## 2 Related Work  
### Robotic Walking Assistants  
There are several types of robotic walking assistants (RWAs), such as wearable robots that provide gait [20; 21] or balance [22; 23] rehabilitation or non-wearable robotic systems that provide support during walking [24; 25]. This paper focuses on RWAs that are not wearable. RWAs can have different designs, such as smart canes or walking frames, and different capabilities (e.g., obstacle avoidance, gait analysis, etc.). [PERSON] et al. [26] proposed a walking assistant robot called adaptive robotic nursing assistant (ARNA), which is a service robot that helps patients with day-to-day activities, such as walking and sitting. It comprises an armbar to sense torque and support the patient, a seven-degree-of-freedom (DOF) arm, and a multitude of sensors for obstacle detection, such as an ultrasonic sensor, a LIDAR, and an RGB-Depth (RGB-D) camera. As an additional safety measure, the robot is equipped with a bump sensor to abruptly stop when it hits an obstacle. One of ARNA's tasks is to support a person while walking behind the robot. Although ARNA is able to detect nearby obstacles, it is not designed to navigate around them and relies on the patient to guide the robot around the obstacle. [PERSON] et al. [27] proposed a visual perception pipeline that can help patients cross the obstacle, but their pipeline mainly focuses on the task of crossing rather than maneuvering the obstacles. Another assistive robot is called Mobile Collaborative Robotic Assistant (MOCA) [12] and comprises an omnidirectional robot with a 7-DOF robotic arm along with a soft hand as an end effector. MOCA is a collaborative robot, and its primary purpose is to collaborate with humans on industrial work, such as drilling, tasks that require teleoperation, or co-manipulation of objects. MOCA has been used as a platform to improve standing balance performance while measuring body posture [28]. However, the system has not been used for walking assistance. Moreover, [PERSON] et al. [24] proposed a custom-made intelligent robotic rollator called iWalk, which uses LIDAR for gait detection and an RGB-D camera for detecting if the patient loses balance and falls to the ground. While iWalk calculates the patient's gait parameters and provides extra functionality for patient fall detection, it is still not designed to detect obstacles and maneuver the patient around them. In the previous examples, it is obvious that the human is mainly in control of the robot, and the robot is compliant with the user's commands. The systems presented so far focus on supporting the patient and rely on human guidance to avoid obstacles. This may burden the patient as they have to focus on their walk and, at the same time, guide the robot around obstacles. However, to achieve an intuitive interaction between the robot and the patient, a shared navigation approach is essential. This means that whenever the robot detects an obstacle (static or dynamic), it should gently steer the patient away from the obstacle without losing contact with the patient. This behavior can be called shared control between the patient and the robot. In order to avoid static obstacles and support the patient at the same time, [PERSON] et al. [29] proposed the use of a commercially available socially assistive robot called Pepper, which is a humanoid robot. The Pepper robot is equipped with touch sensors on the left and right shoulders that sense the pressure applied by the patient and move forward. In addition, the Pepper robot comes with built-in LIDAR, infrared, and sonar sensors used for obstacle avoidance by reducing the robot's reliance on the user's input. The system is able to avoid static obstacles but does not take into account dynamic obstacles, e.g., humans in the environment. [PERSON] et al. [30] proposed a shared control strategy for walking assistance for a robot.