Motion planning for mobile robots has several important applications in industry, planetary operations, defence, and medical automation. Planning an optimal path for nonholonomic (such as car-like) mobile robots is a vital aspect of this domain. Rapidlyexploring Random Tree Star (RRT*) has gained immense popularity due to its feasibility for path planning of non-holonomic mobile robots. Moreover, it does not require explicit information of environment obstacles and also supports complex high dimensional problems very well. Though RRT* is widely used method for path planning of mobile robots; slow convergence rate, large memory requirements and sub-optimal jagged paths are its proven problems. Such jagged paths consume more fuel and time during path following process and exert robot’s controller module also. Incorporating smoothness in jagged paths by satisfying differential constraints during planning phase increases the complexity of problem. Another solution is to use post processing smoothness techniques. However, after applying smoothness, resultant smooth path deviates the robot from planned path and introduces collision again. Since, most of the robots are battery operated; therefore planned path is required to be time and energy efficient, i.e., smooth and short. This thesis presents a comprehensive overview of state of the art path planning and path smoothing approaches. Secondly, a planning algorithm RRT*-Adjustable Bounds (RRT*-AB) is proposed to resolve the aforementioned issues in RRT*. The proposed planner has introduced novel strategies for space exploration and path optimization. Robustness and efficiency of proposed algorithm is tested using different environment maps of standard robotic datasets. These environment maps are cluttered with structured and unstructured obstacles, including narrow and complex maze cases. A thorough performance comparison along with numerical and theoretical complexity analysis of the proposed approach with state of the art techniques, i.e., RRT* and RRT*-Smart is also presented. Performance analysis shows that proposed approach has significantly improved path length, execution time and memory requirements even in narrow and dense environment. It has improved convergence rate up to 93 percent. Further, a path smoothing approach is applied to make the planner generated path feasible for non-holonomic mobile robots. The proposed smoothing approach uses clamped B-spline with automatic and economical control point adjustment while maintaining collision-free route. It also improves smooth path by eliminating post smoothness collisions, if any with desired smoothness. Proposed smoothing approach generates collision-free smooth path with reduced path length and execution time. In the end, thesis concludes with future research directions.