Topology-Inspired Morphological Descriptor for Soft Continuum Robots

Abstract: This paper presents a topology-inspired morphological descriptor for soft continuum robots by combining a pseudo-rigid-body (PRB) model with Morse theory to achieve a quantitative characterization of robot morphologies. By counting critical points of directional projections, the proposed descriptor enables a discrete representation of multimodal configurations and facilitates morphological classification. Furthermore, we apply the descriptor to morphology control by formulating the target configuration as an optimization problem to compute actuation parameters that generate equilibrium shapes with desired topological features. The proposed framework provides a unified methodology for quantitative morphology description, classification, and control of soft continuum robots, with the potential to enhance their precision and adaptability in medical applications such as minimally invasive surgery and endovascular interventions.