中间关节为欠驱动的平面多连杆二阶非完整系统分段控制方法

The project studies the control method and robustness design problem of planar second-order nonholonomic systems by taking a planar multi-link systems with an underactuated middle joint as object. A piecewise control method is presented to divide the system into a planar virtual second-order nonholonomic system with the underactuated last joint and a planar virtual first-order nonholonomic system with the underactuated first joint according to the structure characteristics of the underactuated middle joint. A model reduction method is studied to reduce the planar second-order nonholonomic system into a planar virtual first-order nonholonomic system by determining the target region of the underactuated joint according to the geometric relation of the system, and by realizing the control object of the underactuated joint based on the nonlinear characteristics of the planar virtual second-order nonholonomic system. A stability control strategy based on a continuous state feedback is presented to design the controllers based on the actuated joints to achieve the control objective of the planar virtual first-order nonholonomic system, where the coupling relationship among all links of the system is used and an online intelligent optimizing algorithm is employed to optimize the control parameters. A robust control design method is studied to restrain the external disturbances and the perturbation of the parameters. A computer simulation and experiment platform of the system is established for the control performance analysis and practical application research. This project will provide a feasible and effective new method for the control and robustness design of planar second-order nonholonomic systems, and has important theoretical significance and applied value.

本项目以中间关节为欠驱动的平面多连杆系统为对象，研究二阶非完整系统的控制方法及鲁棒性设计问题。根据中间关节为欠驱动的结构特点，提出将系统划分为末关节为欠驱动的平面虚拟二阶非完整系统和首关节为欠驱动的平面虚拟一阶非完整系统的分段控制方案；研究模型降阶方法，根据系统几何关系确定欠驱动关节目标区域，基于平面虚拟二阶非完整系统的非线性特性设计控制器，实现欠驱动关节的控制目标，从而将原系统降阶为平面虚拟一阶非完整系统；提出基于连续状态反馈的一阶非完整系统控制策略，根据系统连杆之间的耦合关系，针对驱动关节设计控制器，利用在线智能优化算法优化控制器参数，实现平面虚拟一阶非完整系统的控制目标；研究能够有效抑制外界扰动和克服参数摄动的鲁棒控制设计方法；建立仿真与实验系统，进行控制性能分析与实际控制应用研究。本项目为平面二阶非完整系统控制及鲁棒性设计提供一种有效可行的新方法，具有重要的理论意义和和应用前景。

本项目以中间关节为欠驱动的平面多连杆系统（AmPAn）为对象，研究二阶非完整系统的控制策略及鲁棒性设计方法。通过分析AmPAn系统的结构特点，将系统划分为末关节为欠驱动的平面虚拟AmP系统和首关节为欠驱动的平面虚拟PAn系统，提出了基于两种虚拟系统的分段控制策略；提出了一种模型降阶方法，根据系统几何关系确定欠驱动关节目标区域，基于平面虚拟AmP系统的幂零近似模型与链式结构设计控制器，实现欠驱动关节的控制目标，从而将原系统降阶为平面虚拟PAn系统；提出了通过智能优化方法，寻找适当的驱动连杆目标角度及其相应的控制器设计参数的控制策略，实现平面虚拟PAn系统的控制目标；通过分析AmPAn系统连杆间的耦合关系，提出了基于智能优化算法的轨迹规划与跟踪控制策略，该方法适用于欠驱动关节位于任意位置的机械臂；此外，提出了一种基于神经网络方法的不确定性补偿控制策略和误差在线迭代修正算法，确保系统的控制精度；同时，建立了中间关节为欠驱动的平面多连杆控制实验系统，进一步分析所提方法控制性能。通过本项目的研究，为中间关节为欠驱动的平面多连杆系统的稳定控制及鲁棒性设计提供了有效可行的新方法，具有显著的科学意义和实际应用价值。