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基于微分几何的蛇形机器人动力学与控制统一模型
Alternative TitleDynamics-control unified model of a snakelike robot based on differential geometry
郭宪; 马书根; 李斌; 王明辉; 王越超
Department机器人学研究室
Source Publication中国科学:信息科学
ISSN1674-7267
2015
Volume45Issue:8Pages:1080-1094
Indexed ByCSCD
CSCD IDCSCD:5526893
Contribution Rank1
Funding Organization国家自然科学基金(批准号:61333016)资助项目
Keyword蛇形机器人 非完整约束 微分几何 动力学与控制 纤维丛
Abstract蛇形机器人进行力矩控制时,其动力学系统为非线性控制系统.当蛇形机器人模块数增大时,非线性系统变得冗繁而不易于计算和控制.本文利用微分几何的方法,将欧拉—拉格朗日(EulerLagrange)动力学方程进行了扩展,得到了任意基底下的动力学方程,将蛇形机器人的动力学方程化简成标准的仿射控制系统方程,得到动力学与控制统一的模型,使得蛇形机器人的动力学方程变得简洁易于计算和控制.基于此模型,利用部分反馈线性化的方法将控制方程进行线性化,并设计了头部轨迹跟踪控制器.蛇形机器人的构型空间对应着流形空间,速度空间对应着切空间,力矩空间对应着余切空间,动能提供了流形空间上的一个黎曼(Riemann)度量,因此...
Other AbstractWhereas the inputs for a snakelike robot are torques, the dynamics system is a nonlinear control system. With increasing modules in a snakelike robot, its nonlinear control system becomes complex and inconvenient for regulation and control. In this paper, the differential geometry method is used, and the Euler-Lagrange equations are extended to equations under any base. Thus, the dynamics equations are reduced to the standard affine control system, and the dynamics-control unified model is derived; this simplifies the regulation and control of the snakelike robot. Based on the unified model, a partial feedback linearization method is developed, and the head trajectory controller is designed. The configuration space of a snakelike robot corresponds to the manifold space, the velocity corresponds to the tangent space, the torque space corresponds to the cotangent space, and the kinematic energy provides a Riemann measure on the manifold. Thus, the dynamics of a snakelike robot can be described by Riemann geometry. Additionally, the passive wheels installed under the snakelike robot introduce the velocity constraint, which constrains the velocity space to a subspace of the tangent space. That is, the velocity space forms a distribution, and the dynamics system becomes a nonholonomic dynamics system. For a snakelike robot with passive wheels, the configuration is a Riemann manifold with a distribution. In the distribution, the appropriate base can be chosen to simplify the dynamics. In this paper, a base model is built based on the fiber bundle theory. Any set base is only a section in the fiber bundle. The orthogonal normalization technique is adopted to derive a set base that can simplify the dynamics calculation, and the dynamics-control unified model is derived. Finally, a nine-module snakelike robot is used as an example of the partial feedback linearization method.
Language中文
Citation statistics
Cited Times:2[CSCD]   [CSCD Record]
Document Type期刊论文
Identifierhttp://ir.sia.cn/handle/173321/17147
Collection机器人学研究室
Affiliation1.中国科学院沈阳自动化研究所机器人学国家重点实验室
2.中国科学院大学
3.日本立命馆大学机器人系
Recommended Citation
GB/T 7714
郭宪,马书根,李斌,等. 基于微分几何的蛇形机器人动力学与控制统一模型[J]. 中国科学:信息科学,2015,45(8):1080-1094.
APA 郭宪,马书根,李斌,王明辉,&王越超.(2015).基于微分几何的蛇形机器人动力学与控制统一模型.中国科学:信息科学,45(8),1080-1094.
MLA 郭宪,et al."基于微分几何的蛇形机器人动力学与控制统一模型".中国科学:信息科学 45.8(2015):1080-1094.
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