Control Barrier Functions-based Trajectory Planning for Unmanned Ground Vehicles in Unknown Environment

doi:10.12382/bgxb.2023.0882

Abstract

Abstract:

The ummaned ground vehicles (UGVs)have become a practical alternative to humans in performing tasks in high-risk, high-pollution are as due to their strong adaptability and low cost. As a key technology of mission system for UGV, the trajectory planning is to develop a motion trajectory that meets the constraints based on mission objectives. However, the current navigation controllers rely primarily on the pre-acquired maps and prior knowledge, and are lacking in the ability to cope with unknown environments, making UGVs unable to adapt to complex and changing task environments. Therefore, a trajectory planning method based on the control barrier function (CBF) is proposed to solve the autonomous obstacle avoidance and trajectory planning problems of UGVs in unknown environments. The front end of the method utilizes a laser radar to perceive environmental depth information, while its back end uses a least squares support vector machine (LSSVM) to fit the boundary of obstacles to estimate the control barrier function and compensate for negative sample misclassification. Finally, the safety control instruction is obtained by solving a quadratic programming problem. A segmented detection and elimination method is proposed to address the issue of deadlocks that may occur when UGVs come to a standstill. The results of numerical simulation experiments and semi-physical experiments show that the proposed method has good obstacle avoidance and trajectory planning capabilities in various obstacle environments, and is superior to traditional control methods in terms of path length and other aspects.

Key words: unmanned ground vehicle, trajectory planning, control barrier function, least squares support vector machine

CLC Number:

TP273.1

FANG Qiuyu, ZHANG Yunlin, MA Zhuangzhuang, SHAO Jinliang. Control Barrier Functions-based Trajectory Planning for Unmanned Ground Vehicles in Unknown Environment[J]. Acta Armamentarii, 2023, 44(S2): 90-102.

Figures/Tables 11

Fig.1 Flow diagramof algorithm

算法1 基于在线CBF估计的控制算法
1.初始化数据集T和历史数据集T_h 2.REPEAT 3. 获取当前位置坐标x和激光雷达数据z_t 4. IF ‖x-x_g‖>η 5. 依概率式(11)重组数据集 $T ˜$ 6. 数据预处理及模型训练 7. 估计安全边界,基于式(9)、式(11)生成CBF 8. 求解安全控制器式(13) 9. 更新控制量u←u^*(x) 10.END IF 11.UNTIL轨迹规划任务完成

算法1 基于在线CBF估计的控制算法
1.初始化数据集T和历史数据集T_h 2.REPEAT 3. 获取当前位置坐标x和激光雷达数据z_t 4. IF ‖x-x_g‖>η 5. 依概率式(11)重组数据集 $T ˜$ 6. 数据预处理及模型训练 7. 估计安全边界,基于式(9)、式(11)生成CBF 8. 求解安全控制器式(13) 9. 更新控制量u←u^*(x) 10.END IF 11.UNTIL轨迹规划任务完成

算法2 死锁检测与消除算法

1.初始化样本集X和死锁持续时间t_s
2.REPEAT
3. 更新样本集X
4. 计算方差S²和死锁持续时间t_s
5. 根据式(16)计算δ
6. IF δ=1
7. 进入死锁消除算法,建立搜索空间H
8. 更新集合H₀
9. 根据式(13)计算下一子目标点
10. 生成相应标称控制器k^*(x)
11. 求解安全控制器式(8)
12. 更新控制量u←u^*(x)
13. END IF
14.UNTIL死锁消除任务完成

Fig.2 Effectiveness visualization of obstacle boundary fitting

Table 1 Actual obstacle area and estimated area

障碍物类型	实际面积/m	圆形近似面积/m²	LSSVM近似面积/m²
圆形	3.783	3.901	4.399
椭圆形	4.875	9.975	6.953
长方形	2.522	6.283	4.757
多边形	3.300	5.726	4.379
不规则型	3.320	5.147	3.971

Fig.3 Trajectory planning comparison

Table 2 Average trajectory length and obstacle distance

轨迹长度和障碍物距离	A^*算法	APF算法	CBF	直线距离
轨迹长度/m	10.348	12.698	11.375	8.731
障碍物距离/m	0.987	1.276	1.132	—

Fig.4 Trajectories of deadlock elimination algorithm

Table 3 Average deadlock time under different parameters

扩展类函数 (d₀=0.05)	死锁时间/s	搜索距离 (α=0.3* $h ˜ 3$ (x))	死锁时间/s
α= $h ˜$ (x)	—	d₀=0.5	19.691
α= $h ˜ 3$ (x)	16.691	d₀=0.2	15.726
α=0.5* $h ˜ 3$ (x)	16.223	d₀=0.1	14.304
α=0.3* $h ˜ 3$ (x)	15.066	d₀=0.05	15.066
α=0.1* $h ˜ 3$ (x)	16.187	d₀=0.01	26.548
α=0.01* $h ˜ 3$ (x)	—	d₀=0.001	—

Table 3 Average deadlock time under different parameters

扩展类函数 (d₀=0.05)	死锁时间/s	搜索距离 (α=0.3* $h ˜ 3$ (x))	死锁时间/s
α= $h ˜$ (x)	—	d₀=0.5	19.691
α= $h ˜ 3$ (x)	16.691	d₀=0.2	15.726
α=0.5* $h ˜ 3$ (x)	16.223	d₀=0.1	14.304
α=0.3* $h ˜ 3$ (x)	15.066	d₀=0.05	15.066
α=0.1* $h ˜ 3$ (x)	16.187	d₀=0.01	26.548
α=0.01* $h ˜ 3$ (x)	—	d₀=0.001	—

Fig.5 Semi-physical platform and experimental ground

Fig.6 Semi-physical experimental operation diagram

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