This dissertation examines the trajectory planning problem for the end-effector of any redundant robot manipulator which operates in an environment with obstacles. The main goal was: introducing, using, and examining the performance and ability of genetic algorithms (gas) to solve the problem. The dissertation's results show that gas can be successfully applied to the solution of this problem. Their main contributions are: 1. Gas are independent of the robot's anatomy, 2. Gas are independent of the type of the desired task, 3. Can be easily manipulated by the user, 4. Provide robust search in large and complex spaces with discontinuities and non-linearities.