Motion planning in dynamic environments using the relative velocity paradigm

A simple and efficient approach to the computation of avoidance maneuvers among moving obstacles is presented. The method is discussed for the case of a single maneuvering object avoiding several obstacles moving on known linear trajectories. The original dynamic problem is transformed into several static problems using the relative velocity between the maneuvering object and each obstacle. The static problems are converted into a single problem by means of a vector transformation, and the set of velocity vectors guaranteeing the avoidance of all the obstacles is computed. Within this set, the best maneuver for the particular approach can be selected. The geometric background of this approach is developed for both 2-D and 3-D cases, and the method is applied to an example of a 3-D avoidance maneuver.>