Block backstepping stabilization control of underactuated USV in polar coordinate system
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摘要: 针对非对称欠驱动无人艇的镇定控制问题, 提出了基于极坐标系的一类多输入多输出分块反步法, 设计了一种漂角极坐标系作为艇体的动坐标系, 以极坐标系代替直角坐标系作为大地坐标系, 将漂角、艏向角与极角融合处理, 获得了极坐标系下无人艇水平面运动的运动学和动力学方程, 使直角坐标系下的欠驱动问题简化为极坐标系下的全驱动问题。结合李亚普诺夫稳定性理论和反步法设计了一种极坐标系下的多输入多输出分块反步镇定控制律, 实现了非对称欠驱动无人艇的镇定控制。在实验室半物理仿真平台下, 以某长度为1.2m、质量为17.5kg的无人艇模型为实例进行镇定控制仿真试验, 对比分析了分块反步镇定控制算法与传统基于对称模型的反步控制算法的控制结果。分析结果表明: 分块反步镇定控制算法的位姿收敛速度提高了约10s, 位置和艏向角镇定误差分别降低了约0.3m和10°, 线速度和角速度超调量分别降低了约0.6m·s-1和2rad·s-1, 因此, 基于非对称模型的极坐标系下欠驱动分块反步法具有较大的可靠性、稳定性和精确性。Abstract: To the stabilization problem of underactuated unsymmetrical unmanned surface vessel(USV), a block backstepping approach with multiple inputs and multiple outputs(MIMO)was proposed in polar coordinate system.A drift angle polar coordinate system was designed as bodyfixed moving coordinate system, and Cartesian coordinate system was replaced by polar coordinate system as earth-fixed coordinate system.By combining the drift angle, yaw angle and polar angle, the kinematics and dynamics equations of USV horizontal plane motion in polar coordinate system were obtained, so that the underactuated problem in Cartesian coordinate systems was simplified to the full actuated problem in polar coordinate system.Based on Lyapunov stability theory and the backstepping approach, MIMO block backstepping stabilization control laws for underactuated unsymmetrical USV in polar coordinate system was designed.With the aid of semi-physical simulation platform in the laboratory, an USV model with 1.2 m and 17.5 kg was taken for stabilization control simulation experiment.The proposed block backstepping stabilization control algorithm was compared with the traditional backsteppingcontrol algorithm based on symmetry model.Comparison result shows that the convergence rates of position and yaw attitude increase by about 10 s, the stabilization errors of position and yaw angle decrease by about 0.3 mand 10° respectively, the overshoots of linear velocity and yaw angle velocity reduce by about 0.6m·s-1 and 2 rad·s-1 separately, so the proposed backstepping control method has higher reliability, stability and accuracy.
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表 1 无人艇模型参数
Table 1. Parameters of USV model
表 2 无人艇初始状态
Table 2. Initial state of USV
表 3 控制器参数
Table 3. Parameters of controller
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