This study presents a methodology for determining the optimal base placement of a Fanuc CRX10iA/L collaborative robot for a desired trajectory corresponding to an industrial task. The proposed method uses a particle swarm optimization algorithm that explores the search space to find positions for performing the trajectory. An $α$-shape algorithm is then used to draw the borders of the feasibility areas, and the largest circle inscribed is calculated from the Voronoi diagrams. The aim of this approach is to provide a robustness criterion in the context of robot placement inaccuracies that may be encountered, for example, if the robot is placed on a mobile base when the system is deployed by an operator. The approach developed uses an inverse kinematics model to evaluate all initial configurations, then moves the robot end-effector along the reference trajectory using the Jacobian matrix and assigns a score to the attempt. For the Fanuc CRX10iA/L robot, there can be up to 16 solutions to the inverse kinematics model. The calculation of these solutions is not trivial and requires a specific study that planning tools such as MoveIt cannot fully take into account. Additionally, the optimization process must consider constraints such as joint limits, singularities, and workspace limitations to ensure feasible and efficient trajectory execution.