中文摘要：

为实现欠驱动水下机器人（autonomousunderwatervehicle，AUV）的精确地形跟踪控制，设计了一种基于Lyapunov稳定性理论的非线性反步（backstepping）法控制器．基于虚拟向导的方法，结合AUV艇体的动力学特性，建立AUV垂直面地形跟踪误差方程，采用backstepping法设计地形跟踪控制器，利用Lyapunov稳定性理论分析了整个系统的稳定性．仿真实验中选择海底斜坡地形进行跟踪实验，且要求AUV相对地形保持一个恒定的高度偏差，结果表明该控制方法可实现对斜坡地形的精确跟踪．

英文摘要：

To realize the bottom following control for underactuated autonomous underwater vehicle （AUV） , a nonlinear backstepping controller based on Lyapunov stability theory is presented. Combined with the dynamic characteristics of AUV, the bottom following error equations in the vertical plane are established based on virtual guide method. Backstepping method is adopted to design the bottom following controller, then the stability of the whole system can be analyzed by Lyapunov stability theory. Bottom profile with constant slopes is used to evaluate the performance of the bottom following controller, and AUV is set to keep a constant height to the desired bottom profile. Results show that the designed controller can achieve accurate tracking of bottom profile with constant slopes.