Mobile robots are increasingly being used to perform tasks in unknown environments. The potential of robots to undertake such tasks lies in their ability to intelligently and efficiently locate and interact with objects in their environment. My research focuses on developing algorithms to plan paths for mobile robots in a partially known environment observed by an overhead camera. The environment consists of dynamic obstacles and targets. A new methodology, Extrapolated Artificial Potential Field, is proposed for real time robot path planning. An algorithm for probabilistic collision detection and avoidance is used to enhance the planner. The aim of the robot is to select avoidance maneuvers to avoid the dynamic obstacles. The navigation of a mobile robot in a real-world dynamic environment is a complex and daunting task. Consider the case of a mobile robot working in an office environment. It has to avoid the static obstacles such as desks, chairs and cupboards and it also has to consider dynamic obstacles such as humans. In the presence of dynamic obstacles, the robot has to predict the motion of the obstacles. Humans inherently have an intuitive motion prediction scheme when planning a path in a crowded environment. A technique has been developed which predicts the possible future positions of obstacles. This technique coupled with the generalized Voronoi diagram enables the robot to safely navigate in a given environment.