Robust Robot Placement and Tool Geometry Optimization for Continuous Cutting and Welding Trajectories Under Positioning Uncertainty

Abstract This article presents a task-oriented computational framework for robot base placement and tool center point (TCP) selection in continuous robotic applications such as welding and cutting, with a particular focus on robustness to placement inaccuracies. Rather than searching for a single optimal configuration, the proposed approach aims to identify feasible placement regions and to quantify their robustness with respect to positioning deviations, which are common in industrial deployments, especially for mobile or reconfigurable robotic systems. The method relies on kinematic trajectory simulation, including inverse kinematics initialization, singularity detection, joint-limit enforcement, and collision checking. A particle swarm optimization strategy is employed as a guided exploration mechanism to efficiently sample the configuration space and identify feasible regions without resorting to exhaustive grid-based sampling. Feasibility regions are reconstructed using an α-shape algorithm, and robustness is quantified through a geometric criterion defined as the radius of the largest admissible placement tolerance, computed via a Voronoi-based largest inscribed circle method. In addition, TCP geometric parameters are incorporated into the optimization through a catalog-based discretization that reflects industrial tooling constraints. The proposed framework is validated on two industrial case studies involving continuous cutting and welding trajectories using different robotic platforms: the Fanuc CRX10iA/L and the WeezLight collaborative robot developed by Weez-U Welding. The results demonstrate the ability of the method to efficiently identify robust placement regions and suitable TCP configurations.