Simultaneous control of position and orientation for ball-plate manipulation problem based on time-State control form
Simultaneous control of position and orientation for ball-plate manipulation problem based on time-State control form
复制标题
基于时间-状态控制形式的球盘操纵问题位置与姿态同步控制
DOI：
10.1109/tra.2004.825267
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
M. Koga
中科院分区：
文献类型：
--
作者：
H. Date;M. Sampei;M. Ishikawa;M. Koga
本文讨论了球板操纵问题，它被认为是一个典型而复杂的无漂移非完整系统模型。由于球板系统的强非线性，运动学模型的状态方程不能转化为链式形式，这对于构造一些无漂移非完整系统的反馈控制律是有效的。为了解决这个问题，我们利用了一种时间状态控制形式，这是一种规范形式，它比链式形式涵盖了更广泛的系统类别。这种形式首先应用于两个不同的子问题，位置控制和方向控制，在位置控制中，球的平面位置被控制而不是方向，在方向控制中，在不改变球和板之间的位置关系的情况下控制方向。结果表明，在变换后的子系统中存在一个线性不可控的子空间，该子空间通过坐标的变化变为可控的。这意味着该系统具有具有两个发电机的系统结构。我们提出了一种迭代改变坐标的控制策略，确保在原点附近收敛。最后，我们将这些子问题统一为位置和姿态的同时控制，即系统的整体构型。同时控制中的重要思想是坐标变换，它使我们避免了奇点。仿真结果表明，该方法对测量噪声和球半径摄动具有较好的鲁棒性。
This paper deals with the ball-plate manipulation problem considered as a typical but complicated model of a driftless nonholonomic system. Due to a strong nonlinearity of the ball-plate system, a state equation of the kinematic model cannot be transformed into a chained form, which is known to be effective in constructing a feedback control law for some driftless nonholonomic systems. To address this problem, we utilize a time-state control form, a kind of canonical form which covers a broader class of systems than the chained form. This form is first applied to two separate subproblems, position control, in which the planar position of the ball is controlled but not the orientation, and orientation control, in which the orientation is controlled without changing the positional relation between the ball and the plates. It turns out that there exists a linearly uncontrollable subspace in the transformed subsystem, which turns into controllable by a change of coordinates. This implies that the system has the structure of a system with two generators. We propose a control strategy using iterative changes of coordinates, ensuring convergence in the neighborhood of the origin. Finally, we unify the subproblems into simultaneous control of position and orientation, i.e., the whole configuration of the system. The important idea in the simultaneous control is the coordinate transformation, which enables us to avoid a singular point. Results of simulations show that the proposed method achieve robustness to a measurement noise and perturbation of radius of the ball.