Computer-implemented method for estimating tilt states of parts which are to be cut-out of a workpiece by means of a laser cutting head of a laser machine and which are placed on a support element of a support structure, wherein the method is used for collision avoidance for the laser cutting head when controlling the same in connection with a laser cutting process, wherein the method comprises: - Receiving a cutting plan (cp) with position data, inter alia representing a relative position and/or orientation of the workpiece with the parts to be cut and a support element of the support structure; - Accessing a tilt estimator with an implemented and executable probability function; - Executing the probability function for each of the parts to be cut, for calculating a probability-assigned tilt volume ( prob-vol), wherein the probability function calculates all possible tilting states of the parts to be cut, based on at least the received position data and wherein the probability function further assigns to each calculated tilting state a probability, indicating the tilting risk that the part will be transferred in said calculated tilting state after complete cutting-out the part of the workpiece, wherein the space is partitioned into equally sized or variable sized collision volumes and occupancy of each collision volume is calculated as the sum of probabilities that this volume is occupied in any of the tilting outcomes, wherein the probability function is executed prior to cutting in an offline mode, wherein the probability-assigned tilt volume is calculated by taking into account a cutting property, and wherein the cutting property is a kerf width; - Providing the calculated probability-assigned tilt volume ( prob-vol); - Accessing an instructor for determining instructions for controlling the laser cutting process, wherein accessing is executed in response to the calculated probability-assigned tilt volume, - wherein the instructions comprise issuance of: - detouring instructions for controlling a set of drives for laser cutting head movement according to a three-dimensional trajectory for collision-avoidance free cutting head movement, wherein the detouring instructions are calculated such that the calculated, probability-based tilt volume ( prob-vol) is taken into account for generating a new trajectory which prevents the laser cutting head from colliding with presumably tilted parts. - Receiving a cutting plan (cp) with position data, inter alia representing a relative position and/or orientation of the workpiece with the parts to be cut and a support element of the support structure; - Accessing a tilt estimator with an implemented and executable probability function; - Executing the probability function for each of the parts to be cut, for calculating a probability-assigned tilt volume ( prob-vol), wherein the probability function calculates all possible tilting states of the parts to be cut, based on at least the received position data and wherein the probability function further assigns to each calculated tilting state a probability, indicating the tilting risk that the part will be transferred in said calculated tilting state after complete cutting-out the part of the workpiece, wherein the space is partitioned into equally sized or variable sized collision volumes and occupancy of each collision volume is calculated as the sum of probabilities that this volume is occupied in any of the tilting outcomes, wherein the probability function is executed prior to cutting in an offline mode, wherein the probability-assigned tilt volume is calculated by taking into account a cutting property, and wherein the cutting property is a kerf width; - Providing the calculated probability-assigned tilt volume ( prob-vol); - Accessing an instructor for determining instructions for controlling the laser cutting process, wherein accessing is executed in response to the calculated probability-assigned tilt volume, - wherein the instructions comprise issuance of: - detouring instructions for controlling a set of drives for laser cutting head movement according to a three-dimensional trajectory for collision-avoidance free cutting head movement, wherein the detouring instructions are calculated such that the calculated, probability-based tilt volume ( prob-vol) is taken into account for generating a new trajectory which prevents the laser cutting head from colliding with presumably tilted parts. - detouring instructions for controlling a set of drives for laser cutting head movement according to a three-dimensional trajectory for collision-avoidance free cutting head movement, wherein the detouring instructions are calculated such that the calculated, probability-based tilt volume ( prob-vol) is taken into account for generating a new trajectory which prevents the laser cutting head from colliding with presumably tilted parts.