7.1 Time-Varying Problems

This section brings time into the motion planning formulation. Although the robot has been allowed to move, it has been assumed so far that the obstacle region ${\cal O}$ and the goal configuration, ${q_{G}}\in {\cal C}_{free}$, are stationary for all time. It is now assumed that these entities may vary over time, although their motions are predictable. If the motions are not predictable, then some form of feedback is needed to respond to observations that are made during execution. Such problems are much more difficult and will be handled in Chapters 8 and throughout Part IV.