Masters Theses

Date of Award

8-1995

Degree Type

Thesis

Degree Name

Master of Science

Major

Mechanical Engineering

Major Professor

Rajiv V. Dubey

Committee Members

Bill Hamel, C. Kawiecki

Abstract

Motion of a manipulator within its workspace is restricted by singularities, joint limits, joint velocity limits and obstacles. To ensure smooth motion of the manipulator, in the presence of the above limitations, the joint motion of the manipulator has to be optimized. To completely control the three position and orientation coordinates of the end-effector in three dimensional space, a minimum of six degrees of freedom are required. A manipulator possessing more than the minimum required degrees of freedom for complete control of the end-effector motion is called a redundant manipulator. Redundant joint motion or self-motion of the manipulator moves the joints of the manipulator without affecting the end-effector position or orientation. A performance criterion is a function of the joint angles of the manipulator for which the manipulator motion is being optimized. The redundant degrees of freedom are used to optimize a performance criterion to overcome the limitations to the manipulator motion. Optimization of the performance criterion is performed by employing schemes to calculate the redundant joint motion in a manipulator. This redundant joint motion or self-motion applied to the manipulator helps in collision avoidance, joint limit avoidance and singularity avoidance. Collision is an inherent problem with manipulators working in environments clustered with obstacles. This thesis is related to the implementation and testing of two optimization schemes for collision avoidance in manipulators. The two schemes, namely "Variable Dimension Task Space" and "Singularity Robust Inverse"[25,26], provide different approaches to solving the problem of collision in manipulators. The Variable Dimension Task Space utilizes the fact that some motion directions in the task space are more relevant to the task than other directions. Neglecting control of the less important motion directions results in an increase in the redundancy of the manipulator. This additional redundancy can be used for optimization of a performance criterion to overcome the problem of collision. On the other hand, the Singularity Robust Inverse uses the existing redundancy for optimization. This method sacrifices the accuracy of the solution for the feasibility of solution. A feasible solution, in this case, is one which helps the manipulator avoid obstacles. The amount of error introduced in the trajectory is dependent on the scale factor and weighting matrices used. To study the effect of the scale factor on the error in the motion of the manipulator, constant and variable scale factors are used in the experiments. The two collision avoidance schemes are implemented and tested on the seven degree of freedom Robotics Research Corporation K2107 manipulator[23]. These schemes are also implemented on the seven degree of freedom Long Reach Manipulator. The Long Reach Manipulator[1-5] is a redundant joint manipulator used in cleanup operations of nuclear waste tanks with hazardous waste. Since the manipulator is operating within the waste tank clustered with obstacles, the tested collision avoidance schemes will help optimize the motion of the Long Reach Manipulator for collision avoidance. Results of experiments for both schemes and their implementation on the RRC K2107 manipulator and the Long Reach Manipulator are presented in this thesis.

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