In the realm of robotics, the ability to efficiently match point clouds is crucial for tasks such as environment understanding, localization, and object manipulation. Point clouds, representing intricate 3D surfaces, serve as the primary source of spatial information for robotic systems. While existing methods like Iterative Closest Point algorithms and deep learning approaches have their merits, they often fall short in capturing the nuanced topological features essential for robust point cloud matching. To overcome these limitations, this project proposes the integration of multi-parameter persistence analysis, an advanced mathematical framework from computational algebraic topology, into robotics applications, offering enhanced perception and manipulation capabilities. Project Objectives:

Multi-parameter Persistence Computation:

1.Develop algorithms for efficiently computing multi-parameter persistence diagrams for point clouds.

2.Investigate computational complexity.

3.Explore novel techniques for capturing multi-scale and multi-dimensional features inherent in complex point cloud data.