## 1 Introduction  
Laser-material processing is gaining importance in different fields of applications due to the contactless energy input, high intensities and high flexibility in manufacturing components based on various materials [1; 2]. Laser-beam welding is highly attractive for these reasons and widely used in different industrial sectors, e.g., for manufacturing processes in automotive industry [3], electronics [4], and household appliances [5; 6]. These industries are accompanied by large production quantities and require automated processes. The demands on economic efficiency are increasing at the same time, i.e., minimization of rejects and increased flexibility of production are required. Adaptive and flexible production processes are gaining relevance in the field of laser welding for these reasons, allowing an in-process adjustment of various control parameters. First, this requires process data to be obtained from the welding process itself and these must be related to the material behavior and resulting seam imperfections [7]. Second, an adjustment of process conditions during welding must occur. Mostly, laser-dependent conditions are considered for an active adjustment nowadays, e.g., via controlling the beam power for specific events [8] or continuously [9], manipulating the beam shape [10] or adjusting the beam position [11]. This enables deviations in penetration depth, melt-pool geometry and laser-beam trajectory to be addressed and minimized, for example, while actively manipulating the workpiece position or geometry is not currently state of the art. The welding process leads to an inhomogeneous and transient temperature distribution, resulting in residual stresses that can cause deformation [12]. Distortion is based on plastic deformation and induces a displacement of the parts to be welded, which affects the energy deposition in the workpiece [13] and causes changes in weld-seam geometry and penetration depth in particular [14]. The process is interrupted when the displacement reaches a critical gap size, i.e., the melt pool is no longer able to bridge the gap between the parts to be welded, or the laser beam is transmitted through the gap in the case of butt welds [15]. These challenging weld discontinuities are material dependent [12] and well-known for laser beam welding of high-alloy steels highly tending to thermal distortion due to due their low thermal conductivity and high thermal expansion [15; 16]. A precise prediction is not possible, as batches have each different material histories, which then also manifest themselves in differently pronounced distortion [16]. This problem can be countered by exceedingly massive and therefore cost-intensive fixtures [17]-or by an adjustment the workpiece position or clamping situation directly. It was shown that the manipulation of the workpiece and the clamping situation can significantly effect resulting residual stresses and thus distortion [18]. The possibility of workpiece handling and welding via two robots was also demonstrated, however, high distortion was found to be critical for such non-adaptive jigless welding setups [19]. Therefore, certain defect patterns caused by distortion require process control and workpiece manipulation capabilities to counteract workpiece displacement by adaptively adjusting the resulting gaps through the clamping device. This requires the utilization of sensors to detect the gap on the one hand and actuators to enable mechanical intervention on the other hand. The gap can be detected directly via non-contact sensors integrated in the processing optics or mounted to it, e.g., by triangulation [20] or imaging [21]. A different approach is the integration of sensors into the clamping device being in contact with the sheet to measure the displacement of the workpiece to provide a value of the gap size indirectly [15; 16].