Robotic arms require precise, task-aware trajectory planning, yet sequence models that ignore motion structure often yield invalid or inefficient executions. We present a Path-based Transformer that encodes robot motion with a 3-grid (where/what/when) representation and constraint-masked decoding, enforcing lattice-adjacent moves and workspace bounds while reasoning over task graphs and action order. Trained on 53,755 trajectories (80% train / 20% validation), the model aligns closely with ground truth -- 89.44% stepwise accuracy, 93.32% precision, 89.44% recall, and 90.40% F1 -- with 99.99% of paths legal by construction. Compiled to motor primitives on an xArm Lite 6 with a depth-camera digital twin, it attains up to 97.5% reach and 92.5% pick success in controlled tests, and 86.7% end-to-end success across 60 language-specified tasks in cluttered scenes, absorbing slips and occlusions via local re-grounding without global re-planning. These results show that path-structured representations enable Transformers to generate accurate, reliable, and interpretable robot trajectories, bridging graph-based planning and sequence-based learning and providing a practical foundation for general-purpose manipulation and sim-to-real transfer.