1. Introduction

Nowadays, the off-road autonomous ground vehicle has been widely applied in various industries, such as military [1, 2] and space applications [3, 4]. Furthermore, this kind of vehicle also received focused attention in mining [5], agriculture and forestry sectors [6].

In order to improve the stability and safety of off-road autonomous vehicles, the path planning of these vehicles should be considered as the priority of current research. The path planning of autonomous vehicle includes two stages: the trajectory planning in the upper-level and trajectory tracking control in the lower-level. The upper-level trajectory planner considers the surrounding environment information according to the various sensors and selects the best desired trajectory, while the lower-level trajectory tracking controller controls the steering and driving actuators to achieve the desired trajectory.

In the current literature, the path planning of autonomous vehicle has attracted focused attention. Particularly, the spatial-based path planning methods are widely applied, but the time parameter is not considered [7]. For example, for the direct tracking method, the steering system is controlled to follow the pre-planned spatialbased desired path exactly at every time step [8, 9]. In the potential field method proposed in [10], the desired path is planned within a potential field with a tracking error tolerance along the road centreline. In this way, the autonomous vehicle does not need to strictly follow the road centreline, and smaller steering control effort is required compared with the direct tracking method. The spatiotemporal-based trajectory planning concept, on the other hand, considers the kinematic constraints and generates time-parameterised trajectories. Several typical spatiotemporal-based trajectory planning methods, such as the methods proposed in [11–13], aim to find the best suitable time-parameterised trajectory connecting the initial vehicle states with exactly defined goal states. These methods rely on discrete geometric structure, such as the rapidly exploring random trees (RRT) [14] and state lattice [13]. However, the generation of candidate trajectories requires large computational work. When the surrounding environment is unconstructed and complex, these methods may not be computational efficient. In [15, 16], the proposed trajectory planning strategies utilise 'deliberated multiple final states' method. This method deliberately generates multiple alternative final states which can respond to traffic changes very fast. In study [17], based on the concept of 'deliberated multiple final states', the combined trajectory planning of the longitudinal and lateral motion of autonomous vehicle are proposed, and the 'deliberated multiple final states' are described as the offset error values from the target reference final states. The most suitable trajectory which satisfies the initial and ending states with certain terminal time can be selected from candidate trajectory set, and the kinematic constraints are satisfied.

2. Vehicle dynamics modelling

DOI: http://dx.doi.org/10.5772/intechopen.85384

Path Planning for Autonomous Vehicle in Off-Road Scenario

model is presented in Figure 1.

Izr\_ <sup>¼</sup> lf Fyfl <sup>þ</sup> Fyfr � lr Fyrl <sup>þ</sup> Fyrr <sup>þ</sup>

The vector diagram of 4WIS-4WID vehicle dynamics model.

Longitudinal motion:

Lateral motion:

Yaw motion:

Roll motion:

Pitch motion:

Figure 1.

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In this section, a 4WIS-4WID vehicle model is utilised first to describe the dynamic motion of an off-road autonomous vehicle [18]. The information of road slope and bank angle is included in the vehicle longitudinal and lateral dynamics equations. Furthermore, vehicle roll dynamics equation and pitch dynamics equation are included in the dynamics model to better present the effect of bank angle and road slope on the vehicle dynamics. The vector diagram of vehicle dynamics

mv\_<sup>x</sup> <sup>¼</sup> mvyr <sup>þ</sup> Fxfl <sup>þ</sup> Fxfr <sup>þ</sup> Fxrl <sup>þ</sup> Fxrr <sup>þ</sup> mg sin <sup>θ</sup><sup>s</sup> (1)

mv\_ <sup>y</sup> ¼ �mvxr <sup>þ</sup> Fyfl <sup>þ</sup> Fyfr <sup>þ</sup> Fyrl <sup>þ</sup> Fyrr <sup>þ</sup> mg sin <sup>θ</sup><sup>b</sup> (2)

Fxfl � Fxfr <sup>þ</sup>

Ixϕ€ ¼ �merv\_ <sup>y</sup> � mervxr <sup>þ</sup> mger sin <sup>ϕ</sup> � <sup>K</sup>ϕϕ � <sup>C</sup>ϕϕ\_ (4)

Iyφ€ ¼ �mepv\_<sup>x</sup> � mepvyr þ mgep sin φ � Kφφ � Cφφ\_ (5)

br

<sup>2</sup> ð Þ Fxrl � Fxrr (3)

bf 2

The equations of motion of this model are described as follows:

Motivated by the widely application of the off-road autonomous vehicle in various industries and based on above research studies on path planning, this chapter proposed a two-level real-time dynamically integrated spatiotemporalbased trajectory planning and control method by considering the off-road scenario. The major innovative part of this chapter is the development of the spatiotemporalbased trajectory planning method and considering the off-road topography information in trajectory planning. In the upper-level trajectory planner, a number of candidate spatiotemporal-based trajectories with various terminal times and state-ending conditions are generated. These candidate trajectories also include the road topography information—the bank angle and road slope. The best suitable trajectory can be selected from these candidate trajectories based on the optimised cost function which is used to minimise the tracking error, terminal time spent and the effect of road topography on the vehicle. After that, trajectory tracking controller in the lower-level is proposed based on the sliding-mode technique and vehicle dynamics model in order to track the selected best suitable trajectory. In addition, the vehicle dynamics model of this chapter is based on a four-wheel-independent-steering (4WIS) and four-wheel-independent-driving (4WID) electric vehicle. Due to a large number of available control actuators, the 4WIS-4WID electric vehicle shows advantages over the traditional vehicle. This chapter also discusses the advantage of 4WIS-4WID electric vehicle on trajectory planning and trajectory tracking control over traditional two-wheel vehicle.

In this chapter, Section 2 first discusses the vehicle dynamics model based on 4WIS-4WID electric vehicle. Then Section 3 describes the upper-level trajectory planner, and Section 4 shows the lower-level trajectory tracking control. After that, Section 5 presents the simulation results to verify the proposed trajectory planning and control method. Finally, the conclusion is given in Section 6.
