The present invention relates to a method for monitoring the operation of a robot, in particular an articulated arm robot having, for example, 6 axes, in a protective field, wherein the protective field has an outer boundary, wherein a respective space occupied by the robot is determined for different robot positions, the space occupied by the robot in the respective robot position is removed from the protective field, wherein an inner boundary of the protective field is created and/or changed by removing the occupied space.

A method determines a feedrate of a tool machining a workpiece according to a path. The method partitions the path into a set of segments, such that within each segment a function of engagement of the tool and the workpiece is substantially constant. Next, the method determines a feedrate for each segment in the set.

Collision detection useful in motion planning for robotics advantageously represents planned motions of each of a plurality of robots as obstacles when performing motion planning for any given robot in the plurality of robots that operate in a shared workspace, including taking into account the planned motions during collision assessment. Edges of a motion planning graph are assigned cost values, based at least in part on the collision assessment. Obstacles may be pruned as corresponding motions are completed. Motion planning requests may be queued, and some robots skipped, for example in response to an error or blocked condition.