Using a discrete distance transform one can quickly build a map of the distance from a goal to every point in a digital map. Using this map, one can easily solve the shortest path problem from any point by simply following the gradient of the distance map. This technique can be used in any number of dimensions and can incorporate obstacles of arbitrary shape (represented in the digital map) including pseudo-obstacles caused by unattainable configurations of a robotic system. This paper further extends the usefulness of the digital distance transform technique by providing an efficient means for dealing with objects which undergo motion. In particular, an algorithm is presented that allows one to update only those portions of the distance map that will potentially change as an object moves. The technique is based on an analysis of the distance transform as a problem in wave propagation. The regions that must be checked for possible update when an object moves are those that are in its "shadow", or in the shadow of objects that are partially in the shadow of the moving object. The technique can handle multiple goals, and multiple objects moving and interacting in an arbitrary fashion.

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Updating Distance Maps When Objects Move

An efficient means for dealing with obstacles in motion is provided to extend the usefulness of digital distance maps. An algorithm is presented that allows one to compute what portions of a map will probably be affected by an obstacle's motion. The algorithm is based on an analysis of the distance transform as a problem in wave propagation. The regions that must be checked for possible updates when an obstacle moves are those that are in its or in the shadow of obstacles that are partially in the shadow of the moving obstacle. The technique can handle multiple fixed goals, multiple obstacles moving and interacting in an arbitrary fashion, and it is independent of the technique used for calculation of the distance map. The algorithm is demonstrated on a number of synthetic two-dimensional examples, and example timing results are reported. >

Dynamic digital distance maps in two dimensions

: The Naval Postgraduate School (NPS) is currently involved in a long- term project to investigate and develop real-time control software, artificial intelligence, computer architecture and control systems theory as they pertain to U.S. Navy autonomous vehicle programs. In support of this goal, the NPS is currently designing and fabricating a testbed autonomous underwater vehicle. This work describes the design, development, and testing of a Guidance Subsystem for this testbed vehicle which uses portions of cubic spirals as the desired path to follow between waypoints. In addition, data translation firmware and real-time software for the control surfaces and main motors is designed, implemented and tested. The process of selecting and implementing an appropriate computer architecture in support of these goals is also discussed and detailed, along with the choice of associated computer hardware and real-time operating system software. (rh)

Guidance and Control System for an Autonomous Vehicle

Computational complexity of two path planning approaches for a two-dimensional (2D) work space is considered: The approach using safe triangles and the approach based on quadtree. The average cost of establishing work space representation, i.e. of building the safe triangles and the quadtree respectively, are estimated. Both approaches are simulated to plan paths for numerous work spaces with obstacles which are generated at random. The results of the simulation are summarized to show the expected behavior of each approach. Comparison based on analyses and simulation is presented.

Tindjaja Soetadji

Papers

Cube Based Representation of Free Space for the Navigation of an Autonomous Mobile Robot