# α-Potential Game

Task allocation for collaborative robotic welding of dissimilar steel joints no longer divides work by robot-to-seam distance alone. The framework treats each robot as a player in an α-potential game and uses a physics-informed neural-network surrogate for repeated thermo-mechanical evaluation, so allocation accounts for residual stress and carbon-depleted-zone width. Across computational cases with 50 tasks and 2 robots, 100 tasks and 3 robots, and 200 tasks and 4 robots, it reduced normalized makespan and energy relative to distance-driven allocation while keeping lower predicted residual stress and carbon-depleted-zone width; these are computational predictions requiring independent experimental validation.

Task allocation for collaborative robotic welding of dissimilar steel joints no longer divides work by robot-to-seam distance alone. The framework treats each robot as a player in an α-potential game and uses a physics-informed neural-network surrogate for repeated thermo-mechanical evaluation, so allocation accounts for residual stress and carbon-depleted-zone width. Across computational cases with 50 tasks and 2 robots, 100 tasks and 3 robots, and 200 tasks and 4 robots, it reduced normalized makespan and energy relative to distance-driven allocation while keeping lower predicted residual stress and carbon-depleted-zone width; these are computational predictions requiring independent experimental validation.