Laser microforming is extensively used to align components with submicrometer accuracy, often after assembly. While laser-bending sheet metal is the most common laser-forming mechanism, the in-plane upsetting mechanism is preferred when a high actuator stiffness is required. A three-bridge planar actuator made out of Invar 36 sheet was used to characterize this mechanism by experiments, finite element method modeling, and a fast-reduced model. The predictions of the thermal models agree well with the temperature measurements, while the final simulated displacement after 15 pulses deviates up to a factor of 2 from the measurement, using standard isotropic hardening models. Furthermore, it was found from the experiments and models that a small bridge width and a large bridge thickness are beneficial to decrease the sensitivity to disturbances in the process. The experiments have shown a step size as small as 0.1 μm, but with a spread of 20%. This spread is attributed to scattering in surface morphology, which affects the absorbed laser power. To decrease the spread and increase the positioning accuracy, an adapted closed-loop learning algorithm is proposed. Simulations using the reduced model showed that 78% of the alignment trials were within the required accuracy of ±0.1 μm.