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基于纤维丛理论的二维蛇形机器人建模与控制方法研究
Alternative TitleModeling and Control of a Planar Snake-like Robot Based on the Fiber Bundle Theory
郭宪1,2
Department机器人学研究室
Thesis Advisor马书根 ; 王越超
ClassificationTP242
Keyword蛇形机器人 多体动力学 几何力学建模 微分几何 步态控制
Call NumberTP242/G96/2015
Pages116页
Degree Discipline机械电子工程
Degree Name博士
2015-11-28
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract蛇形机器人是由多个模块通过旋转关节前后串联而成,是典型的多刚体移动基座欠驱动系统。它通过周期地改变身体的形状(驱动自由度)与环境相互作用从而实现整个身体的位置和姿态的改变(欠驱动自由度)。将蛇形机器人整个身体的位置和姿态的改变称为整体运动,通常以头部位姿或质心的位姿来表示。对整体运动进行控制时,已有的方法是事先给定步态形式,通过调整步态参数来实现。这种方式需要传感器数据和较长的调整时间,有时甚至无论如何调整步态参数都无法实现给定的整体运动。本文“反其道而行”,通过研究蛇形机器人整体运动与步态之间的关系,实现由整体运动自动生成或选择所需步态。围绕着这个目标本文进行以下方面的研究: 1.基于纤维丛理论对陆地二维蛇形机器人进行运动学和动力学建模对于n模块二维陆地蛇形机器人,其头部位置和姿态构成二维特殊欧式群G=SE(2),n-1个关节角构成Sn-1 ,因此构型空间为G×Sn-1,构成一个主纤维丛。为了模仿生物蛇腹部鳞摩擦方向异性的特点,蛇形机器人每个模块都安装了一个被动轮。在蛇形机器人运动过程中,被动轮侧向无滑移,因此每个模块引入了一个非完整约束。对于n模块蛇形机器人,可以利用n个非完整约束构造约束联络,从离散体的视角得到蛇形机器人整体运动与步态之间的显示关系。 将二维陆地蛇形机器人视为连续变形梁时,其构型空间为G×S,此时S为身体形状曲线空间。利用速度连续模型可构造连续体联络,从连续体的视角得到蛇形机器人整体运动和身体曲线的显示关系。考虑非完整约束,对蛇形机器人进行动力学建模时可将动力学方程约化到速度分布空间中。对速度分布空间基底进行纤维丛建模,选择正交归一化基底和伪速度,利用玻尔兹曼方程得到蛇形机器人的动力学方程,这种方法可使得动力学方程的复杂度约化为自由度的一次函数。 2. 利用纤维空间控制方法对蛇形机器人的运动进行控制蛇形机器人的整体运动等价于蛇形机器人在纤维空间中的运动,而纤维空间的运动与步态之间运动学关系可用联络来表示。在研究了纤维空间的可控性之后,考虑约束联络时,本文提出基于速度扰动的控制方法,由约束联络和扰动速度反向生成步态。该方法的优势是步态并非预先选定的,而是由目标速度和联络关系生成的,而且采用该步态时,侧向无滑移同时避免了奇异位形。考虑连续体运动联络时,本文提出基于波动方程的控制方法。该方法能给出蛇形机器人整体运动的波动方程,将蛇形机器人的运动控制简化为三个有物理意义的参数控制。另外,为了实现上述步态,本文提出基于最小无穷范数力矩补偿和最小侧向摩擦力力矩补偿控制算法。 3. 基于纤维丛理论生成水下蛇形机器人广义步态水下二维蛇形机器人的构型空间也为SE(2)×Sn-1,同样构成主纤维丛。为了得到主纤维丛的联络,将蛇形机器人与周围的流体视为整体,利用拉格朗日法对水下蛇形机器人进行动力学建模。由于初始状态为静止状态,所以蛇形机器人与水的整体动量为零,利用动量守恒可得到水动力联络,进而得到水下蛇形机器人整体运动与步态的关系。为了将纤维空间的运动分量转化为直观的面积积分,本文引入投影矩阵,将多关节自由度投影到两维空间,得到步态平面图,利用步态平面图设计和分析广义转弯步态和前向运动步态,为了验证所设计步态的有效性利用迭代牛顿- 欧拉法进行仿真,利用探查者~III~进行试验验证。综上所述,将纤维丛理论引入到蛇形机器人的建模与控制中从几何的角度揭示了蛇形机器人整体运动与步态之间的关系,不仅可以丰富研究蛇形机器人的手段,简化蛇形机器人的运动学和动力学方程,而且能从更直观更高的角度去设计蛇形机器人的步态。
Other AbstractA snake-like robot is consisted of serial chains of rigid modules connected by rotating joints, which is also a classical mobile base multi-body under-actuated system. The snake-like robot changes its shape of body periodically(actuated degrees of freedom) to realize the change of the pose of the whole body(under-actuated degrees of freedom) by interaction between the body and its surrounding. The change of the pose of the whole body is called the whole movement which are often represented by the pose of the head or the pose of the center of mass. In order to control the whole movement, the existed method is to adjust the parameters of the gaits which are given in advance. Using this method, sensor data is needed and long adjustment time is spent. Some time the desired whole movement even can not be realized no matter how to a adjust the parameters of gaits. In this paper, we deal with this problem in the opposite direction. By studying the relation between the gaits and the whole movement, the gaits can be generated automatically or chosen from the desired whole movement. Surrounding this goal, the following studies are made: 1. The kinematics and dynamics model is proposed based on the fiber bundle theory for the terrestrial planar snake-like robot. For the n links terrestrial planar snake-like robot, the position and posture angle of the head compose the Special Euclidean group SE(2) , the n-1 joint angles compose Sn-1, so the configuration space is G×Sn-1 that is a principle fiber bundle. In order to imitate the friction anisotropy of the snake's belly, passive wheels are installed in the middle of the terrestrial planar snake-like robot. Each link can not move laterally which introduce a nonholonomic constraint. For an n-links snake-like robot, the fiber connection can be derived by the n nonholonomic constraints. So the relation between the net pose and gaits is derived from the view of the discrete multi-body. Additionally, the snake-like robot can be considered as the deformed beam and its configuration is G×S that is also a fiber bundle, where S is a curve space. Using the continuous velocity model, the continuum connection can be derived. So the relation between the net pose and gaits is derived from the view of the continuum. Considering the nonholonomic constraints, the feasible velocity space is a velocity distribution space. The dynamics equation can be projected to the distribution space by choosing orthogonal normalization base. The base can also be modeled by fiber bundle theory. 2. The locomotion control algorithms for the planar snake-like robot is derived based on the fiber bundle theory. The movement of the whole body for the snake-like robot equals the locomotion in fiber space. The fiber velocity can be derived from the connection. Considering the nonholonomic constraints, this paper proposes a method, which can derive the gaits from the connection. The advantage is that the gait is not preset but derived from the target velocity and the connection. Additionally, considering the continuum model, this paper also proposes a control method based on the wave equation. In order to optimize the torque, this paper proposes torque compensation method based on the minimum infinity norm considering the torque and side friction. 3. General gaits for the underwater planar snake-like robot based on the fiber bundle theory. The configuration space for the underwater planar snake-like robot is also a manifold SE(2)× Sn-1, which is also a principle fiber bundle. In order to derive the connection, considering the snake-like robot and the surrounding fluid as a whole, the dynamics equations can be derived by using the Lagrange method. Since the robot begins at rest, the total momentum of the robot and fluid remains identically zero through the motion of the robot. So the hydrodynamic connection can be constructed. In order to transform the motion into the intuitive geometric figure, the projection matrix is introduced and the gait planar figure is derived. The gait planar figure is used to design and analyze the general turning gait and forward gait. Finally, the iterative Newton-Euler method and the Perambulator III are used to prove the chosen gait .All in all, introducing the fiber bundle theory to the modeling and control of the snake-like robot reveals the locomotion relation between the net pose and gaits, which not only riches the study method for the snake-like robot and simplifies the kinematics and dynamics equations, but also are valuable for gaits design and the control of the snake-like robot from higher views.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/17536
Collection机器人学研究室
Affiliation1.中国科学院沈阳自动化研究所
2.中国科学院大学
Recommended Citation
GB/T 7714
郭宪. 基于纤维丛理论的二维蛇形机器人建模与控制方法研究[D]. 沈阳. 中国科学院沈阳自动化研究所,2015.
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