Trajectory Tracking and Obstacle Avoidance Control of Six-wheel Independent Drive and Steering Robot in Complex Terrain

doi:10.12382/bgxb.2023.0533

Abstract

Abstract:

In order to study the motion control method of six-wheel mobile robot in complex terrain environment, a predictive control and dynamic compensation control method is proposed for the trajectory tracking problem of six-wheel independent drive and steering robot in complex terrain. This method is based on the nonholonomically constrained linear six-wheeled mobile robot kinematics model and the model predictive control algorithm, and introduces a proportional-integral-derivative compensation controller to suppress the tracking error caused by dynamic hysteresis. Coping with the effect of terrain disturbance on trajectory tracking. the collision avoidance problem of obstacles in the process of robot movement is analyzed, an obstacle avoidance planner that can solve the obstacle avoidance trajectory is designed to track and control the local obstacle avoidance trajectory through the trajectory tracking system, thus realizing the trajectory tracking and automatic collision avoidance of robot, and the trajectory tracking algorithm and obstacle avoidance algorithm were simulated experiments. The experimental results show that the robot can complete the sinusoidal trajectory tracking control and the static and dynamic obstacle collision avoidances in concave slope, convex slope and uneven terrain under typical working conditions, which verifies the effectiveness of the method.

Key words: six-wheel independent drive and steering robot, trajectory tracking control, model predictive control, PID compensation control, obstacle avoidance control

CLC Number:

TP242.6

LIU Jiangtao, ZHOU Lelai, LI Yibin. Trajectory Tracking and Obstacle Avoidance Control of Six-wheel Independent Drive and Steering Robot in Complex Terrain[J]. Acta Armamentarii, 2024, 45(1): 166-183.

Figures/Tables 35

Fig.1 Kinematic model of non-complete constraint six-wheel independent drive independent steering robot

Fig.2 Block diagram of robot trajectory tracking control in complex terrain

Fig.3 Comparison of robot steerings in different terrain environments

Fig.4 Deviation of robot from the reference trajectory

Fig.5 Three-dimensional coordinate angle representation

Fig.6 PID compensation correction

Fig.7 Block diagram of trajectory planning control system combined with obstacle avoidance control

Fig.8 Obstacle expansion and splitting point

Fig.9 Obstacle avoidance penalty function

Fig.10 Fitting results of partial segment trajectory

Table 1 Robot parameters

参数	取值
机器人尺寸(长×宽×高)/mm	700×500×550
机器人整机质量/kg	212
轮胎尺寸/mm	宽80,直径215
驱动电机最大扭矩/(N·m)	500
转向电机最大扭矩/(N·m)	500

Fig.11 Simulation of operating platform and robot control

Fig.12 Comparison of trajectory tracking errors of four-wheeled robot and six-wheeled robot

Fig.13 Concave slope coordinates during robot motion

Table 2 Concave slope experimental parameters

控制器类型	参数	数值
PID控制器	系数	k_p:110, k_i:0.1, k_d:0.30
	采样时间/ms	10
Pure Pursuit	前视距离系数	0.15
控制器	前视距离/m	1.2
	采样时间/ms	10
	MPC采样周期/ms	50
MPC控制器	MPC控制步长	30
	MPC预测步长	60
	MPC采样周期/ms	50
	MPC控制步长	30
	MPC预测步长	60
本文控制器	PID采样周期/ms	10
	Yaw角放大倍数	1.13~1.25
	PID常数项比例系数	k_p:0.25, k_i:0.05, k_d:0.10
	PID增益项比例系数	λ₁:5, λ₂:1.5, λ₃:2

Fig.14 Trajectory tracking simulation on concave slope

Fig.15 Comparison of tracking trajectories of concave ramp controllers

Fig.16 Comparison of tracking errors of concave ramp contrllers

Fig.17 Comparison of steering angles of concave slope controllers

Fig.18 Convex slope coordinates duringrobot motion

Table 3 Convex ramp experimental parameters

控制器类型	参数	数值
PID控制器	系数	k_p:110, k_i:0.1, k_d:0.30
	采样时间/ms	10
Pure Pursuit	前视距离系数	0.15
控制器	前视距离/m	1.2
	采样时间/ms	10
	MPC采样周期/ms	50
MPC控制器	MPC控制步长	30
	MPC预测步长	60
	MPC采样周期/ms	50
	MPC控制步长	30
	MPC预测步长	60
本文控制器	PID采样周期/ms	10
	Yaw角放大倍数	1.13~1.35
	PID常数项比例系数	k_p:0.30, k_i:0.10, k_d:0.15
	PID增益项比例系数	λ₁:5.5, λ₂:1.5, λ₃:2.5

Fig.19 Trajectory tracking simulation on convex slope

Fig.20 Comparison of tracking trajectories of convex ramp controllers

Fig.21 Comparison of tracking errors of convex ramp controllers

Fig.22 Comparison of steering angles of convex ramp controllers

Fig.23 The change in the height of robot’s center of mass during trajectory tracking

Table 4 Experimental parameters of uneven and convex roads

控制器类型	参数	数值
PID控制器	系数	k_p:110, k_i:0.1, k_d:0.30
	采样时间/ms	10
Pure Pursuit	前视距离系数	0.15
控制器	前视距离/m	1.2
	采样时间/ms	10
	MPC采样周期/ms	50
MPC控制器	MPC控制步长	30
	MPC预测步长	60
	MPC采样周期/ms	50
	MPC控制步长	30
	MPC预测步长	60
本文控制器	PID采样周期/ms	10
	Yaw角放大倍数	1.2~1.4
	PID常数项比例系数	k_p:0.32, k_i:0.13, k_d:0.16
	PID增益项比例系数	λ₁:5.8, λ₂:1.6, λ₃:2.8

Fig.24 Comparison of tracking trajectories of concave and convex pavement controllers

Fig.25 Comparison of tracking errors of concave and convex pavement controllers

Fig.26 Comparison of steering angles of concave and convex road controllers

Fig.27 Flowchart of robot obstacle avoidance

Table 5 Obstacle information

参数	障碍物A	障碍物B
质心初始坐标/m	(0.8,3.2)	(5.4,3.2)
长×宽×高/m	0.3×0.3×0.5	0.3×0.3×0.5
质量/kg	50	50
移动速度/(m·s^-1)	0	0.14~0.15

Fig.28 Comparison of obstacle avoidance trajectories of robot by using the dynamic window method and the obstacle avoidance method in the paper

Fig.29 Representation of distance deviation between the robot and the reference trajectories by the dynamic window method and the obstacle avoidance method in the paper

Fig.30 The distance between the robot’s center of mass and the center of the obstacle’s center of mass expressed by the dynamic window method and the obstacle avoidance method in the paper

References 23

[1]	SONKER R, DUTTA A. Adding terrain height to improve model learning for path tracking on uneven terrain by a four-wheel robot[J]. IEEE Robotics and Automation Letters, 2020, 6(1): 239-246. doi: 10.1109/LSP.2016. URL
[2]	TAGHAVIFAR H, RAKHEIA S. A novel terramechanics-based path-tracking control of terrain-based wheeled robot vehicle with matched-mismatched uncertainties[J]. IEEE Transactions on Vehicular Technology, 2020, 69(1):67-77. doi: 10.1109/TVT.25 URL
[3]	GE C, QIAN S Q. An adaptive MPC trajectory tracking algorithm for autonomous vehicles[C]// Proceedings of the 2021 17th International Conference on Computational Intelligence and Security.Chengdu,China:IEEE, 2021:197-201.
[4]	SUN Q P, WANG Z H, LI M, et al. Path tracking control of wheeled mobile robot based on improved pure pursuit algorithm[C]// Proceedings of the 2019 Chinese Automation Congress. Hangzhou, China:IEEE, 2019:4239-4244.
[5]	ERNÓ H, CSABA H, KÓRÖS P. Novel Pure-Pursuit trajectory following approaches and their practical applications[C]// Proceedings of the 2019 10th IEEE International Conference on Cognitive Infocommunic-Ations. Naples, Italy: IEEE, 2019:597-602.
[6]	HUA Q, PENG B S, MOU X L, et al. Model prediction control path tracking algorithm based on adaptive stanley[C]// Proceedings of the 2022 IEEE 96th Vehicular Technology Conference.London, UK: IEEE, 2022:1-5.
[7]	ZUO Z Q, YANG X, LI Z, et al. MPC-based cooperative control strategy of path planning and trajectory tracking for intelligent vehicles[J]. IEEE Transactions on Intelligent Vehicles, 2020, 6(3):513-522. doi: 10.1109/TIV.2020.3045837 URL
[8]	ZHAI L, WANG C P, HOU Y H, et al. MPC-based integrated control of trajectory tracking and handling stability for intelligent driving vehicle driven by four hub motor[J]. IEEE Transactions on Vehicular Technology, 2022, 71(3):2668-2680. doi: 10.1109/TVT.2022.3140240 URL
[9]	LI Z J, DENG J, LU R Q, et al. Trajectory-tracking control of mobile robot systems incorporating neural-dynamic optimized model predictive approach[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2016, 46(6):740-749. doi: 10.1109/TSMC.6221021 URL
[10]	CHU D F, LI H R, ZHAO C Y, et al. Trajectory tracking of autonomous vehicle based on model predictive control with PID feedback[J]. IEEE Transactions on Intelligent Transportation Systems, 2023, 24(2):2239-2250.
[11]	YANG H J, FAN X Z, SHI P, et al. Nonlinear control for tracking and obstacle avoidance of a wheeled mobile robot with nonholonomic constraint[J]. IEEE Transactions on Control Systems Technology, 2016, 24(2):741-746.
[12]	ZHANG X L, ZHANG W X, ZHAO Y Q, et al. Personalized motion planning and tracking control for autonomous vehicles obstacle avoidance[J]. IEEE Transactions on Vehicular Technology, 2022, 71(5):4733-4747. doi: 10.1109/TVT.2022.3152542 URL
[13]	GUO B H, GUO N, CEN Z S. Obstacle avoidance with dynamic avoidance risk region for mobile robots in dynamic environments[J]. IEEE Robotics and Automation Letters, 2022, 7(3):5850-5857. doi: 10.1109/LRA.2022.3161710 URL
[14]	GUO H Y, SHEN C, ZHANG H, et al. Simultaneous trajectory planning and tracking using an MPC method for cyber-physical systems: a case study of obstacle avoidance for an intelligent vehicle[J]. IEEE Transactions on Industrial Informatics, 2018, 74(9):4273-4283.
[15]	LU Q, ZHANG D, YE W J, et al. Targeting posture control with dynamic obstacle avoidance of constrained uncertain wheeled mobile robots including unknown skidding and slipping[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(11):6650-6659. doi: 10.1109/TSMC.2019.2962732 URL
[16]	XIANG L D, LI X M, LIU H, et al. Parameter fuzzy self-adaptive dynamic window approach for local path planning of wheeled robot[J]. IEEE Open Journal of Intelligent Transportation Systems, 2022, 3:1-6. doi: 10.1109/OJITS.2021.3137931 URL
[17]	LYNCH K M, PARK F C. Modern robotics: mechanics, planning, and control[M]. Beijing: China Machine Press, 2019:328-350.
[18]	严浙平, 杨皓宇, 张伟, 等. 基于模型预测—中枢模式发生器的六足机器人轨迹跟踪控制[J]. 机器人, 2023, 45(1):58-69.
	YAN Z P, YANG H Y, ZHANG W, et al. Trajectory tracking control of hexapod robot based on model prediction and center pattern generator[J]. Robot, 2023, 45(1):58-69. (in Chinese)
[19]	RASHIDI B, ESMAEILPOOR M, HOMAEINEZHAD M R, et al. Error-based self-regulating PID angle control of variable structure redundant brushed DC motors[C]// Proceedings of the 2014 Second RSI/ISM International Conference on Robotics and Mechatronics. Tehran, Iran:IEEE, 2014: 274-279.
[20]	张超省, 王健, 张林, 等. 面向复杂障碍场的多智能体系统集群避障模型[J]. 兵工学报, 2021, 42(1):141-150.
	ZHANG C S, WANG J, ZHANG L, et al. A multi-agent system flocking model with obstacle avoidance in complex obstacle field[J]. Acta Armamentarii, 2021, 42(1): 141-150. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.01.016
[21]	邓海鹏, 麻斌, 赵海光, 等. 自主驾驶车辆紧急避障的路径规划与轨迹跟踪控制[J]. 兵工学报, 2020, 41(3): 585-594. doi: 10.3969/j.issn.1000-1093.2020.03.020
	DENG H P, MA B, ZHAO H G, et al. Path planning and tracking control of autonomous vehicle for obstacle avoidance[J]. Acta Armamentarii, 2020, 41(3): 585-594. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.03.020
[22]	杜广泽, 张旭东, 邹渊, 等. 非结构道路场景下轮式无人车辆避障算法[J]. 兵工学报, 2020, 41(10): 2096-2105. doi: 10.3969/j.issn.1000-1093.2020.10.020
	DU G Z, ZHANG X D, ZOU Y, et al. Obstacle avoidance algorithm for autonomous wheeled vehicle in unstructured environments[J]. Acta Armamentarii, 2020, 41(10): 2096-2105. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.10.020
[23]	张家闻, 房浩霖, 李家旺. 基于复杂约束条件的欠驱动AUV三维路径规划[J]. 兵工学报, 2022, 43(6): 1407-1414. doi: 10.12382/bgxb.2021.0340
	ZHANG J W, FANG H L, LI J W. 3D Path planning of underactuated AUV based on complex constraints[J]. Acta Armamentarii, 2022, 43(6): 1407-1414. (in Chinese) doi: 10.12382/bgxb.2021.0340