## 3 Problem Statement  
The hypothesis and significance of this research are that developing an intelligent multi-purpose robotic assistant, which can support and guide patients while walking, as well as help them maneuver obstacles in a crowded hospital environment using deep reinforcement learning models, could be a promising solution to assist nurses with non-critical tasks and enhance patient care. The primary objective of this work is to explore the development of a model architecture capable of providing adequate support to patients during walking tasks while also facilitating their ability to navigate through obstacles. In patient-robot co-navigation, the goal is to guide a patient from one location to another while avoiding static obstacles, such as furniture, and navigating through crowds. The patient's gait velocity in x- and y-directions, denoted as \(v^{t}_{p,x}\) and \(v^{t}_{p,y}\) at time \(t\), respectively, can be affected by noise. To ensure safe navigation, a parameterized function must be created to output the optimal velocity for the robot based on the current environmental state and the patient's gait velocity. The function should take into account the locations of the patient and obstacles (both static and dynamic), as well as the patient's gait velocity. The robot should stop when the patient stops and guide the patient's ambulation when in close proximity, safely leading the patient to the destination while avoiding collisions with any obstacles. The representation of the position of the individuals in a crowd can be described mathematically as \((p_{cn,x}^{t},p_{cn,y}^{t})\), where \(n\) represents the index of the \(n^{th}\) human. The velocity of the robot is represented by \(v_{r,x}^{t},v_{r,y}^{t}\), and its heading angle is represented by \(\beta_{r}^{t}\). Information on the static obstacles in the environment can be obtained using a LIDAR sensor, which can be encoded into an array \(\bigcup_{i=1}^{n_{L}}{{{L}_{i}^{t}}}\), where \(n_{L}\) is the number of obstacles and can be calculated by dividing the LIDAR's angular coverage by its angular resolution. A multi-output parameterized function can be defined to model the relationship between the crowd, the robot, and the obstacles, as shown below in Equation (1):  
\[v_{r,x}^{t},v_{r,y}^{t}=f_{\theta}(\bigcup_{i=1}^{n}(p_{ci,x}^{t-1}-p_{rx}^{t-1 },p_{ci,y}^{t-1}-p_{ry}^{t-1}),\bigcup_{i=1}^{n_{L}}{{{L}_{i}}},v_{p,x}^{t-1},v_ {p,y}^{t-1},v_{r,x}^{t-1},v_{r,y}^{t-1},\beta_{r}^{t}) \tag{1}\]  
The function \(f_{\theta}\) can be learned using reinforcement learning, where \(\theta\) represents the set of parameters of the function. To handle the complexity of this massive model with multiple inputs, the learning process is divided into two stages. In the first stage, a reinforcement learning model, referred to as Model V1, is trained to consider only the dynamic obstacles. In the second stage, another reinforcement learning model with a similar architecture, referred to as Model V2, is trained to incorporate both dynamic and static obstacles. Finally, Model V2 is deployed in a realistic simulation environment Gazebo to test Model V2. For the development of the system, it is assumed that the patient can ambulate independently (does not fall) yet requires minimal assistance from the healthcare professionals, i.e., nurses. The manual muscle testing (MMT) [47] scale is a widely recognized method for assessing the strength of various muscle groups in patients. This scale assigns a numerical rating to each muscle group, ranging from 0 to 5, based on the patient's ability to move against resistance. A rating of 4/5 indicates that the muscle group in question is capable of movement against resistance but with less than full strength. In the context of robotic assistance by the proposed RWA for patients, a minimum MMT score of 4/5 for both the arms and legs is recommended, but its usage must depend on the discretion of the physician. This can be considered one of the limitations.