Optimal path planning for a non-holonomic robot using interval analysis

Path planning of autonomous mobile robots in cluttered environment is a challenging and a well studied problem. The configuration space based methods are typically used for finding out the feasible and non-feasible areas for a mobile robot. Finding an optimal path considering admissible control inputs is challenging as it needs to explore all the possible options, present and future. The interval analysis approach can used for dividing the configuration space into feasible and non-feasible spaces. This technique is capable of dividing the space into intervals of different sizes which helps to cover the obstacles in a refined manner. This paper presents the computation of collision-free path using interval analysis between any two points in a 2D-environment cluttered with obstacles for a non-holonomic robot. The admissible control inputs for the robot are considered as constraints and are included in the configuration space parameters while computing the collision-free regions. The optimal shortest path between two points is computed using A* search algorithm and Pontryagin's minimum principle. Simulation results are shown using MATLAB by computing the path between two points considering selected control inputs as constraints.