基于滑模理论的欠驱动UUV空间曲线路径跟踪控制
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摘要
空间曲线路径跟踪控制是欠驱动自治水下机器人(UUV or AUV:Unmanned Underwater Vehicle or Autonomous Underwater Vehicle)完成海底探测、海底管道监测和光缆维护等使命任务的重要技术保障。本课题针对欠驱动UUV的非完整约束特性,考虑其动力学模型的非线性、各自由度之间的耦合性、水动力参数的不确定性以及存在非定常海流干扰的特点,对滑模控制理论在欠驱动UUV空间曲线路径跟踪控制中的应用进行了深入的研究,主要研究内容有以下四部分：
第一部分：针对某型UUV对其运动与建模问题展开研究并对该系统模型进行控制特性分析。
首先,为完善欠驱动UUV空间六自由度运动模型,建立执行机构的非线性数学模型和海流干扰模型。该运动模型不仅包含艇体水动力的非线性项和耦合性项,而且考虑了执行机构的饱和特性和海流干扰下的平衡点特性,从而提高了数字化仿真模型的精确性,操纵性仿真实验验证了所建立的欠驱动UUV运动模型的正确性。
其次,针对欠驱动UUV运动模型,基于非完整系统理论和微分几何方法,证明欠驱动UUV属于二阶非完整系统,并且具有小时间局部可控性。该系统的特点是：不存在任何光滑时不变的反馈控制使得系统在平衡点渐近稳定,但系统在平衡点是小时间局部可控的,从而为欠驱动UUV运动控制器的设计奠定了理论基础。
第二部分：提出基于视线法(LOS:Line of Sight)设计自适应PID控制器,以实现欠驱动UUV空间曲线路径跟踪控制。
首先,针对欠驱动UUV不存在任何光滑时不变的反馈控制使得系统在平衡点渐近稳定的问题,提出基于视线法建立空间路径跟踪的运动误差模型。该方法将欠驱动UUV位置误差的跟踪控制转化为航速误差、艏向角误差和纵倾角误差的渐近稳定控制,实现了非完整系统的镇定控制问题转化为完整系统的镇定控制问题,从而避开了Brockett定理必要条件的约束,为传统控制方法在欠驱动UUV空间曲线路径跟踪控制中的应用提供了设计思路。
其次,针对常规PID控制方法参数调整不具有智能性且整定参数较难的问题,提出自适应PID方法实现空间曲线路径跟踪控制。该方法参数的整定不依赖于欠驱动UUV精确数学模型,且能够在线调整以满足实时控制的要求,同时具有常规PID控制器结构简单、可靠性高的优点。欠驱动UUV在不同航速下的空间正弦曲线路径跟踪控制仿真验证了此方法的有效性。
第三部分：提出基于虚拟向导的迭代滑模控制(ISMC:Iterative Sliding Mode Control)方法,以提高欠驱动UUV在时变海流干扰下空间曲线路径跟踪控制的精确性和鲁棒性。
首先,针对基于视线法的空间曲线路径跟踪控制存在非连续跟踪误差且容易导致执行机构饱和的问题,提出基于虚拟向导方法建立空间曲线路径跟踪误差模型。该方法不仅结合空间曲线特性和欠驱动UUV运动特性,建立光滑连续的空间误差运动模型,而且给定虚拟向导一定的移动速度,能够避免路径跟踪的奇异值问题。
其次,针对自适应PID控制器难以抑制时变海流干扰的问题,提出基于增量反馈的迭代滑模控制方法设计空间曲线路径跟踪控制器。该方法的滑模迭代设计思想能够避免滑模面的切换引起的抖振,增量反馈控制能够缓解传统反馈的积分超调和稳态误差的矛盾问题,具有很强的鲁棒性。时变海流干扰下的空间曲线路径跟踪控制仿真实验验证了该方法的抗干扰能力。
第四部分：提出基于预测控制思想设计离散滑模预测控制器(DSMPC:Discrete-time Sliding Mode Predictive Controller),以实现空间曲线路径跟踪的优化控制。
针对基于连续时间系统设计的迭代滑模控制器在数字控制器上难以达到满意控制性能的问题,引进单值滑模预测控制算法,该算法计算简单,易于工程实现,其滚动优化和反馈校正环节补偿欠驱动UUV运动模型不确定项和定常非连续海流干扰对离散滑模面的影响,不仅增强控制系统的鲁棒性,而且提高空间曲线路径跟踪的精确性。
The spatial curvilinear path following control is the essential basis of underactuated Unmanned Underwater Vehicle's (UUV) mission implement, such as seabed survey, submarine pipeline monitoring, and cable maintenance. This paper deals with the characteristics of nonholonomic restriction for underactuated UUV, considering the nonlinear of dynamic motion, the dynamic coupling between the degrees of freedom, the uncertainties of hydrodynamic and unsteady ocean current disturbance. Sliding mode control theory for underactuated UUV as well as its practical applications in curve path following control are deeply investigated in this paper, and the main contents contain the following four parts:
The first section:the motion and modeling of a certain underactuated UUV are fully investigated and its characteristics of the control system are studied in this paper.
Firstly, in order to improve the mathematical models of underactuated UUV motion for six degrees of freedom, the nonlinear mathematical models of actuators and the disturbance model of ocean current are established. The motion models include the nonlinear terms and coupling characteristics of hydrodynamic, also contain the saturation characteristics of actuators and the equilibrium point characteristics under the disturbance of ocean current. Thus the accuracy of digital models are improved and the validity of the models is verified through the maneuverability experiments.
Secondly, the underactuated UUV motion models are investigated based on the theory of nonholonomic system and differential geometry. It is proved that the underactuated UUV is second-order nonholonomic system, which has the small-time local controllability. It is demonstrated there is no continuous time-invariant feedback control law that makes underactuated UUV asymptotically stabilization to a single equilibrium, but the system is small-time local controllable. All of that lay a theoretical foundation for motion controller design.
The second section:the line-of-sight method is proposed to design the adaptive PID controller, thus the spatial curvilinear path following control for underactuated UUV is actualized.
Firstly, aiming at the problem that there is no continuous time-invariant feedback control law to make system be asymptotically stabilized to a single equilibrium, the line-of-sight method is proposed to establish the space movement error models of underactuated UUV. Then the problem of position error's stabilization control is turned into the asymptotic stability design of the speed error, heading error and pitch error, by which the nonholonomic stabilization can be transformed into control problems of holonomic systems. Thus the restrictions of Brockett theorem are avoided and the traditional control methods could be applied to the spatial path following control for underactuated UUV.
Secondly, according to the classical PID parameters are difficult to setting, the motion controller is designed based on adaptive PID algorithm for underactuated UUV. The adaptive PID parameters'setting are independent of the accurate mathematical models, which on-line adjustment could realize real-time control. It also has the advantages of simple structure, high reliability as the PID controller. The validity of the method is test and verified through the simulation experiments for spatial curvilinear path following control under the different velocity of underactuated UUV.
The third section:the nonlinear iterative sliding mode control based on virtual guide method is proposed, thus the accuracy and robustness of path following are improved under the time-varying ocean current disturbance.
Firstly, in allusion to the discontinuity tracking errors which result in saturation characteristic of actuators in LOS method, the virtual guide method is proposed to establish the space movement error models of underactuated UUV. Considering the characteristic of spatial curve and the movement characteristics of underactuated UUV, the smooth continuous space movement error model is established based on virtual guide method, which gives a speed on the path could avoid the occurrence of a singularity.
Secondly, aiming at the difficulty for adaptive PID controller to restrain the time-varying ocean current disturbance, the iterative sliding mode control method based on increment feedback is proposed to design the spatial curve path following controller. The recursive sliding mode designing procedure could avoid the problem of the chattering, the increment feedback control method could reduce the overshoot and static error. The anti-interference ability of controller is verified by the simulation experiments for spatial curvilinear path following control under the time-varying continuous ocean current disturbance.
The fourth section:the discrete-time sliding mode predictive control method is proposed to achieve the path following receding-horizon control.
According to the problem that the ISMC which designed based on continuous-time system can't attain the satisfying control performance, The single-value sliding mode predictive control algorithm is introduced, which is convenient for engineering realization. Feedback correction and receding horizon optimization approaches are employed to compensate the uncertainties of dynamic model and the influence of steady discontinuous ocean current disturbances, thus the spatial curve path following control system possesses stronger robustness and higher accuracy for underactuated UUV.
第一部分：针对某型UUV对其运动与建模问题展开研究并对该系统模型进行控制特性分析。
首先,为完善欠驱动UUV空间六自由度运动模型,建立执行机构的非线性数学模型和海流干扰模型。该运动模型不仅包含艇体水动力的非线性项和耦合性项,而且考虑了执行机构的饱和特性和海流干扰下的平衡点特性,从而提高了数字化仿真模型的精确性,操纵性仿真实验验证了所建立的欠驱动UUV运动模型的正确性。
其次,针对欠驱动UUV运动模型,基于非完整系统理论和微分几何方法,证明欠驱动UUV属于二阶非完整系统,并且具有小时间局部可控性。该系统的特点是：不存在任何光滑时不变的反馈控制使得系统在平衡点渐近稳定,但系统在平衡点是小时间局部可控的,从而为欠驱动UUV运动控制器的设计奠定了理论基础。
第二部分：提出基于视线法(LOS:Line of Sight)设计自适应PID控制器,以实现欠驱动UUV空间曲线路径跟踪控制。
首先,针对欠驱动UUV不存在任何光滑时不变的反馈控制使得系统在平衡点渐近稳定的问题,提出基于视线法建立空间路径跟踪的运动误差模型。该方法将欠驱动UUV位置误差的跟踪控制转化为航速误差、艏向角误差和纵倾角误差的渐近稳定控制,实现了非完整系统的镇定控制问题转化为完整系统的镇定控制问题,从而避开了Brockett定理必要条件的约束,为传统控制方法在欠驱动UUV空间曲线路径跟踪控制中的应用提供了设计思路。
其次,针对常规PID控制方法参数调整不具有智能性且整定参数较难的问题,提出自适应PID方法实现空间曲线路径跟踪控制。该方法参数的整定不依赖于欠驱动UUV精确数学模型,且能够在线调整以满足实时控制的要求,同时具有常规PID控制器结构简单、可靠性高的优点。欠驱动UUV在不同航速下的空间正弦曲线路径跟踪控制仿真验证了此方法的有效性。
第三部分：提出基于虚拟向导的迭代滑模控制(ISMC:Iterative Sliding Mode Control)方法,以提高欠驱动UUV在时变海流干扰下空间曲线路径跟踪控制的精确性和鲁棒性。
首先,针对基于视线法的空间曲线路径跟踪控制存在非连续跟踪误差且容易导致执行机构饱和的问题,提出基于虚拟向导方法建立空间曲线路径跟踪误差模型。该方法不仅结合空间曲线特性和欠驱动UUV运动特性,建立光滑连续的空间误差运动模型,而且给定虚拟向导一定的移动速度,能够避免路径跟踪的奇异值问题。
其次,针对自适应PID控制器难以抑制时变海流干扰的问题,提出基于增量反馈的迭代滑模控制方法设计空间曲线路径跟踪控制器。该方法的滑模迭代设计思想能够避免滑模面的切换引起的抖振,增量反馈控制能够缓解传统反馈的积分超调和稳态误差的矛盾问题,具有很强的鲁棒性。时变海流干扰下的空间曲线路径跟踪控制仿真实验验证了该方法的抗干扰能力。
第四部分：提出基于预测控制思想设计离散滑模预测控制器(DSMPC:Discrete-time Sliding Mode Predictive Controller),以实现空间曲线路径跟踪的优化控制。
针对基于连续时间系统设计的迭代滑模控制器在数字控制器上难以达到满意控制性能的问题,引进单值滑模预测控制算法,该算法计算简单,易于工程实现,其滚动优化和反馈校正环节补偿欠驱动UUV运动模型不确定项和定常非连续海流干扰对离散滑模面的影响,不仅增强控制系统的鲁棒性,而且提高空间曲线路径跟踪的精确性。
The spatial curvilinear path following control is the essential basis of underactuated Unmanned Underwater Vehicle's (UUV) mission implement, such as seabed survey, submarine pipeline monitoring, and cable maintenance. This paper deals with the characteristics of nonholonomic restriction for underactuated UUV, considering the nonlinear of dynamic motion, the dynamic coupling between the degrees of freedom, the uncertainties of hydrodynamic and unsteady ocean current disturbance. Sliding mode control theory for underactuated UUV as well as its practical applications in curve path following control are deeply investigated in this paper, and the main contents contain the following four parts:
The first section:the motion and modeling of a certain underactuated UUV are fully investigated and its characteristics of the control system are studied in this paper.
Firstly, in order to improve the mathematical models of underactuated UUV motion for six degrees of freedom, the nonlinear mathematical models of actuators and the disturbance model of ocean current are established. The motion models include the nonlinear terms and coupling characteristics of hydrodynamic, also contain the saturation characteristics of actuators and the equilibrium point characteristics under the disturbance of ocean current. Thus the accuracy of digital models are improved and the validity of the models is verified through the maneuverability experiments.
Secondly, the underactuated UUV motion models are investigated based on the theory of nonholonomic system and differential geometry. It is proved that the underactuated UUV is second-order nonholonomic system, which has the small-time local controllability. It is demonstrated there is no continuous time-invariant feedback control law that makes underactuated UUV asymptotically stabilization to a single equilibrium, but the system is small-time local controllable. All of that lay a theoretical foundation for motion controller design.
The second section:the line-of-sight method is proposed to design the adaptive PID controller, thus the spatial curvilinear path following control for underactuated UUV is actualized.
Firstly, aiming at the problem that there is no continuous time-invariant feedback control law to make system be asymptotically stabilized to a single equilibrium, the line-of-sight method is proposed to establish the space movement error models of underactuated UUV. Then the problem of position error's stabilization control is turned into the asymptotic stability design of the speed error, heading error and pitch error, by which the nonholonomic stabilization can be transformed into control problems of holonomic systems. Thus the restrictions of Brockett theorem are avoided and the traditional control methods could be applied to the spatial path following control for underactuated UUV.
Secondly, according to the classical PID parameters are difficult to setting, the motion controller is designed based on adaptive PID algorithm for underactuated UUV. The adaptive PID parameters'setting are independent of the accurate mathematical models, which on-line adjustment could realize real-time control. It also has the advantages of simple structure, high reliability as the PID controller. The validity of the method is test and verified through the simulation experiments for spatial curvilinear path following control under the different velocity of underactuated UUV.
The third section:the nonlinear iterative sliding mode control based on virtual guide method is proposed, thus the accuracy and robustness of path following are improved under the time-varying ocean current disturbance.
Firstly, in allusion to the discontinuity tracking errors which result in saturation characteristic of actuators in LOS method, the virtual guide method is proposed to establish the space movement error models of underactuated UUV. Considering the characteristic of spatial curve and the movement characteristics of underactuated UUV, the smooth continuous space movement error model is established based on virtual guide method, which gives a speed on the path could avoid the occurrence of a singularity.
Secondly, aiming at the difficulty for adaptive PID controller to restrain the time-varying ocean current disturbance, the iterative sliding mode control method based on increment feedback is proposed to design the spatial curve path following controller. The recursive sliding mode designing procedure could avoid the problem of the chattering, the increment feedback control method could reduce the overshoot and static error. The anti-interference ability of controller is verified by the simulation experiments for spatial curvilinear path following control under the time-varying continuous ocean current disturbance.
The fourth section:the discrete-time sliding mode predictive control method is proposed to achieve the path following receding-horizon control.
According to the problem that the ISMC which designed based on continuous-time system can't attain the satisfying control performance, The single-value sliding mode predictive control algorithm is introduced, which is convenient for engineering realization. Feedback correction and receding horizon optimization approaches are employed to compensate the uncertainties of dynamic model and the influence of steady discontinuous ocean current disturbances, thus the spatial curve path following control system possesses stronger robustness and higher accuracy for underactuated UUV.
引文
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