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基于前饋非線性模型預測控制的類車機器人路徑跟蹤

Path tracking for car-like robots based on feed-forward nonlinear model predictive control

  • 摘要: 類車機器人由于零件標準化程度低,側偏剛度等輪胎力學參數難以準確獲得,存在動力學建模十分困難的問題,因此現有研究工作通常以運動學模型作為類車機器人的控制模型,但由于其運動學模型存在模型失配,導致類車機器人與參考路徑之間的誤差、類車機器人的前輪轉角和前輪轉角速度出現劇烈振蕩現象. 針對前述問題,本文基于非線性模型預測控制(Nonlinear model predictive control, NMPC)的滾動優化原理,引入基于逆運動學模型的前饋轉角信息,將前輪轉向角作為預測模型的第四維,提出了一種基于前饋非線性模型預測控制(Feedforward NMPC, FNMPC)的類車機器人路徑跟蹤控制算法. 并通過Simulink和CarSim進行了聯合仿真,結果表明FNMPC有效減小了模型失配導致的振蕩現象,同時具有較高的跟蹤精度. 其中前饋非線性模型預測控制器的位移誤差幅值不超過0.1106 m,航向誤差幅值不超過0.1253 rad. 在相同工況下,線性模型預測控制、前饋線性模型預測控制、純跟蹤控制和Stanley控制誤差發散,而本文提出的FNMPC相比已有NMPC跟蹤精度更高,且控制增量絕對累計值相比NMPC控制器減小67.53%. 通過線控類車機器人底盤作為實驗平臺完成的測試結果表明,NMPC系統在進入彎道時出現控制失控現象,在相同工況下,FNMPC系統能夠有效完成對參考路徑的跟蹤,同時將位移誤差幅值控制在0.1624 m以內,航向誤差幅值控制在0.1138 rad以內.

     

    Abstract: Car-like robots often struggle with dynamics modeling owing to the use of nonstandardized parts and the complexity of accurately determining mechanical parameters, particularly tire characteristics like lateral deflection stiffness. Consequently, most current research and applications have relied on kinematic models for control, which frequently lead to inaccuracies and mismatches. These issues result in significant errors between actual and desired paths, causing erratic oscillations in the front wheel angle and angular velocity and adversely affecting the robot’s performance and smoothness. To address these issues, this paper introduces a novel approach: Feed-forward nonlinear model predictive control (FNMPC). This method is built on the principles of inverse kinematics and rolling optimization. Unlike other traditional methods, FNMPC incorporates feed-forward corner information into its predictive model, treating the front wheel angle as an additional dimension. This enhancement allows the model to better predict and correct deviations, thereby improving path-tracking accuracy. Extensive simulations conducted using Simulink and CarSim demonstrated the efficacy of the FNMPC approach. Results indicated that FNMPC significantly reduces the oscillations caused by model inaccuracies while maintaining high tracking accuracy. Specifically, FNMPC managed to keep displacement errors below 0.1106 m and heading errors within 0.1253 radians. When compared with other control strategies such as linear model predictive control, feed-forward linear model predictive control, pure tracking control, and Stanley control, FNMPC consistently demonstrated smaller and less dispersed errors, highlighting its superior performance in handling the complex dynamics of car-like robots. Moreover, FNMPC showed a remarkable improvement over traditional nonlinear model predictive control (NMPC), reducing the absolute cumulative control increment by 67.53% at its maximum values. Experimental validations using a wire-controlled car-like robot further validated FNMPC’s practical benefits. In these tests, the robot under FNMPC control maintained displacement errors within 0.1624 m and heading errors within 0.1138 radians, whereas traditional NMPC lost control of entering curves. In summary, FNMPC presents a substantial advancement in controlling car-like robots, offering enhanced accuracy and smoothness over existing methods. By effectively incorporating feed-forward corner information into the predictive model, FNMPC addresses the inherent challenges in car-like robot dynamics more efficiently. This approach not only improves control performance but also offers a more reliable and accurate method that could enhance the development of car-like robotic systems.

     

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