This article, modeling a mobile robot as a point, discusses on a problem of trajectory planning in transient environment. When a robot moves over a plane, every stationary environment is representable as some subspace of two-dimensional Euclidean space while every transient environment, as some subspace of three-dimensional Euclidean space obtained by adding the time axis to the two-dimensional space. Given a transient environment
E and a start point B and a goal point G of the robot, by applying a paint procedure supported by graphics library in computer, examine an area
DB being accessible from B and another area
DG being accessible to G. Next, select an arbitrary point M just on the boundary between
DB and
DG. Then, the original problem is decomposed into “a problem of trajectory planning from B to M in environment
DB” and “another problem of trajectory planning from M to G in environment
DG.” By repeating this decomposition, each problem becomes primitive problem joining some adjacent two points in small environment. The trajectory joining the original B and G is a sequence of many short trajectories solved thus.
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