Optimal visibility-based path and motion planning of mobile observers for 3-D objects

Various optimization problems derived from visibility-based path and motion planning of mobile observers for three-dimensional objects such as asteroids are considered. First, the mathematical formulations of these problems are presented. These problems are generally non-smooth. Then, sufficient conditions for the existence of solutions are established. The nature of the optimal solutions to some of the posed problems is illustrated by simple examples. Next, the computational complexities in the solution of these problems are discussed briefly. Finally, explicit necessary optimality conditions for asteroid-observer optimal motion planning problems are presented. (C) 2008 Elsevier Ltd. All rights reserved.