If we give a robot the task of moving an object from its current position to another location in an unknown environment, the robot must explore the map, identify all types of obstacles, and then determine the best route to complete the task. We proposed a mathematical model to find an optimal path planning that avoids collisions with all static and moving obstacles and has the minimum completion time and the minimum distance traveled. In this model, the bounding box around obstacles and robots is not considered, so the robot can move very close to the obstacles without colliding with them. We considered two types of obstacles: deterministic, which include all static obstacles such as walls that do not move and all moving obstacles whose movements have a fixed pattern, and non-deterministic, which include all obstacles whose movements can occur in any direction with some probability distribution at any time. We also consider the acceleration and deceleration of the robot to improve collision avoidance.