When applying this method to real-world robotic systems with sensor uncertainties and modeling errors, several limitations and challenges may arise. One significant challenge is the accuracy of sensor data, as sensor uncertainties can introduce noise and inaccuracies in the information used for obstacle detection and distance computation. This can lead to errors in the construction of control barrier functions (CBFs) and affect the robot's ability to navigate safely in dynamic environments.
Another limitation is the complexity of modeling real-world environments, which may involve a wide range of obstacle shapes, sizes, and dynamics. Inaccuracies in the modeling of obstacles can impact the effectiveness of the CBF approach, as the computed distances may not accurately represent the true distances between the robot and obstacles. This can result in suboptimal or unsafe navigation decisions by the robot.
Moreover, the computational complexity of the approach may pose challenges in real-time implementation, especially in dynamic environments where obstacles are moving and the robot needs to make rapid decisions to ensure safety. The time required to compute the distance between the robot and obstacles, as well as to formulate the CBF constraints, could impact the responsiveness of the control system and the robot's ability to react quickly to changing environments.