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工程设计学报
Chin J Eng Design  2022, Vol. 29 Issue (2): 123-132    DOI: 10.3785/j.issn.1006-754X.2022.00.032
Design Theory and Method     
Ackerman steering trajectory planning and position estimation of 4WID-4WIS intelligent vehicle
Pei-cheng SHI1(),Xu CHEN1,Ai-xi YANG2,Liang ZHANG1
1.Anhui Engineering Technology Research Center of Automotive New Technology，Anhui Polytechnic University，Wuhu 241000，China
2.Polytechnic Institute，Zhejiang University，Hangzhou 310000，China
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Abstract  

Aiming at the steering driving conditions of four-wheel independent drive and four-wheel independent steering (4WID-4WIS) intelligent vehicles, a new method for trajectory planning using third-order Bézier curve was proposed based on the Ackerman steering principle. Firstly, an optimal trajectory with minimum curvature difference was obtained by using the optimal function, which met the initial state constraints and target state constraints of intelligent vehicle and the curvature continuity constraints. Then, a position estimation algorithm was proposed, which calculated the position increment of intelligent vehicle based on the navigation angle measured by the inertial navigation system and the pulse number of encoder, so as to estimate its position during driving and calculate the driving trajectory length. Finally, the planned intelligent vehicle trajectory was simulated in the MATLAB software, and the rationality and feasibility of the trajectory planning method and position estimation algorithm were verified on the real vehicle test platform. The results showed that the 4WID-4WIS intelligent vehicle could drive to the given end point according to the planned trajectory, and its lateral position estimation error was 0.19%, the longitudinal position estimation error was 0.20% and the driving trajectory length calculation error was 0.22%; compared with other single algorithms such as mileage calculation method and ranging method, the proposed position estimation algorithm had high precision, which can provide reference for trajectory planning and position estimation of other mobile robots.

Key words： four-wheel independent drive and four-wheel independent steering (4WID-4WIS)      Ackerman steering      Bézier curve      trajectory planning     
Received: 14 July 2021      Published: 06 May 2022
CLC:  TH 721  
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Pei-cheng SHI
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Cite this article:

Pei-cheng SHI,Xu CHEN,Ai-xi YANG,Liang ZHANG. Ackerman steering trajectory planning and position estimation of 4WID-4WIS intelligent vehicle. Chin J Eng Design, 2022, 29(2): 123-132.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2022.00.032     OR     https://www.zjujournals.com/gcsjxb/Y2022/V29/I2/123


4WID-4WIS智能车阿克曼转向轨迹规划及位置估算

针对四轮独立驱动与四轮独立转向（four-wheel independent drive and four-wheel independent steering, 4WID-4WIS）智能车的转向行驶工况，基于阿克曼转向原理，提出一种利用三阶贝塞尔曲线进行轨迹规划的新方法。首先，采用最优函数获取一条满足智能车初始状态约束、目标状态约束和曲率连续约束且曲率差值最小的最优轨迹。然后，提出一种位置估算算法，即基于惯性导航系统测量的航向角和编码器的脉冲数对智能车的位置增量进行计算，从而估算其行驶时的位置，并推算运行轨迹的长度。最后，在MATLAB软件中对所规划的智能车轨迹进行仿真计算，并在实车试验平台上验证轨迹规划方法和位置估算算法的合理性和可行性。结果表明，4WID-4WIS智能车能够按规划的轨迹行驶到给定终点，其横向位置估算误差为0.19%，纵向位置估算误差为0.20%，运行轨迹长度推算误差为0.22%；相比于其他里程计算法、测距法等单一算法，所提出的位置估算算法的精度高，可为其他移动机器人的轨迹规划和位置估算提供参考。


关键词： 四轮独立驱动与四轮独立转向（4WID-4WIS）,  阿克曼转向,  贝塞尔曲线,  轨迹规划 
Fig.1 Schematic diagram of third-order Bézier curve
Fig.2 Schematic diagram of intelligent vehicle trajectory planning based on third-order Bézier curve
Fig.3 Trajectory planning simulation results of 4WID-4WIS intelligent vehicle obtained by changing control point P2
Fig.4 Trajectory planning simulation results of 4WID-4WIS intelligent vehicle obtained by changing control point P1
Fig.5 Simulation results of trajectory planning of 4WID-4WIS intelligent vehicle obtained by changing control point P1 and P2 at the same time
寻优方式曲率差值4个控制点的坐标/m
P2纵坐标寻优0.046 3

（0, 0），（10, 0），

（20, 9），（20, 30）

P1横坐标寻优0.045 6

（0, 0），（13, 0），

（20, 15），（20, 30）

P1、P2坐标同时寻优0.045 2

（0, 0），（13, 0），

（20, 16），（20, 30）
Table 1 Comparison of simulation results of optimal trajectory control points of 4WID-4WIS intelligent vehicle
Fig.6 Ackerman steering model of 4WID-4WIS intelligent vehicle
Fig.7 Calculation principle of trajectory of 4WID-4WIS intelligent vehicle
Fig.8 Physical object of 4WID-4WIS intelligent vehicle
参数数值
前、后驱动轮轴距W/m0.580
左、右侧驱动轮轮距D/m0.498
轮毂电机半径/m0.233
编码器旋转一周的脉冲数N4 096
惯性导航系统精度/（°）0.05
Table 2 Parameters of 4WID-4WIS intelligent vehicle
Fig.9 Navigation angle and pulse number of 4WID-4WIS intelligent vehicle during driving
Fig.10 Calculation results of trajectory of 4WID-4WIS intelligent vehicle
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