Route-planning for vehicles and motion-planning for robots is most effective, and most challenging technically, when it is performed in realtime by on-board computer-processors. The realtime planning allows for responses to changes in the surroundings as the vehicle or robot proceeds towards a goal from a start. En route planning is accomplished by the repeated execution of sophisticated search procedures on the computer-processors to identify the quickest route to the goal from the current location, which route also avoids obstacles and minimizes the exposure to hazards and threats along the way. The present effort is to develop search-procedures not for a plane surface, but for a curved surface, namely the earth modeled as a spheroid. The earth's terrain, that is, the actual surface of the earth as it lies above or below the spheroidal model at each pair of numerical values for longitude and latitude, is modeled by a digital terrain elevation matrix (DTEM.) This DTEM imposes a grid on the spheroid consisting of regularly spaced parallels of latitude and regularly spaced meridians of longitude, a geometry different from the rectilinear gridding on the plane surface, which rectilinear gridding is the geometric basis for conventional search-procedures. The grid imposed on the spheroid by the DTEM will be accommodated by the search-procedures to be developed on the present effort. Realtime, on-board route-planners are already in use, as, for example, on Army aircraft. These existing route-planners do not, however, accommodate curved surfaces gridded by DTEMs, but only plane surfaces gridded by straight lines. These Army aircraft, and potentially, robotic, unmanned, military aircraft are existing military markets for the product or service arising as a commercial follow-on to the present effort. A potentially big civilian market exists for motion-planning for mobile robots or the multi-jointed arms of stationary robots. The mobile robots could be either robotic ground-vehicles traveling on or robotic aircraft traveling slightly above the surface of the earth on possibly hazardous missions on or over rugged or inhospitable terrain. The mobile robots could also be specialized vehicles for exploring the surfaces of planetary bodies in the solar system, or service robots on not only a planetary surface, but also the surface of a space station. These route-planners require sensor systems in addition to a DTEM, and for the robots one such sensor system would be the vision system which these robots already possess. An important special use is route-planning to avoid shady country where a mobile robot's solar power collector would not receive sunlight. The multi-jointed arms of stationary robots could benefit from motion-planning constrained to a surface, not necessarily a plane surface, as an efficient alternative to time-consuming motion-planning in three dimensions. The curved surfaces in which the multi-jointed arm could be constrained to move might be identified in realtime by a vision-system mounted on the robot. All of these civilian robotic applications would require significant follow-on effort to become commercial services or products.
