The Traveling Salesman Problem in parallel robotics: definitions, optimization and performance

A frequent task for industrial robots is to visit a set of target points in a closed path. If the sequence of operations is not constrained by the task, one may wish to minimize the path length. This means solving a Traveling Salesman Problem (TSP), a classic topic in Operations Research. The TSP has already been applied to mobile robots and to serial manipulators. We formulate the TSP for parallel robots, whose end-effector is connected to the base by two or more kinematic chains. We define the goal function as the maximum absolute change in joint coordinates (for all motors), which we take as proportional to the task time. We show that this is not equivalent to minimizing the geometric distance. Finally, we benchmark representative TSP solvers on an example planar robot, comparing heuristic methods and an exact solver based on mixed integer programming, which provides a reference optimal solution. We then report the solution time and quality. Our results show that TSP-based path planning with appropriate definitions can improve the efficiency of parallel robots.