Optimal Trajectory Selection for a Three DOF Manipulator with Minimum Energy Consumption

Trajectory planning of redundant manipulator is a very active area since many tasks are requiring special characteristics to be satisfied. The importance of redundant manipulators has been increased for the last two decades because of the possibility to avoid singularities as well as obstacles within the course of motion. The angle that the last link of a 3 DOF manipulator makes with the x-axis is required to find the solution for the inverse kinematics problem. This angle needs to be optimized while the end effector performs two trajectories in the task space: A straight line between two arbitrary points and a circle. Geometric approach is carried out to identify the boundaries of the maximum reach corresponding to tow different trajectories of the end effector. On the other hand, the Genetic Algorithm is utilized to optimize the angle within the set range and to make sure that the end effector follows the prescribed trajectory with minimum kinetic energy. Numerical simulation for the two trajectories of the end effector is presented to validate the proposed algorithm.