Traditional path planning for robots is a well-studied problem. However, the classical setting of the problem is simple to state: plan a path for a robot, starting from an initial point, and ending at a desired target point, given an environmental map, usually in the form of an occupancy grid. In this setting though, no special consideration is given to humans; they are thought of simply, as being obstacles in the environment, equivalent to chairs or walls. However, with more robots entering human spaces, special consideration needs to be given: humans need special treatment as obstacles, and furthermore humans can also serve the goal of goal points, towards starting a social interaction; either individual humans or groups of humans. Also, special mechanisms are required for engaging and disengaging in such interactions, taking into account psychological considerations of proxemics. In this paper, we first introduce our unifying theoretical framework for all the subproblems of social path planning; then, we propose an extended mode for engaging groups of people; and then, by using a special version of the fast-marching square planning method, we present and demonstrate actual algorithmic solutions for the social path planning subproblems. Our results prove the strengths of our approach and its generalizability. Finally, concrete further steps are discussed.