Matching large point clouds is an important task in robotics since it enables robots to perceive and understand their environment in a three-dimensional (3D) space. A point cloud is a set of points in 3D space that represents the surface of an object or environment. Matching point clouds involves finding the transformation that maps one point cloud to another, which can be used for tasks such as localization, mapping, and object recognition. There are existing techniques like Iterative Closest Point algorithm, Feature-based methods and Optimization-based method which are computationally expensive, and they do not consider rich topological features for effective matching. The drawback of deep learning-based methods is that they require large amount of training data. Towards this problem, in the current project, we propose to apply persistence homology-based techniques which have proven to be very effective in topological data analysis and machine learning