Kinematic Isotropy and Robot Design Optimization using A Genetic Algorithm Method

The optimal kinematic design of robots is an interesting problem in contemporary robotics. It is important to have measures for determining the precision of the mechanism and size of the robot manipulator at the design phase. This all has been done before mostly on the basis of experience. The most essential issue for setting up any measures seems to be the ease of changing arbitrarily the position and orientation of the endeffector at the tip of the manipulator. In the majority of recent works on optimal robot design, one of the most important criteria is that the robot can achieve isotropic configurations. The operation near isotropic configuration is considered as a high performance for robotic manipulators. At these configurations, the best servo accuracy can be achieved, the likelihood of error is equal in all directions, and equal forces may be exerted in all directions [29]. A measure of isotropy called the Global Isotropy Index or G i l [49] has been used in this work, which is based on the robot behavior in the entire workspace. The G i l is computed as the ratio of the minimum singular value of a robot's Jacobian matrix to the maximum one throughout its workspace. In search for finding the optimum design parameters that provide the most isotropic performance, the positions that offer the minimum ratio of singular values for each set of design parameters are compared to each other to find the maximum one. This strategy illustrates in fact a minimax optimization problem. A "Genetic Algorithm" has been developed to optimize the minimax problem in order to find optimal design parameters such as link lengths of the best isotropic robot configurations at optimal working points of the end-effector and later, it has been implemented to optimize globally throughout the whole robot workspace. The method has been demonstrated for two types of robotic manipulators.