2024/01/31 by Jackson Pierce, Pierce, Jackson
Engineering · Computer Science · #Robotic Mechanisms and Dynamics #Robot Manipulation and Learning #Robotic Path Planning Algorithms
paper · pdf · doi:10.48550/arxiv.2402.00079
In this paper, we develop the theory of constrained motion spaces of robotic arms. We compute their homology groups in two cases: when the constraint is a horizontal line and when it is a smooth curve whose motion space is a smooth manifold. We show the computation of homology amounts to counting the collinear configurations, reducing a topological problem to a combinatorial problem. Our results rely on Morse theory, along with Walker's and Farber's work on polygonal linkages.