A wide range of approaches and solutions for improving the performance of robotic manipulators exist. The least costly approach, in terms of material and time, is probably off-line modification of the path of the robot such that a set of operational performance parameters of the robot will improve. For instance, the path of the manipulator could be created in order to minimize the required torque, power consumption, operations time, etc.

To minimize a cost function, most of the existing methods search for a trajectory in the configuration space of the manipulator to connect two task points defined in the Cartesian space considering a one to one mapping between the two spaces. But most robotic manipulators have multiple IK solutions. Hence, the mapping from each task point in the cartesian space into the configuration space is not unique. In other words, the problem of connecting a start point to an end point in the cartesian space should be mapped into a problem in the configuration space where the start and end points can be chosen from any of their corresponding IK solutions.

Furthermore, the operation of the industrial manipulators consists of numerous repetitive tasks. The sequence that the robot performs these tasks is of no importance in numerous applications such as inspection. If each task is represented with a task point in the cartesian space, another problem that could be addressed in path planning is how to arrange the sequence of task points to achieve a performance boost. In other words, if there exist a set of task points, in what order the start and end point couples should be chosen to further increase the performance of the manipulator.

In this research, a formulation for considering multiple IK solutions in the multi-goal path planning problem is presented. Moreover, an efficient algorithm for solving for exact solutions of the proposed formulation is presented. The algorithm utilizes a Generalized Traveling Salesman solver as the primary solver.