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253 |                                                                 Sabeeh & Al-Furati

    Efficiency is a critical criterion, focusing on minimiz-          hospital environment safely while avoiding obstacles. The
ing factors like time, energy consumption, or distance trav-          simulation environment was carefully tailored to meet the
eled [41]. Obstacle avoidance ensures safe navigation around          specific requirements of the path-planning problem, making
obstacles. Smooth trajectories with minimal changes in direc-         use of the following adjustments:
tion and velocity enhance stability and reduce physical deterio-
ration. Dynamic constraints account for limits on acceleration             • Robot Model: The robot utilized in the simulation is a
or deceleration. Task-specific objectives vary depending on                  wheeled mobile robot designed for efficient workspace
the mission, while trajectory optimization can be global or                  navigation. It features motorized wheels for motion
local. In dynamic environments, real-time adaptation may be                  control and an array of sensors, including ultrasonic,
necessary.                                                                   infrared (IR), temperature and humidity sensors. The
                                                                             robot’s kinematics guarantee smooth and precise move-
6) Objective Function for Optimal Trajectory                                 ments, and its dynamic capabilities enable it to adapt
In the pursuit of finding the optimal trajectory for a mobile                paths based on sensor inputs and potential field calcula-
robot, an objective function that plays a pivotal role in bal-               tions during planning.
ancing various objectives is employed, such as minimizing
time while simultaneously avoiding obstacles. This objective               • Obstacles: Both static and dynamic obstacles emulate
function, denoted as J, is defined in equation (7).                          real-world situations in the simulation. Static obstacles
                                                                             are immovable rectangular blocks carefully placed to
J = ?timeT + ?obstacleUobs  (7)                                              create challenging navigation scenarios. In contrast, dy-
                                                                             namic obstacles represent moving individuals (people)
Where:                                                                       within the workspace. The motion of dynamic obstacles
?time and ?obstacle: These are weighting factors assigned to                 is randomized to replicate unpredictable human move-
the time and obstacle avoidance components of the objective                  ment, requiring the robot to skillfully navigate while
function, respectively. They allow to prioritize one aspect over             avoiding collisions with them.
the other based on their relative importance in the context of
the task. T : This represents the total time required for the              • Sensor Simulation: The simulation incorporates sen-
robot to reach its goal along a specific trajectory. It is a crucial         sor emulation to enable the robot’s sensing and navi-
metric in scenarios where minimizing the time of traversal is                gation abilities. The ultrasonic sensor provides short-
a primary objective.                                                         range distance measurements, detecting nearby obsta-
                                                                             cles, while the IR sensor offers medium-range distance
    The overarching aim is to minimize the value of the cost                 readings. The temperature and humidity sensor sup-
function J. Through optimizing the trajectory, a balance be-                 ply environmental data, allowing the robot to adapt
tween minimizing the time taken to reach the goal while also                 its behavior to the prevailing conditions. The sensor
considering the importance of avoiding obstacles is a stroke                 simulation ensures the robot effectively perceives and
to ensure the safety and efficiency of the robot’s path.                     responds to its surroundings.

             V. EXPERIMENTAL SETUP                                    B. Performance Metrics
                                                                      The effectiveness of the algorithm was evaluated through an
In this section, we explain how we set up our experiments             examination of three critical performance metrics: average
to test different path-planning algorithms. We start by de-           path length, average computational time, and average smooth-
scribing the simulation environment we used for testing and           ness. These metrics were computed using straightforward
then discuss how we configured the performance evaluation.            mathematical formulas. • Average path length: measures the
We also explain the metrics and criteria we used to measure           average length of the paths generated by each algorithm. A
how well the algorithms worked. This experimental setup is            shorter average path length means that the robot can reach
crucial because it ensures that the results we collect from the       its destination using the minimum distance possible. This is
evaluation are reliable and unbiased.                                 more efficient, as it reduces energy consumption and overall
                                                                      travel time.
A. Simulation Environment
The code was tested in a 2D healthcare simulation with static              • Average computational time: measures the average
and moving obstacles. The robot used sensor data including                   time it takes each algorithm to calculate a feasible path
ultrasonic and IR readings to plan its path efficiently, and                 from the starting point to the goal. Faster computa-
avoiding collisions. This setup simulated real-world health-                 tional times are especially important in dynamic envi-
care scenarios, evaluating the robot’s ability to navigate a                 ronments, as they allow for real-time or near-real-time
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