The minimum-time motion coordination is an important subject in robotics. In this study, the arrangement of several goals, which is treated as a traveling salesman problem (TSP), is incorporated to this subject. Although TSP has been studied in most previous works; but, solving a TSP that takes into account collision occurrences has not received much attention. This instance arises when a robot arm has to plan a sequence of reaching goals with other moving objects and/or other robot arms. If goals are also moving, then the problem becomes more complex since the end configuration of robot arm is undefined when reaching a goal. In this study, in particular, a 6-DOF robot arm has to reach several goals found in an object while a 1-axis positioning table simultaneously positions the object; thereby changing the goal locations and collision occurrences are inevitable. For the purpose of this study, the TSP is solved effectively with motion coordination and collision avoidance. The collision-free configurations of a robot arm when reaching goals are solved through motion coordination. Collision is avoided by exploiting the redundancy of the system. The above-mentioned solution is verified through a simulation utilizing an object with various numbers of goals and their positions, and is proven effective.