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This article presents contributions in the field of path planning for industrial robots with 6 degrees of freedom. This work presents the results of our research in the last 4 years at the Institute for Process Control and Robotics at the University of Karlsruhe. The path planning approach we present works in an implicit and discretized C-space. Collisions are detected in the Cartesian workspace by a hierarchical distance computation. The method is based on the A* search algorithm and needs no essential off-line computation. A new optimal discretization method leads to smaller search spaces, thus speeding up the planning. For a further acceleration, the search was parallelized. With a static load distribution good speedups can be achieved. By extending the algorithm to a bidirectional search, the planner is able to automatically select the easier search direction. The new dynamic switching of start and goal leads finally to the multi-goal path planning, which is able to compute a collision-free path between a set of goal poses (e.g., spot welding points) while minimizing the total path length.

This paper is based on a path planning approach we reported earlier for industrial robot arms with 6 degrees of freedom in an on-line given 3D environment. It has on-line capabilities by searching in an implicit and descrete configuration space and detecting collisions in the Cartesian workspace by distance computation based on the given CAD model. Here, we present different methods for specifying the C-space discretization. Besides the usual uniform and heuristic discretization, we investigate two versions of an optimal discretization for an user-predefined Cartesian resolution. The different methods are experimentally evaluated. Additionally, we provide a set of 3- dimensional benchmark problems for a fair comparison of path planner. For each benchmark, the run-times of our planner are between only 3 and 100 seconds on a Pentium PC with 133 MHz.

Given a finite set of points in the plane and a forbidden region R, we want to find a point X not an element of int(R), such that the weighted sum to all given points is minimized. This location problem is a variant of the well-known Weber Problem, where we measure the distance by polyhedral gauges and allow each of the weights to be positive or negative. The unit ball of a polyhedral gauge may be any convex polyhedron containing the origin. This large class of distance functions allows very general (practical) settings - such as asymmetry - to be modeled. Each given point is allowed to have its own gauge and the forbidden region R enables us to include negative information in the model. Additionally the use of negative and positive weights allows to include the level of attraction or dislikeness of a new facility. Polynomial algorithms and structural properties for this global optimization problem (d.c. objective function and a non-convex feasible set) based on combinatorial and geometrical methods are presented.