Automated Guided Method for Roadheader fuselage

： Autonomous Navigation of roadheader is a hot topic in recent research. The subject of this paper mainly focuses on the motion control of the roadheader fuselage. Because of the particularity of its work content and operational environment, the motion control is different from that of the traditional differential-drived vehicle. This paper introduces a method to detect the position and posture of roadheader fuselage in harsh underground environment, which lays a foundation for motion control. In addition, a path planning method based on prediction model is proposed to reduce the control effort while ensuring enough control accuracy. Then the kinematics characteristics of roadheader fuselage with and without the path planning process are analyzed and compared by simulation. The result shows that the proposed method makes the movement of the roadheader smoother and more suitable for the tunneling process compared with the conventional method.


Introduction
Automatic tunneling is of great significance to improve the excavation efficiency and reduce the labor of workers (Wang et al. 2019;. As the roadheader is the core equipment for tunneling, the automatic control of roadheader is the premise of automatic tunneling (Wang et al. 2017). A roadheader can be regarded as a tracked vehicle so called fuselage on which a cutting mechanism loaded. Thus, the automatic control of roadheader includes two issues, the automated guided control of the tracked vehicle (i.e. the fuselage) and movement control of the cutting mechanism joint. Our work mainly focuses on the former.
For the motion control of roadheader, the fuselage pose should be firstly detected because it provides necessary reference parameters in the control process.
However, it is not an easy task due to the poor GPS signals, strong vibration, high dust and other adverse factors in the tunnel. The traditional methods, including inertial navigation (Tian et al. 2019), iGPS , radar scanning (Zhao. 2011), UWB based local positioning ) method cannot work well in the harsh underground environment. A laser guided method (Li. 2012) is used for the pose detection of the fuselage in this paper. This method originates from the present wide-used device called laser orientation instrument. The improvement is that the transmitter is replaced by a device which can generate a laser plane as a measurement reference. At the same time, photoelectric sensors are mounted on the fuselage to receive the laser information. As the fuselage deviate from the expected pose, the sensed data of photoelectric sensors vary with the change of the fuselage pose. Then the pose can be calculated based on the sensed data.
Then we step to the motion control issue. At present, the algorithms in common usage include PID feedback control, pure pursuit tracking algorithm, predictive following algorithm and Stanley method. PID control is a simple and effective method widely used in industry. However, it is difficult to apply to multivariable systems or time-varying systems (Moshayedi et al. 2019). The implementation of pure pursuit tracking algorithm is described in reference (Coulter. 1992), including the geometric derivation of the method, and the influence of some key parameters on the performance of the algorithm. The application of pure pursuit tracking algorithm in reactive tracking path is studied in reference (Morales et al. 2009) and experiments are carried out with tracked mobile robot in indoor environment. It is proved that the controller has reliable and smooth path tracking characteristics.
Preview tracking algorithm is to detect forward in the process of driving, so as to imitate the real driving of the driver (Hu et al. 2019). The vehicle can detect the change of the forward path ahead of time and use it as an optimization goal to adjust the angle ahead of schedule. The algorithm can reduce the fluctuation of lateral displacement and heading angle, and make the vehicle move more smoothly. The Stanley method (Skakauskas et al. 2021) used by Stanford University unmanned vehicle is a nonlinear feedback function based on cross track error, and can realize the exponential convergence of the cross track error to zero. This method is based on the front axle control algorithm of wheeled vehicle platform, which is not suitable for differential driven tracked vehicle.
For the motion control of the roadheader fuselage, additional factors should take account into, including the width of the tunnel, the operation range of cutting mechanism, and even the process flow of tunneling excavation. Compared with common automated guided vehicle issue, the motion control of roadheader has the following remarkable features. Second, the control strategy contains two steps, path planning and trajectory tracking. Formerly, it is thought that the path has been determined, that is, the middle line of tunnel (Zhang et al. 2021). However, as mention above, for a point-to-point control problem, the first thing we should do is to plan the path between the start point and the goal point. The remainder of this paper is organized as follows: Section 2 introduces the overall scheme of the control system. Section 3 introduces the pose detection method. Section 4 introduces the motion control method. Section 5 introduces the simulation experiments. Section 6 summarizes the whole paper and draws a conclusion.

Overall Design
The system consists of two subsystems, pose detection system and motion control system. The former is used to detect the pose and position of the roadheader relative to the tunnel, and the latter is used to correct the movement of the roadheader fuselage to make sure the position and attitude are as expected at the working position. Fig. 1 shows the overall design.  )cos sin arctan ( )sin sin cos sin cos   In any case, the path which needs to be tracked will not be the tunnel middle line. The path planning in different cases is described mathematically as follows.
(1) eT<e0 The predicted position error eT is less than the initial deviation e0, so no control input is required in ideal situation. The roadheader needs walking along the initial direction as shown in (2) eT≥e0 If the predicted position eT is larger than the initial deviation e0, the path should be re-planned. In Fig. 5, the dotted line denotes the planned path, a smooth curve joining starting point P and goal point T.
where e0 represents the initial position error of the roadheader at the starting point, α0 represents the heading angle of the roadheader at the starting point.
These two terms can be measured by pose detection system. l is the forward distance of each excavation cycle, which is determined by the requirement of tunneling process.
In addition, there is an extreme case needs to be taken into account. If the initial position error is at extreme high level, it is considered to correct the deviation of the roadheader in multiple excavation cycles. Fig. 6 shows the principle of this strategy. Note that the ultimate goal of motion control is to ensure the accuracy of tunnel direction and the tunnel section and make both sides of the tunnel as smooth as possible.
This means that the position difference between the starting point and the goal point in a driving cycle should not be too large. Therefore, when the initial position error is too large, it may be necessary to gradually correct the lateral displacement deviation in multiple driving cycles.

Trajectory tracking
Firstly, the kinematics model of the roadheader is built as shown in Fig. 8.
where,  Fig. 9 illustrates the control model.

Tracking of straight line
For the case mentioned in Fig. 4, the planned path is a straight line with equation (3)    The findings are as follows: (1) When the target path is the planned path, the tracking trajectory coincides with the planned path, the velocity of roadheader fuselage is constant, the angular velocity of roadheader fuselage and accelerations of both driving wheels are always zero.
(2) When the target path is the tunnel middle line, the velocity of the fuselage has a slight fluctuation at initial stage, the angular velocity at initial point reaches 0.15 rad/s and gradually decreases to zero. The worst part is that the maximum accelerations of both driving wheels are about 0.8 rad/s 2 at the starting point, which are far larger than that of the planned path.
It is concluded that in this case, the proposed motion method performs well than that without path planning in terms of motion smoothness, although the position error of the proposed method is slightly larger than that of the conventional method.

Tracking of polynomial curve
For the case mentioned in Fig. 5, the planned path is a cubic polynomial with equation (4) rather the x-coordinate which represents the middle line of the tunnel. The setting is as follows: the initial position error is assumed to be e0=0.04 m, initial heading angle is α0=2°, the remaining initial conditions are the same as previously described. Fig. 15-19 show the kinematic characteristics of the roadheader of different target paths.  The findings are as follows: (1) When the target path is the planned path, the tracking trajectory seems smoother than which tracks the tunnel middle line. the velocity of roadheader fuselage barely changes, the angular velocity of roadheader fuselage changes linearly, the angular velocity of roadheader fuselage and accelerations of both driving wheels has little change at 0.027 rad/s 2 .
(2) When the target path is the tunnel middle line, the velocity of the fuselage has a slight fluctuation at initial stage as well, the angular velocity at initial point reaches 0.2 rad/s and gradually decreases to zero.
Similarly, the accelerations of both driving wheels at the starting point are high, about 44 times to that with path planning.
To estimate the amount of control input, a performance index called control effort is defined. The control effort is scored as the absolute value of the curvature increments for all the control intervals (Jes u´s M 2009). Table 1 show the comparison of the control effort with and without path planning. It is easy to find that the control effort is smaller when the path planning link is added.

Conclusion
The motion control method of roadheader fuselage is proposed in this paper, which plans the path for tracking based on the predicted position of goal point.
Then a trajectory tracking method based on Lyapunov stability theory is used to track the planned path. To verify the performance of the proposed motion control method, simulation experiments were carried out.
Experiment results shows that on different initial conditions, the proposed control method is with low control effort and high stability. It is especially adapted for the motion control of roadheader fuselage with huge mass. Figure 1 Overall design of motion control system Principle of motion control method based on deviation prediction model Figure 4 Path planning when eT<e0 Figure 5 Path planning when when eT≥e0 Figure 6 The control strategy in multiple excavation cycles