Unified formulation of robotic systems with holonomic and nonholonomic constraints
Unified formulation of robotic systems with holonomic and nonholonomic constraints
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DOI：
10.1109/70.704238
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发表时间：
1998-08
期刊：
影响因子：
--
通讯作者：
X. Yun;N. Sarkar
中科院分区：
文献类型：
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作者：
X. Yun;N. Sarkar
许多机器人系统受到非完整约束和完整约束。两个刚体之间的滚动接触是这种系统的典型示例。在这项研究中，一个统一的状态空间制定的机器人系统受到完整和非完整约束。首先用一组渐近收敛于原完整约束的速度级约束方程代替位置级完整约束。在用一种通用的形式表示完整约束和非完整约束后，给出了约束系统的状态空间表示。还描述了用于实现状态空间表示的数值算法。所提出的配方消除了需要解决完整的约束无论是解析或数值，并确保完整的约束总是满足，特别是在计算机模拟。该公式使得在统一的框架下处理具有完整约束、非完整约束或完整约束和非完整约束的系统成为可能。文中给出了两个例子来说明统一公式的应用。
Many robotic systems are subject to nonholonomic as well as holonomic constraints. Rolling contact between two rigid bodies is a typical example of such a system. In the study, a unified state space formulation of robotic systems subject to both holonomic and nonholonomic constraints is presented. The position-level holonomic constraints are first replaced by a set of velocity-level constraint equations that asymptotically converge to the original holonomic constraints. Having represented both holonomic and nonholonomic constraints in a common form, a state space representation of the constrained systems is then developed. A numerical algorithm for implementing the state space representation is also described. The proposed formulation eliminates the need to solve holonomic constraints either analytically or numerically, and ensures that holonomic constraints are always satisfied, particularly in computer simulations. The formulation makes it possible to treat systems with holonomic constraints, with nonholonomic constraints, or with both holonomic and nonholonomic constraints in a unified framework. Two examples are presented to illustrate the application of the unified formulation.