of the model's equilibrium state, feedforward control compensation was implemented based on this model. Secondly, this paper analyzes the effect of weight coefficients of the LQR controller on the vehicle's tracking capability. In order to achieve a balance between control stability and tracking accuracy, an enhanced genetic algorithm is applied for optimize the LQR weighting factors. Finally, the study concludes by conducting simulation experiments on both the pre-optimized and post-optimized LQR controllers. The results consistently demonstrate the superior performance of the GA-LQR controller devised in this research.

2 Vehicle Path Tracking Control Model

2.1 Vehicle Dynamic Model

The vehicle's lateral dynamics are influenced by a multitude of factors. The complexity of the vehicle model in controller design needs to be minimized for theoretical analysis, requiring certain assumptions to be made for driverless trucks:

  1. (1)

    Neglecting the influence of lateral and longitudinal aerodynamics;

  2. (2)

    Assuming that the vehicle solely moves in a two-dimensional plane without accounting for the effects of the suspension system;

  3. (3)

    By solely considering the lateral characteristics of the tire, it is understood that the lateral force acting on the tire exhibits a linear relationship with the lateral angle;

  4. (4)

    Neglecting the impact of the steering system and utilizing the front wheel angle as the direct input;

  5. (5)

    Neglecting the transfer of load between the front and rear axles.

Considering the aforementioned assumptions, driverless trucks exhibit only two degrees of freedom: motion in the horizontal direction along the y-axis and movement in the direction of orientation around the z-axis. Here is the corresponding linear model depicting the two degrees of freedom, as depicted in Fig. 1, where O-x-y-z is the coordinate system of the vehicle.

Fig. 1
A trajectory of the vehicle lateral dynamic model. It has a triangle, which is divided into two equal parts by the midline O O prime. The distances between the two parts are a and b. The coordinate system lies at point O, along with the movement of vehicle motion.

Vehicle dynamics model

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Assuming a uniform speed for the vehicle and considering a small front wheel angle \(\delta\) (less than 5°), expressed as \(\cos \delta \approx 1\), the vehicle dynamics equation can be represented as:

$$\left\{ \begin{aligned} & ma_{y} = F_{yf} + F_{yr} = C_{f} \alpha_{f} + C_{r} \alpha_{r} = C_{f} \left( {\frac{{\dot{\varphi }a + v_{y} }}{{v_{x} }} - \delta_{f} } \right) + C_{r} \left( {\frac{{v_{y} - \dot{\varphi }b}}{{v_{x} }}} \right) \\ & I_{z} \ddot{\varphi } = aF_{yf} - bF_{yr} = aC_{f} \alpha_{f} - bC_{r} \alpha_{r} \\ & \quad \;\; = aC_{f} \left( {\frac{{\dot{\varphi }a + v_{y} }}{{v_{x} }} - \delta_{f} } \right) - bC_{r} \left( {\frac{{v_{y} - \dot{\varphi }b}}{{v_{x} }}} \right) \hfill \\ \end{aligned} \right.$$
(1)

where the moment of inertia about the z-axis is denoted as \(I_{z}\); the vehicle mass is represented by \(m\); the vehicle’s heading rate is given by \(\dot{\varphi }\); the lateral forces of the front and rear wheels are indicated as \(F_{yf}\) and \(F_{yr}\); the values representing the distances from the vehicle's center of mass to the front and rear axles are identified as \(a\) and \(b\); the lateral stiffness of the front and rear wheels is represented as \(C_{f}\) and \(C_{r}\); the longitudinal speed of the vehicle is denoted by \(v_{x}\); and finally, the lateral velocity of the vehicle is given by \(v_{y}\).

Simplify the above equation and define \(v_{y} = \dot{y}\), thus obtaining the matrix form of the vehicle dynamics equation:

$$\left( {\begin{array}{*{20}l} {\ddot{y}} \hfill \\ \\ {\ddot{\varphi }} \hfill \\ \end{array} } \right) = \left( {\begin{array}{*{20}l} {\frac{{C_{f} + C_{r} }}{{mv_{x} }}} \hfill & {\frac{{aC_{f} - bC_{r} }}{{mv_{x} }} - v_{x} } \hfill \\ \\ {\frac{{aC_{f} - bC_{r} }}{{I_{z} v_{x} }}} \hfill & {\frac{{a^{2} C_{f} + b^{2} C_{r} }}{{I_{z} v_{x} }}} \hfill \\ \end{array} } \right)\left( {\begin{array}{*{20}l} {\dot{y}} \hfill \\ \\ {\dot{\varphi }} \hfill \\ \end{array} } \right) + \left( {\begin{array}{*{20}c} { - \frac{{C_{f} }}{m}} \\ \\ { - \frac{{aC_{f} }}{{I_{z} }}} \\ \end{array} } \right)\delta_{f}$$
(2)

2.2 Lateral Error Model for Vehicle Path Tracking

By applying coordinate transformation to the existing model depicting the vehicle's dynamics with two degrees of freedom, we can obtain a lateral error model specifically designed for path tracking, illustrated in Fig. 2.

Fig. 2
A diagram of the lateral error model. A 2 D bottom view of the vehicle is drawn in the x y coordinate plane and an arc for reference path projection is drawn below. The distance between the vehicle center and path projection is e d. A horizontal line is drawn from the center at an angle of theta.

Path tracking lateral error model

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Among them, the lateral error \(e_{d}\) is defined as the shortest distance between the vehicle centroid and the reference path projection point. The heading angle error \(e_{\varphi } = \varphi - \theta_{r}\) may be described as the difference between the true heading angle \(\theta\) of the vehicle and the specified reference heading angle \(\theta_{r}\). In real-life control applications, it becomes essential to develop a controller capable of eradicating these two errors instantaneously. This guarantees real-time accurate tracking of the intended path by the vehicle. The first derivatives of the lateral error \(\dot{e}_{d}\) and heading angle error \(\dot{e}_{\varphi }\) are computed by differentiating the lateral error \(e_{d}\) and heading angle error \(e_{\varphi }\) with respect to time.

$$\dot{e}_{d} = v_{x} e_{\varphi } + v_{y}$$
(3)
$$\dot{e}_{\varphi } = \dot{\varphi } - \dot{\varphi }_{r}$$
(4)

By combining Eq. (1), we can obtain the second derivatives of both the lateral error \(\ddot{e}_{d}\) and the heading angle error \(\ddot{e}_{\varphi }\).

$$\begin{aligned} \ddot{e}_{d} & = \left( {\frac{{C_{f} + C_{r} }}{{mv_{x} }}} \right)\dot{e}_{d} + \left( { - \frac{{C_{f} + C_{r} }}{m}} \right)e_{\varphi } + \left( {\frac{{aC_{f} - bC_{r} }}{{mv_{x} }}} \right)\dot{e}_{\varphi } \\ & \quad + \left( {\frac{{aC_{f} - bC_{r} }}{{mv_{x} }} - v_{x} } \right)\dot{\theta }_{r} + \left( { - \frac{{C_{f} }}{m}} \right)\delta_{f} \\ \end{aligned}$$
(5)
$$\begin{aligned} \ddot{e}_{\varphi }& = \left( {\frac{{aC_{f} - bC_{r} }}{{I_{z} v_{x} }}} \right)\dot{e}_{d} + \left( { - \frac{{aC_{f} - bC_{r} }}{{I_{z} }}} \right)e_{\varphi } + \left( {\frac{{a^{2} C_{f} + b^{2} C_{r} }}{{I_{z} v_{x} }}} \right)\dot{e}_{\varphi } \\ & \quad + \left( {\frac{{a^{2} C_{f} + b^{2} C_{r} }}{{I_{z} v_{x} }}} \right)\dot{\theta }_{r} + \left( { - \frac{{aC_{f} }}{{I_{z} }}} \right)\delta_{f} \\ \end{aligned}$$
(6)

By further modifying the above mentioned formula, the derivation of state space equations capturing lateral and heading errors in unmanned vehicle steering is achievable. The obtained equations are as follows:

$$\begin{aligned} \left( {\begin{array}{*{20}c} {\dot{e}_{d} } \\ {\ddot{e}_{d} } \\ {\dot{e}_{\varphi } } \\ {\ddot{e}_{\varphi } } \\ \end{array} } \right) & = \left( {\begin{array}{*{20}c} 0 & 1 & 0 & 0 \\ 0 & {\frac{{C_{f} + C_{r} }}{{mv_{x} }}} & { - \frac{{C_{f} + C_{r} }}{m}} & {\frac{{aC_{f} - bC_{r} }}{{mv_{x} }}} \\ 0 & 0 & 0 & 1 \\ 0 & {\frac{{aC_{f} - bC_{r} }}{{I_{z} v_{x} }}} & { - \frac{{aC_{f} - bC_{r} }}{{I_{z} }}} & {\frac{{a^{2} C_{f} + b^{2} C_{r} }}{{I_{z} v_{x} }}} \\ \end{array} } \right)\left( {\begin{array}{*{20}c} {e_{d} } \\ {\dot{e}_{d} } \\ {e_{p} } \\ {\dot{e}_{\varphi } } \\ \end{array} } \right) \\ & \quad + \left( {\begin{array}{*{20}c} 0 \\ { - \frac{{C_{f} }}{m}} \\ 0 \\ { - \frac{{aC_{f} }}{{I_{z} }}} \\ \end{array} } \right)\delta_{f} + \left( {\begin{array}{*{20}c} 0 \\ {\frac{{aC_{f} - bC_{r} }}{{mv_{x} }} - v_{x} } \\ 0 \\ {\frac{{a^{2} C_{f} + b^{2} C_{r} }}{{I_{z} v_{x} }}} \\ \end{array} } \right)\dot{\theta }_{r} \\ \end{aligned}$$
(7)

The state space equation for the tracking error of vehicle dynamics can be derived as follows:

$${\mathbf{\dot{X} = AX + BU + C}}\dot{\theta }_{r}$$
(8)

3 Design of Path Tracking Controller

The algorithm flowchart of the path tracking controller is depicted in Fig. 3. By combining the given path planning information with real-time vehicle status and pose information, the path tracking error can be calculated. To address the hysteresis in algorithm control, a prediction module is introduced following the real-time vehicle status information. This enables the algorithm to predict road conditions, thereby enhancing control accuracy.

Fig. 3
A flow diagram of path tracking controller. It is equipped with vehicle status and attitude information, prediction module, path planning information, path tracking error model, improving genetics algorithm optimization, L Q R controller, feedforward control module, and vehicle parameters.

Path tracking controller

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3.1 LQR Controller Design

The essence of the LQR controller is to seek the optimal control law for control variables and state variables while operating within linear constraints. Even when the following objective functions reach their minimum values.

$$\min {\text{J}} = \sum\limits_{k = 0}^{\infty } {\left( {{\mathbf{X}}_{{\mathbf{k}}}^{{\mathbf{T}}} {\mathbf{QX}}_{{\mathbf{k}}} + {\mathbf{U}}_{{\mathbf{k}}}^{{\mathbf{T}}} {\mathbf{RU}}_{{\mathbf{k}}} } \right)}$$
(9)
$${\mathbf{Q}} = {\text{diag}} \left[ {q_{1} ,q_{2} ,q_{3} ,q_{4} } \right]$$
(10)
$${\mathbf{R}} = [q_{5} ]$$
(11)

where the control variable of the system is denoted as \({\mathbf{U}}\); the system's state parameter is denoted as \({\mathbf{X}}\); the weighted coefficient \({\mathbf{Q}}\) representing the error represents the extent of significance attached to the corresponding control target; the control weighting matrix is denoted as \({\mathbf{R}}\).

The feedback control law of LQR controller is:

$${\mathbf{U(k)}} = - {\mathbf{KX(k)}}$$
(12)

In the formula: \({\mathbf{K}} = (R + {\mathbf{B}}^{{\mathbf{T}}} {\mathbf{PB}})^{ - 1} {\mathbf{B}}^{{\mathbf{T}}} {\mathbf{PA}}\), where the control gain coefficient is denoted as \({\mathbf{K}}\); \({\mathbf{P}}\) is a constant matrix, consisting of a positive definite solution to the Riccati equation as follows.

$${\mathbf{P}} = {\mathbf{Q}} + {\mathbf{A}}^{{\mathbf{T}}} {\mathbf{PA}} - {\mathbf{A}}^{{\mathbf{T}}} {\mathbf{PB}}({\mathbf{R}} + {\mathbf{B}}^{{\mathbf{T}}} {\mathbf{PB}})^{ - 1} {\mathbf{B}}^{{\mathbf{T}}} {\mathbf{PA}}$$
(13)

Substituting Eq. (12) into Eq. (9) yields:

$$\min J = \sum\limits_{k = 0}^{\infty } {{\mathbf{X}}^{T} (} {\mathbf{Q}} + {\mathbf{K}}^{{\mathbf{T}}} {\mathbf{RK}}){\mathbf{X}}$$
(14)

By introducing a comprehensive deviation of lateral distance deviation and heading angle deviation \(e_{rr}\) as the system state variables, and controlling the front wheel angle \(\delta_{f}\), the LQR controller can acquire the ideal control law for the front wheel angle:

$$\delta_{f} (k) = - {\mathbf{Ke}}_{{{\mathbf{rr}}}} {\mathbf{(k)}}$$
(15)

where \({\mathbf{K}} = [k_{1} ,k_{2} ,k_{3} ,k_{4} ]\) is the feedback gain matrix of the LQR controller; \({\mathbf{e}}_{{{\mathbf{rr}}}} = [e_{d} ,\dot{e}_{d} ,e_{\varphi } ,\dot{e}_{\varphi } ]^{T}\) is the comprehensive deviation amount.

3.2 Feedforward Control

Substituting Eq. (15) into Eq. (8) yields the following result:

$${\dot{\mathbf{X}}} = ({\mathbf{A - Bk}}){\mathbf{X + C}}\dot{\theta }_{r}$$
(16)

Currently, irrespective of the magnitude of \({\mathbf{k}}\), it is impermissible for \({\dot{\mathbf{X}}}\) to be zero. Solely employing LQR feedback control will induce an enduring stagnant error. As a consequence, to eradicate the effect of the \({\mathbf{C}}\dot{\theta }_{r}\) parameter, the feedforward control variable \(\delta_{ff}\) is implemented. The system's state variable, with the inclusion of feedforward control, can be expressed as:

$${\mathbf{U}} = {\mathbf{ - kX}} + \delta_{ff}$$
(17)

In the event that there is zero steady-state error, When \({\dot{\mathbf{X}}} = 0\), the equation for the state variable of the system is as follows:

$${\mathbf{X}} = - ({\mathbf{A}} - {\mathbf{Bk}})^{ - 1} {\mathbf{A}}({\mathbf{B}}\delta_{ff} + {\mathbf{C}}\dot{\theta }_{r} )$$
(18)

According to Eq. (18), it is inferred that attaining the optimal control effect requires determining a suitable value \(\delta_{ff}\) that ensures the system exhibits zero steady-state error. The system's equation for steady-state error is determined by utilizing Eq. (7) and is given by the following expression:

$$\left[ {\begin{array}{*{20}c} {e_{d} } \\ {\dot{e}_{d} } \\ {e_{\varphi } } \\ {\dot{e}_{\varphi } } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\frac{1}{{k_{1} }}\left\{ {\delta_{ff} - \frac{{\dot{\theta }_{r} }}{{v_{x} }}\left[ {a + b - bk_{3} - \frac{{mv_{x}^{2} }}{a + b}\left( {\frac{b}{{C_{f} }} + \frac{a}{{C_{r} }}k_{3} - \frac{a}{{C_{r} }}} \right)} \right]} \right.} \\ 0 \\ { - \frac{{\dot{\theta }_{r} }}{{v_{x} }}\left( {b + \frac{a}{a + b}\frac{{mv_{x}^{2} }}{{C_{r} }}} \right)} \\ 0 \\ \end{array} } \right]$$
(19)

From Eq. (19), it is evident that:

$$e_{\varphi } = - \frac{{\dot{\theta }_{r} }}{{v_{x} }}\left( {b + \frac{a}{a + b}\frac{{mv_{x}^{2} }}{{C_{r} }}} \right) = - \beta$$
(20)

In order to attain sideways deviation \(e_{d} = 0\), the feedforward control amount \(\delta_{ff}\) would be:

$$\delta_{ff} = \rho \left[ {a + b - bk_{3} - \frac{{mv_{x}^{2} }}{a + b}\left( {\frac{b}{{C_{f} }} + \frac{a}{{C_{r} }}k_{3} - \frac{a}{{C_{r} }}} \right)} \right]$$
(21)

where \(\rho = \frac{{\dot{\theta }_{r} }}{{v_{x} }}\) is the path curvature.

3.3 LQR Controller Optimized Based on GA

Genetic algorithm [13, 14] is a series of search algorithms inspired by natural evolution theory. The algorithm's exceptional convergence, efficient computational time, and robustness make it a popular choice for parameter optimization problems. And there are not many mathematical requirements for the optimization problem being solved. Owing to its characteristics, the search process does not rely on the intrinsic properties of the problem and can accommodate any type of objective function and constraint, regardless of whether they are linear or nonlinear, discrete or continuous in nature. In the design of LQR controllers, choosing appropriate Q and R values is crucial for achieving effective tracking with LQR controllers. The specific process of optimizing matrices Q and R using genetic algorithm is shown in Fig. 4.

Fig. 4
A flowchart for genetic optimization. It starts with encoding parameters, followed by genetic population, assign individual population values, calculate the optimal feedback gain matrix, and run L Q R controller model. If termination meet, calculate output. If not, cross and mutation operations.

Genetic algorithm optimization flowchart

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Firstly, encode the parameters, including the fundamental parameters of the vehicle along with the coefficients of the LQR state space equation. Secondly, a population is generated, and each individual population value is assigned sequentially to the randomly generated weight coefficients of LQR, within a feasible range. Reuse the generated weight coefficients Q and R to calculate the optimal feedback gain matrix K of LQR. Finally, the Simulink model is then executed to compute the pertinent parameters, and based on these parameters, the fitness function is evaluated to determine the fitness value of each particle. Once the termination condition is satisfied, the optimal value will be displayed.

Based on the optimization design method described above, the Table 1 displays the optimal values of the final LQR weight matrix.

Table 1 The optimal solution of LQR weight matrix
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4 Simulation Verification

In order to confirm the efficiency of the LQR controller, optimized using the proposed improved genetic algorithm, a joint simulation experiment was conducted using TruckSim and Matlab/Simulink. The primary parameters of the vehicle are shown in Table 2.

Table 2 Main parameters of the vehicle
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In this article, the double lane change scenario is employed as the benchmark path, depicting the standard driving conduct of cars navigating through barriers. The automobile is put to the test on a road with a friction coefficient of 0.85, experiencing two different velocities: 30 and 60 km/h. Simulations are conducted for the LQR and GA-optimized LQR controllers at both speeds. Figure 5 shows the tracking effect of vehicle lateral displacement. The diagram demonstrates that the car exhibits satisfactory performance when following the designated route at both velocities. Nevertheless, the LQR controller designed in this study, using GA-optimized weight coefficients, exhibits superior tracking performance and enhanced stability.

Fig. 5
A multiline graph of lateral displacement versus longitudinal displacement. 5 curves for reference path, L Q R, and G A L Q R begin at (0, 0), increase gradually, reach the peak between 0 and 4, again follow a decreasing trend until (100, negative 1.7), and remain stable up to (150, negative 1.7).

Lateral displacement tracking effect

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In Fig. 6, the tracking accuracy of the LQR controller and the GA-LQR controller in managing lateral errors is showcased in the context of double line shifting situations, precisely at velocities of 30 and 60 km/h. According to the results findings, the LQR controller has the ability to consistently restrict the maximum tracking discrepancy to 0.2848 m at different velocities. The lateral error of the GA-LQR controller designed in this article is considerably lower compared to that of the LQR controller. At a velocity of 30 km/h, the GA-LQR controller can effectively limit the maximum lateral error to 0.0704. This value, however, is approximately 49.7% greater than that of traditional LQR controllers. At a velocity of 60 km per hour, the GA-LQR controller attains a peak lateral deviation of 0.1429. This represents an enhancement of approximately 49.8% compared to the effectiveness of the traditional LQR controller.

Fig. 6
A multiline graph plots lateral error versus longitudinal displacement. 4 lines for L Q R and G A L Q R begin at (0, 0), follow an increasing and decreasing trend to reach positive and negative peaks between negative 0.3 and 0.2, and end at (150, 0). Values are estimated.

Lateral error tracking effect

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This implies that the LQR controller designed in this article can more efficiently minimize errors and enhance the precision of vehicle tracking during path tracking.

Figure 7 illustrates the impact of dual line shifting conditions on the yaw error tracking for both the LQR and the GA-LQR controller at speeds of 30 and 60 km/h. The simulation results demonstrate that the yaw error remains within 0.1145 rad across various vehicle speeds, and the observed variation is insignificant. These findings indicate the vehicle's tracking process maintains a relatively stable performance. The GA-LQR controller successfully limits the maximum yaw error to 0.0984 at a speed of 30 km/h, and 0.1114 at a speed of 60 km/h. These values demonstrate an improvement over the performance of traditional LQR controllers.

Fig. 7
A multiline graph plots yaw angle error versus longitudinal displacement. 4 lines for L Q R and G A L Q R begin at (0, 0), follow an increasing and decreasing trend to reach 1 positive and 2 negative peaks between negative 0.01 and 0.13, and end at (150, 0). Values are estimated.

Yaw error tracking effect

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Figure 8 depicts the performance of the front wheel angle tracking for both the LQR controller and the GA-optimized LQR controller under dual lane shifting conditions, at speeds of 30 and 60 km/h. The simulation results reveal a gradual increase in the front wheel angle as the vehicle speed rises, without any step changes. And the front wheel angle is effectively controlled within a range of −10° to 10° at various vehicle speeds, which strongly suggests a stable tracking process. Overall, the GA-LQR controller demonstrates satisfactory levels of tracking accuracy and stability.

Fig. 8
A multiline graph plots front wheel angle versus longitudinal displacement. 4 lines for L Q R and G A L Q R begin at (0, 0), follow an increasing and decreasing trend to reach 2 positive and 1 negative peaks between negative 8 and 6, and end at (150, 0). Values are estimated.

Front wheel angle tracking effect

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5 Conclusions

This study addresses the issue of low tracking accuracy and poor stability in unmanned trucks during path tracking under traditional LQR controllers. To combat these problems, the inclusion of feedforward control methods is proposed to compensate for the front wheel angle and mitigate steady-state errors resulting from the simplification of the vehicle dynamics model. The weight coefficients are optimized and adjusted using a genetic algorithm to achieve higher tracking accuracy while simultaneously addressing the vehicle's driving stability. The outcomes of the simulation demonstrate that the GA-LQR controller, developed in this article, exhibits commendable tracking accuracy and stability when subjected to the double lane reference path. This research achievement offers innovative insights for designing and optimizing path tracking controllers for driverless trucks. In future research, it is necessary to conduct further validation of the proposed control strategy using an actual vehicle.