A Lumped-Mass Model for Large Deformation Continuum Surfaces Actuated by Continuum Robotic Arms

Currently, flexible surfaces enabled to be actuated by robotic arms are experiencing high interest and demand for robotic applications in various areas such as healthcare, automotive, aerospace, and manufacturing. However, their design and control thus far has largely been based on “trial and error” methods requiring multiple trials and/or high levels of user specialization. Robust methods to realize flexible surfaces with the ability to deform into large curvatures therefore require a reliable, validated model that takes into account many physical and mechanical properties including elasticity, material characteristics, gravity, external forces, and thickness shear effects. The derivation of such a model would then enable the further development of predictive-based control methods for flexible robotic surfaces. This paper presents a lumped-mass model for flexible surfaces undergoing large deformation due to actuation by continuum robotic arms. The resulting model includes mechanical and physical properties for both the surface and actuation elements to predict deformation in multiple curvature directions and actuation configurations. The model is validated against an experimental system where measured displacements between the experimental and modeling results showed considerable agreement with a mean error magnitude of about 1% of the length of the surface at the final deformed shapes.