  Motion planning and navigation, especially for mobile robots operating in
complex navigational environments, has been a central problem since robotics
started. A heuristic way to address it is the construction of a graph-based
representation (a path) capturing the connectivity of the configuration space.
Probabilistic Roadmap is a commonly used method by the robotics community to
build a path for navigational mobile robot path planning. In this study, path
smoothening by arc fillets is proposed for mobile robot path planning after
obtaining the path from PRM in the presence of the obstacle. The proposed
method runs in two steps; the first one is generating the shortest path between
the initial state to one of the goal states in the obstacle presence
environment, wherein the PRM is used to construct a straight-lined path by
connecting the intermediate nodes. The second step is smoothening every corner
caused by node presence. Smoothening the corners with arc fillets ensures
smooth turns for the mobile robots. The suggested method has been simulated and
tested with different PRM features. Experiment results show that the
constructed path is not just providing smooth turning; it is also shorter and
quicker to finish for a robot while avoiding obstacles.
