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Design and Implementation of a Bespoke Robotic Manipulator for Extra-corporeal Ultrasound

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Comprehensive unified control strategy for underactuated two-link manipulators.

Xu-Zhi Lai¹, Jin-Hua She, Simon X Yang

¹School of Information Science and Engineering, Central South University, Changsha, China. xuzhi@mail.csu.edu.cn

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|December 20, 2008

Summary

This summary is machine-generated.

This study unifies motion control for underactuated two-link manipulators like acrobots and pendubots. It introduces novel control laws for swing-up and attractive states, ensuring system stability.

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Area of Science:

Robotics
Control Systems Engineering
Mechanical Engineering

Background:

Underactuated two-link manipulators, such as acrobots and pendubots, present significant challenges in motion control due to their limited actuators.
Existing control strategies often lack a unified approach for different operational states.

Purpose of the Study:

To develop a unified motion control framework for underactuated two-link manipulators.
To design distinct control laws for the swing-up and attractive motion spaces.
To ensure the stability and improve the performance of the manipulator's motion control.

Main Methods:

The motion space is partitioned into swing-up and attractive regions.
A weak-control Lyapunov function (WCLF) is utilized for controlling the actuated link's energy and posture in the swing-up region.
Control law parameters are adapted using nonlinear state-dependent functions to circumvent singularities and enhance performance.
An optimal control law is formulated for the attractive region.
Stability is rigorously proven using LaSalle's invariance principle and a combination of WCLF and nonsmooth Lyapunov functions.

Main Results:

A unified control strategy is presented for underactuated two-link manipulators.
Effective control laws are designed for both swing-up and attractive motion states.
Singularities in control are avoided through adaptive parameter adjustments.
Enhanced control performance is achieved via state-dependent parameter tuning.
Guaranteed stability is demonstrated for the swing-up region and overall system.

Conclusions:

The proposed unified treatment provides a robust and stable motion control solution for underactuated two-link manipulators.
The integration of WCLF and nonsmooth Lyapunov functions ensures global system stability.
The adaptive control approach enhances maneuverability and performance across different operational regimes.