An Adaptive Second Order Sliding Mode Inverse Kinematics Approach for Serial Kinematic Chain Robot Manipulators

Wael Mohammed Elawady,Ahmed Elmogy,Yassine Bouteraa

doi:10.3390/robotics9010004

Abstract

The problem of inverse kinematics is essential to consider while dealing with the robot’s mechanical structure in almost all applications. Since the solution of the inverse kinematics problem is very complex, many research efforts have been working towards getting the approximate solution of this problem. However, for some applications, working with the approximate robot’s model is neither sufficient nor efficient. In this paper, an adaptive inverse kinematics methodology is developed to solve the inverse kinematics problem in such a way that compensate for unknown uncertainty in the Jacobian matrix of the serial kinematic chain robot manipulators. The proposed methodology is based on continuous second order sliding mode strategy (CSOSM-AIK). The salient advantage of the CSOSM-AIK approach is that it does not require the availability of the kinematics model or Jacobian matrix of the robot manipulators from joint space variables to Cartesian space variables. The global stability of the closed-loop system with CSOSM-AIK methodology is proven using the Lyapunov theorem. In order to demonstrate the robustness and effectiveness of the proposed methodology, some simulations are conducted.

Highlights

The last three decades have witnessed the great and the continuous increase in the number of used robots in industry
An adaptation law is addressed to compensate for the unknown uncertainty of the Jacobian matrix
In 2020, order to validate the feasibility and effectiveness of the proposed inverse kinematics strategy, the developed tested for theofinverse kinematics solution of two strategy, different

Summary

Introduction

The last three decades have witnessed the great and the continuous increase in the number of used robots in industry. Dealing with the robot’s mechanical structure in any way (modeling, simulation, etc.) requires solving the problem of kinematics [3]. In forward kinematics, the position of the end-effector can be expressed as a function of the joint positions [1,2,4] which is simple and straightforward. The inverse kinematics [5] is concerned with finding the joints’ positions for a specified end effector position [3]. The inverse kinematics problem is complex due to the nonlinearity and uncertainty of the mapping equations that maps the joint space to the Cartesian space. It becomes a must to consider the inverse kinematics when coming to deal with certain type of tasks in cluttered environments where robotic manipulators with few DOF are unable to operate [6]

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Results

Conclusion