Preface special issue on robotics

Robotics is a multifaceted area requiring tools and principles drawn from many disciplines. Much of this background is classical (e.g., mechanics) or at least well established (e.g., control theory). Computational geometry, or more generally, algorithmics, is a relative newcomer. We believe that the importance of algorithms will continue to increase because the trend in robotics toward general-purpose robots with immense computation powers imply a corresponding sophistication expected of algorithms which accomplish robotic tasks. Brute force or simple heuristic algorithms may no longer suffice--we need to bring to bear all the understanding of data-structures and efficient asymptotic techniques developed over the last two decades. (There is a slight paradox here but the argument is familiar: increased computing power means the size of solvable problems increases correspondingly and asymptotic behavior begins to be felt.) Computational geometry offers new tools and perspective on old problems. Consider the problem of motion planning. This had been well studied even before computational geometry itself became a subject. In artificial intelligence, the find-path problem was posed and many heuristic solutions were proposed. Ideas such as the visibility graph (Nilsson) were suggested. Today, we see that the natural home for such concepts is computational geometry where the power and limitations of these tools are properly understood and fully exploited. Or again, when control theorists approach motion planning, it is almost second nature to attempt to define algorithms in terms of feedback laws. Thus, such papers have proposed the use of potential functions to model obstacles in the terrain, and to model the algorithm by moving in directions which minimize the potential energy. Such local criteria for motion must in general fail. The real issue in motion planning is global searching and involve combinatorial structures. Both these are specialties of computational geometry. (Admittedly control theorists are interested in the nice dynamical properties that comes from potential functions.) In this special issue we attempt to give some representative algorithmic studies in robotics. The repertoire of robotics problems presently treated by computational geometry is admittedly narrow in view of the total scope of robotics: the reader will note that all but one paper here can be construed as treating motion