Robotic joint-motion optimization of functionally-redundant tasks for joint-limits and singularity avoidance

The research objective of this thesis is to develop a redundancy-resolution (RR) algorithm to optimize the joint space trajectory of six-revolute industrial robot as performing manufacturing tasks.

Most of machining operations, such as welding, deburring or milling, have a symmetry axis. Clearly, the rotation of the tool around the symmetry axis is irrelevant to the view of the task to be accomplished. If the task is performed with a six-rotation-axis industrial robot, there is one degrees of freedom (DOF) of kinematic redundancy, which provides the potential of optimization. This kind of redundancy is called as functional redundancy, with contrast to intrinsic redundancy well known by most researchers. Functionally-redundant tasks have very common existence in the industrial robotic field, but still are ignored by most researchers.

Concerning the requirement for applying industrial robot in manufacturing, this thesis proposes a new redundant-resolution approach to solve functionally-redundant robotic tasks. This approach is called Twist Decomposition Approach (TWA). Instead of projecting an optimization criterion onto the null space of the Jacobian matrix as most of the redundancy-resolution schemes do, TWA firstly decomposes the Cartesian twist of the end-effector into two suitable subspaces; one being the subspace where the main task undergoes, while the other one being the redundant subspace. Then, the task can be optimized on the redundant subspace of the twist. In this thesis, joint-limits and singularity avoidance are considered as the two main optimization objectives.

TWA has been demonstrated to be able to optimize effectively the joint space trajectory for various tasks and various types of industrial robots. The possible application of TWA include welding, milling, deburing, painting, laser cutting and many other tasks requiring less than six-DOF in tool frame.

In order to take the full advantage of TWA's potential, there is a critical issue which need to be addressed. It is the weights that play the role of balancing among the subtasks and contribution of each joint in the optimization. Since the weights have such a great influence on the optimization, and even the task success or failure, the weights adaptation issue deserves more study. In this thesis, two weights adaptation methods are proposed, namely the self-adaptation and dynamic-adaptation methods. Both methods identify sensitivity of weights component firstly. Self-adaptation method proposes the use of a linear space searching method to adapt weights, while dynamic-adaptation method develops some empirical functions to dynamically adapt weights at each instant of the trajectory. Both methods succeed in various tasks. However, dynamic-adaptation method has greater application range and reaches better optimization results, since weights are adapted according to the need of each instant (dynamic-adaptation method), instead of keeping them fixed at certain value (self-adaptation method).

This thesis is composed of seven chapters. Chapter 1 introduces the concept of functionally-redundant tasks, and presents the common existence of the functionally-redundant tasks in the industrial robotic field.

Chapter 2 reviews the research works on kinematic redundancy resolution, including the local and global optimization approaches, and the application of intelligent control techniques. Some other developed functional redundancy resolutions are also introduced.

In Chapter 3, TWA is presented and applied on avoiding joint limits problem, while in Chapter 4, the singularity avoidance is added into the optimization objective of the robot joint space trajectory besides the joint limit avoidance.

Chapters 5 and 6 propose two different methods on adapting weights, self-adaptation method in Chapter 5, and dynamic-adaptation method in Chapter 6.

Finally, the conclusions and future works are presented in Chapter 7.