【作者】 韩大鹏；

【导师】 李泽湘； 韦庆；

【作者基本信息】 国防科学技术大学 ， 控制科学与工程， 2008， 博士

【摘要】 任务空间是机械系统的一种典型位形空间,在几何上对应了李群SE(3)。任务空间的控制问题涵盖了丰富的研究对象,但由于任务空间复杂的空间结构,任务空间控制的相关理论研究进展缓慢,而且与工程应用相距甚远。本论文的研究是针对任务空间控制理论研究的缺陷和应用的需求开展的,着重关注任务空间控制的两个难点问题:由李群的矩阵表示带来的运算负担问题,以及无侧移运动控制问题。论文的前半部分面向全任务空间控制问题,致力于减轻控制算法的运算负担。针对姿态控制和位姿控制问题,用四元数代数工具代替矩阵作为空间表示的手段,寻找可以简化计算、同时可以充分利用空间结构特点的控制方法,主要取得了以下三个方面的成果:1.建立了单位四元数和归一化对偶四元数的李群结构,借助单位四元数李群Q_u和对偶四元数李群DQ_u的李代数,分别构造了姿态控制和位姿控制的广义比例—微分控制律,妥善处理了四元数表示方式带来的双平衡点问题,针对全驱动模型实现了镇定控制和跟踪控制。2.使用单位四元数进行了最优姿态控制和旋转轨迹设计的研究:针对自由漂浮空间机器人卫星基座姿态自调整问题,借助Q_u的李代数,使用线性系统最优控制理论实现了具有能量优化特性的姿态控制;针对具有最小加速度约束的两点旋转插值问题,使用多项式样条给出了两点距离较小时的近似解析解。3.使用对偶四元数位姿控制的思想,开展了多体系统控制问题的研究:针对多自由度机械臂,给出了具体模型与广义PD控制律相结合的设计实例;以多自由度机械臂为例推导了全任务空间镇定控制律;提出了双任务空间控制的概念,设计了自由漂浮空间机器人的基座最小扰动控制律。另一方面,考察以飞行器为典型代表的无侧移运动,其模型特性导致难以进行统一的位姿控制,为此对质点轨迹规划和无侧移运动模型分析两个子问题展开研究。此外,作为无侧移运动的一种简化形式,地面移动机器人的控制需要寻找仅依赖角度测量信息的控制律。论文的后半部分着重研究无侧移运动控制的相关问题,取得了三个方面的成果:4.实时轨迹规划:针对恒速质点运动这类典型运动形式,结合飞行器制导设计的思想,依靠视线方位角的变化信息产生法向加速度,从而完成实时轨迹规划。其中视线方位的描述可以使用李群或者旋量进行,由此分别得到了两种实时轨迹规划的方法,在作为制导律使用时,能够克服传统方法依赖通道解耦进行三维制导设计的缺陷,且实现了多约束制导的部分要求。5.模型分析:对无侧移运动的微分平坦分析指出,运动维度的变化影响运动性能。由于运动维度低,基于现有的执行机构,二维无侧移运动自然是微分平坦的;三维无侧移质点运动在线速度不变的情况下是微分平坦的,而运动刚体的主轴与速度矢量的相对方位是进行三维无侧移运动动力学建模与控制的关键。6.控制律设计:对三维无侧移运动的微分平坦输出进行设计,得到了一种恒速质点运动生成轨迹的新方法;对二维无侧移运动模型的微分平坦输出进行设计,可以实现统一的位姿镇定和轨迹跟踪控制律;进行路径跟踪时,设计恰当的微分平坦输出,使用精确线性化方法推导了路径跟踪控制律;在仅有视线角度测量信息的条件下,改造现有的平面比例导引律,增加对线速度的控制,实现了具有能量优化特性的位姿控制。全文的研究采用了代数方法与几何方法结合的思想、空间分解的思想,深化了任务空间上多种运动形式的控制和规划问题的研究,为多自由度机械臂全任务空间控制问题和飞行器制导控制一体化问题的最终解决创造了条件。更多还原

【Abstract】 Task-space is a typical configuration space of mechanical systems, whose geometrical correspondence is the Lie-group SE(3). The control problem on task space covers a variety of cases under research. However, due to the complexity of the space structure, theoretical research on task-space control advances slowly while being away from engineering applications. It is the defects of current research and the demands from engineering applications that initiates the research in this thesis, which focuses on two key issues of task-space control: the computation burden brought by matrix description of Lie-groups, and the no-literal-drift motion control.The first half of this thesis aims at releasing the computation burden within control schemes, in seeking solution for whole task space control. Research on attitude control and posture control were carried out via the usage of quaternion algebra as representing tools, aiming at control schemes with both computational efficiency and utilization of task- space’s geometric structures. The main achievements lay in the following three aspects.1. The Lie-group structures of unit quaternions and normalized dual quaternions were formulated. Thereafter, generalized proportional-derivative(PD) control laws were developed for attitude control and posture control respectively, aiding by the Lie-algebras of the unit-quaternion Lie-group (Q_u) and the dual-quaternion Lie-group (DQ_u). With proper handling of the double-equilibrium problem brought by quaternion-like representations, both regulation and trajectory tracking control were realized for fully-actuated models.2. Research on optimal attitude control and rotational trajectory design were carried out using unit quaternion. In the case study carried on the reorientation problem of free-floating space robot(FFSR), orientation control that can optimizing energy was achieved utilizing the Lie-algebra of Q_u and DQ_u. In discussing the two-point rotating interpolation problem with minimum acceleration, approximate analytical solutions were proposed using polynomial splines.3. Research on control of multi-body mechanisms was carried out based on the notion of using dual-quaternion in posture control. The case study of multi-freedom manipulator shows how to combine a specific system model with the generalized PD law within the structure of the dual-quaternion Lie-Group DQ_u. Regulation law in whole task space was deduced, inducing the notation double task space control which leads to a control law for FFSR with minimum disturbance for the basement.On the other hand, observing driftless motion which has aircrafts as the typical example, the model’s characteristics makes it difficult to perform posture control, leading to the research on two sub-problems: trajectory planning of particles, and model analysis of driftless motion. Also, as a simplified version of driftless motion, control of ground mobile robots calls for a control scheme depending merely on angle detection. The latter part of the thesis has been focused on related problems of driftless motion control, arriving at achievements in three aspects.4. Achievements in real-time trajectory planning: Focusing on the typical motion of moving particles with constant speed, combining with the notion of aircraft guidance, using the information brought by the variation of line-of-sight(LOS)’s orientation, the literal accelaration was calculated and real-time trajectory planning was accomplished. Description of the LOS’s orientation can be performed by Lie-group or twist, yielding two algorithms for real-time trajectory planning. The two algorithms can also be used as guidance laws, which can fix the defects in traditional method where decoupling of channels were demanded, and partly meet the demands in multi-constraints guidance.5. Achievements in model analysis: The analysis of driftless motion points out that, the degree-of-freedom(DOF) of motion affects motion particularity. With the known actuators, 2-dimensional(2D) driftless motion is naturally differential flat due to its minor DOFs. For 3-dimensional(3D) driftless motion, the kinematic model is differential flat only when the longitudinal velocity is constant, and the key for dynamic modeling and control is the relative rotation between the body axis and the velocity vector.6. Achievements in control law design: A design on the flat output of 2D driftless motion results in a unified control law for both posture stabilization and trajectory tacking. When performing path following, the system was simplified to be 1-dimensional; With proper design of flat output, control law can be developed via exact linearizing. When only angle measurement of LOS was available, revising existing 2D guidance law, adding a control on the longitudinal velocity, posture stabilization with certain optimization was developed. For 3D driftless motion, design on the flat output, a new algorithm for trajectory generation is achieved for particle motion with constant speed.The idea of combining algebraic method with geometric method, together with the skill of space decomposition, was utilized in the thesis, which deepens the research on control and trajectory planning of various kind of motion in task-space, and pave the way for a final solution to both the control of manipulators in whole task space and integrated guidance-control of aircrafts.更多还原