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Design and Analysis of Swing-up Control for a 3-Link Gymnastic Robot with Passive First Joint

机译:具有被动第一关节的3联合体操机器人摆动控制的设计与分析

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This paper concerns a swing-up control problem for a 3-link gymnastic planar robot in a vertical plane, whose first joint is passive (unactuated) and the rest are active (actuated). The objectives of this paper are: 1) to design a controller under which the robot can be brought into any arbitrarily small neighborhood of the upright equilibrium point, where all three links of the robot remain in their upright positions; 2) to attain a global analysis of the motion of the robot under the controller. To tailor the energy based control approach to achieve the above objectives, first, this paper considers the links 2 and 3 as a virtually composite link and proposes a coordinate transformation of the angles of active joints. Second, this paper constructs a novel Lyapunov function based on the transformation, and devises an energy based swing-up controller. This paper presents a necessary and sufficient condition for nonexistence of any singular points in the controller for the robot starting from any initial state. Third, this paper carries out a global analysis of the motion of the robot under the controller, and establishes some conditions on control parameters for achieving the swing-up control objective. To validate the theoretical results obtained, this paper provides simulation results for a 3-link robot whose mechanical parameters are obtained from a human gymnast.
机译:本文涉及一种用于在竖直平面内,其第一接头是被动的(未致动),其余的3连杆体操平面机器人的摆动机控制问题是活动的(致动)。本文的目标是:1)来设计的控制器在其下机器人可被带入直立平衡点,其中机器人的所有三个链接保持在其直立位置中的任何任意小邻域; 2)以获得所述控制器根据所述机器人的运动的全局分析。以定制的基于能量控制的方法来实现上述目标,首先,本文考虑的链接2和3几乎复合链路,提出了有源关节的角度的坐标变换。第二,构建基于变换的新的Lyapunov函数,和图谋基于能量摆起控制器。本文介绍了一种在控制器中对任何初始状态开始的机器人任何奇异点的有无的必要和充分条件。第三,本文执行控制器下机器人的运动的全局分析,并建立关于控制参数的一些条件为实现摆起控制目标。为了验证所获得的理论计算结果,本文提供了一种用于3-连杆机器人,其机械参数从人体操运动员获得的模拟结果。

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