Robots must develop the ability to socially navigate in uncontrolled urban environments to be able to be included in our daily lives. This paper presents a new robot navigation framework called the adaptive social planner (ASP) and a robotic system, which includes the ASP. Our results and previous work show that the ASP can adapt to different collaborative tasks involving humans and robots, such as independent robot navigation, human-robot accompaniment, a robot approaching people, robot navigation tasks that combine learning techniques, and human-drone interactions. Our approach in this paper focuses on demonstrating how the ASP can be customized to implement two new methods for group accompaniment: the adaptive social planner using a V-formation model to accompany groups of people (ASP-VG) and the adaptive social planner using a side-by-side model to accompany groups of people (ASP-SG). These two methods result in a robot accompanying groups of people by anticipating human and uncontrolled urban environment behaviors. Also, we develop four new robot skills to deal with unexpected human behaviors, such as rearrangement of the position of the companions inside the group, unforeseen changes in the velocity of the robot companions, occlusions among group members, and changes in the direction toward destinations in the environment. Moreover, we develop different performance metrics, based on social distances, to evaluate the tasks of the robot. In addition, we present the guidelines followed in performing the real-life experiments with volunteers, including a human-robot speech interaction to help humans create a relationship with the robot to be genuinely involved in the mutual accompaniment. Finally, we include an exhaustive validation of the methods by evaluating the behavior of the robot through synthetic and real-life experiments. We incorporate five user studies to evaluate aspects related to social acceptability and preferences of people regarding both types of robot group accompaniment.