This thesis studies motion planning for mobile robots in various environments. The basic tools for the research are the configuration space and the visibility graph. A new approach is developed which generates a smoothed minimum time path. The difference between this and the Minimum Time Path at Visibility Node (MTPVN) is that there is more clearance between the robot and the obstacles, and so it is safer. The accessibility graph plays an important role in motion planning for a massless mobile robot in dynamic environments. It can generate a minimum time motion in 0(n2»log(n)) computation time, where n is the number of vertices of all the polygonal obstacles. If the robot is not considered to be massless (that is, it requires time to accelerate), the space time approach becomes a 3D problem which requires exponential time and memory. A new approach is presented here based on the improved accessibility polygon and improved accessibility graph, which generates a minimum time motion for a mobile robot with mass in O((n+k)2»log(n+k)) time, where n is the number of vertices of the obstacles and k is the number of obstacles. Since k is much less than n, so the computation time for this approach is almost the same as the accessibility graph approach. The accessibility graph approach is extended to solve motion planning for robots in three dimensional environments. The three dimensional accessibility graph is constructed based on the concept of the accessibility polyhedron. Based on the properties of minimum time motion, an approach is proposed to search the three dimensional accessibility graph to generate the minimum time motion. Motion planning in binary image representation environment is also studied. Fuzzy logic based digital image processing has been studied. The concept of Fuzzy Principal Index Of Area Coverage (PIOAC) is proposed to recognise and match objects in consecutive images. Experiments show that PIOAC is useful in recognising objects. The visibility graph of a binary image representation environment is very inefficient, so the approach usually used to plan the motion for such an environment is the quadtree approach. In this research, polygonizing an obstacle is proposed. The approaches developed for various environments can be used to solve the motion planning problem without any modification. A simulation system is designed to simulate the approaches.