Adaptive Time Horizon MPC Path Tracking Control Method for Mowing Robot

doi:10.12133/j.smartag.SA202401010

Abstract

Abstract:

[Objective] The traditional predictive control approach usually employs a fixed time horizon and often overlooks the impact of changes in curvature and road bends. This oversight leads to subpar tracking performance and inadequate adaptability of robots for navigating curves and paths. Although extending the time horizon of the standard fixed time horizon model predictive control (MPC) can improve curve path tracking accuracy, it comes with high computational costs, making it impractical in situations with restricted computing resources. Consequently, an adaptive time horizon MPC controller was developed to meet the requirements of complex tasks such as autonomous mowing. [Methods] Initially, it was crucial to establish a kinematic model for the mowing robot, which required employing Taylor linearization and Euler method discretization techniques to ensure accurate path tracking. The prediction equation for the error model was derived after conducting a comprehensive analysis of the robot's kinematics model employed in mowing. Second, the size of the previewing area was determined by utilizing the speed data and reference path information gathered from the mowing robot. The region located a certain distance ahead of the robot's current position, was identified to as the preview region, enabling a more accurate prediction of the robot's future traveling conditions. Calculations for both the curve factor and curve change factor were carried out within this preview region. The curvature factor represented the initial curvature of the path, while the curvature change factor indicated the extent of curvature variation in this region. These two variables were then fed into a fuzzy controller, which adjusted the prediction time horizon of the MPC. The integration enabled the mowing robot to promptly adjust to changes in the path's curvature, thereby improving its accuracy in tracking the desired trajectory. Additionally, a novel technique for triggering MPC execution was developed to reduce computational load and improve real-time performance. This approach ensured that MPC activation occurred only when needed, rather than at every time step, resulting in reduced computational expenses especially during periods of smooth robot motion where unnecessary computation overhead could be minimized. By meeting kinematic and dynamic constraints, the optimization algorithm successfully identified an optimal control sequence, ultimately enhancing stability and reliability of the control system. Consequently, these set of control algorithms facilitated precise path tracking while considering both kinematic and dynamic limitations in complex environments. [Results and Discussion] The adaptive time-horizon MPC controller effectively limited the maximum absolute heading error and maximum absolute lateral error to within 0.13 rad and 11 cm, respectively, surpassing the performance of the MPC controller in the control group. Moreover, compared to both the first and fourth groups, the adaptive time-horizon MPC controller achieved a remarkable reduction of 75.39% and 57.83% in mean values for lateral error and heading error, respectively (38.38% and 31.84%, respectively). Additionally, it demonstrated superior tracking accuracy as evidenced by its significantly smaller absolute standard deviation of lateral error (0.025 6 m) and course error (0.025 5 rad), outperforming all four fixed time-horizon MPC controllers tested in the study. Furthermore, this adaptive approach ensured precise tracking and control capabilities for the mowing robot while maintaining a remarkably low average solution time of only 0.004 9 s, notably faster than that observed with other control data sets-reducing computational load by approximately 10.9 ms compared to maximum time-horizon MPC. [Conclusions] The experimental results demonstrated that the adaptive time-horizon MPC tracking approach effectively addressed the trade-off between control accuracy and computational complexity encountered in fixed time-horizon MPC. By dynamically adjusting the time horizon length the and performing MPC calculations based on individual events, this approach can more effectively handle scenarios with restricted computational resources, ensuring superior control precision and stability. Furthermore, it achieves a balance between control precision and real-time performance in curve route tracking for mowing robots, offering a more practical and reliable solution for their practical application.

Key words: mowing robot, model predictive control, path tracking, fuzzy control, event-triggered mechanism

HE Qing, JI Jie, FENG Wei, ZHAO Lijun, ZHANG Bohan. Adaptive Time Horizon MPC Path Tracking Control Method for Mowing Robot[J]. Smart Agriculture, 2024, 6(3): 82-93.

Figures/Tables 23

Fig. 1

Fig. 2

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Table 1

Quantization factor of fuzzy input and output

变量	曲度因子 $f s$	曲度变化因子 $f s c$	预测时域 $N p$
基本论域	［0，1］	［0，1］	［15，36］
模糊论域	［0，1］	［0，1］	［0，1］
量化因子	1	1	1/21

Table 1

Table 2

Fuzzy rules for the MPC prediction horizon

$f s c$	$f s$
$f s c$	VL	L	M	H	VH
VL	VS	S	ML	L	VL
L	S	MS	ML	L	VL
M	MS	M	L	VL	VL
H	M	ML	VL	VL	VL
VH	ML	L	VL	VL	VL

Table 2

Fig. 9

Fig. 10

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Fig. 13

Table 3

Experimental parameters for adaptive time horizon MPC control of mowing robots

参数	数值
采样周期 $T$ /s	0.1
权重矩阵 $Q$	$100 I 3 N p$
权重矩阵 $R$	$I 2 N c$
松弛因子最大值 $ε m a x$	1
松弛因子权重系数 $ρ$	10
最大线速度 $v m a x$ /（m/s）	2
最小线速度 $v m i n$ /（m/s）	0.3
预瞄区域最小长度 $l v m i n$ /m	1.5
预瞄区域最大长度 $l v m a x$ /m	5
时域权重系数 $λ$	0.5
曲度变化增益系数 $γ$	0.8
横向误差阈值 $t h r e d$	0.02
航向误差阈值 $t h r e p h i$	0.02
曲度因子阈值 $t h r f s$	0.5
曲度变化因子阈值 $t h r f s c$	0.5

Table 3

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Table 4

MPC Control performance of fixed time horizon and adaptive time horizon in mowing robot experiment

MPC预测时域	第1组 $N p = 14$	第2组 $N p = 22$	第3组 $N p = 27$	第4组 $N p = 32$	自适应时域
MPC控制时域	$N c = 5$	$N c = 14$	$N c = 21$	$N c = 27$	自适应时域
$E d m a x$ /m	0.257 2	0.197 8	0.145 9	0.125 4	0.104 5
$E d m$ /m	0.071 1	0.046 5	0.032 7	0.028 4	0.017 5
$E d s$ /m	0.082 8	0.060 6	0.041 9	0.033 0	0.025 6
$E θ m a x$ /rad	0.236 5	0.174 8	0.152 8	0.140 3	0.128 3
$E θ m$ /rad	0.039 6	0.033 7	0.027 8	0.024 5	0.016 7
$E θ s$ /rad	0.041 0	0.037 5	0.035 0	0.029 4	0.025 5
$t m$ /s	0.006 7	0.010 3	0.012 6	0.015 8	0.004 9

Table 4

Fig. 18

Fig. 19

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