An automated method determines a safety zone for a robot. The robot carries out operations along a specified trajectory. For collision-free operation, a safety zone is determined by: dividing the specified trajectory into a plurality of subtrajectories; determining a plurality of fine-grained envelope cuboids around extreme points of each subtrajectory; and determining a number of optimized envelope cuboids from an enlargement of individual fine-grained envelope cuboids in relation to the volume occupied by the enlarged fine-grained envelope cuboids. The optimized envelope cuboids determined in this way form the safety zone for the trajectory. This automated method can be expanded to multiple trajectories of a robot, multiple robots, and replanning a trajectory for an occupied semaphore zone.

An automated method determines a safety zone for a robot. The robot carries out operations along a specified trajectory. For collision-free operation, a safety zone is determined by: dividing the specified trajectory into a plurality of subtrajectories; determining a plurality of fine-grained envelope cuboids around extreme points of each subtrajectory; and determining a number of optimized envelope cuboids from an enlargement of individual fine-grained envelope cuboids in relation to the volume occupied by the enlarged fine-grained envelope cuboids. The optimized envelope cuboids determined in this way form the safety zone for the trajectory. This automated method can be expanded to multiple trajectories of a robot, multiple robots, and replanning a trajectory for an occupied semaphore zone.

A workpiece machining method that machines a workpiece surface by moving a rotating tool, which has a cutting blade for interrupted cutting of the workpiece surface, relative to the workpiece comprises: a first process of determining the pattern of arrangement of multiple cavities on the surface of the workpiece formed after cutting by the cutting blade; and a second process of determining the tool path of the rotating tool so that the multiple cavities are disposed on the surface of the workpiece according to the pattern of arrangement determined in the first process.