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Real Time Cutter Path Generation and Control of a Hydraulically Actuated Tunneling Robot

A two degree of freedom automated tunneling machine uses a relatively slow but extreme environment hardened digital controller (PLC) to control cutter path on a toroı̈dal surface. A geodesic curve is the shortest distance between two points on any surface. We show how to compute a series of points, approximating those on the shortest geodesic, by projecting points, on a straight line connecting the terminal points, normally onto the surface. This entire cutter trajectory is represented with precision by a sequence of such point-to-point straight line segments of various length. Motion interpolation occurs in increments of equal displacement during an equal time interval. The conventional Bresenham straight line algorithm for plotters and graphical devices is adapted to use time as the unconditional step, i.e., independent variable cardinal axis. Thus the motion of two or more joint axes of a tunneller may be easily coordinated.