Cosserat model improves stiffness prediction for soft helicoid robot arms
Cosserat Modeling of Trimmed Helicoid Soft Arms with a Separated-Section Constitutive Law
Robotics
Summary
Soft robot arms made from twisted helical materials are tricky to model because their load-bearing parts are separated and only loosely connected. The authors developed a new way to calculate how stiff these soft arms are by treating each helix domain separately, then combining their effects while accounting for extra flexibility from loose connections. Their model captures large differences in bending and stretching stiffness compared to twisting stiffness and successfully predicts arm shapes with low errors. This makes fast planning and control of these soft robots more reliable.
What this means in practice
- •For soft robot developers: Accurately predict and plan movements of soft robot arms with complex helicoid geometries using a fast, physics-based model of stiffness and dynamics.
- •For medical device engineers: Design and control flexible surgical tools with separated helicoid structures by applying improved stiffness modeling for precise manipulation.
Authors
Zhihang Qin, Linxin Hou, Zeyu Zhong, Yuchen Sun, Wenci Xin, Yueheng Zhang, Ji Qi, Jie Wang, Muhammad Sunny Nazeer, Yu Jun Tan, Federico Renda, Cecilia Laschi
Abstract
Cosserat rod models for soft robots usually construct sectional stiffness by summing material properties over a common cross-section. This assumption becomes inaccurate for trimmed helicoid arms, where load-bearing helix domains are separated and connected only through sparse fused crossings. This paper formulates a separated-section constitutive law that evaluates each helix domain in its local frame and pulls its constitutive response back to the backbone, yielding an effective backbone stiffness. Sparse-fusion mechanics captures the additional compliance caused by relative motion between neighboring domains and determines channel-wise reduction profiles $η_c(s/L)$ for bending, torsion, and extension. The resulting effective sectional stiffness is strongly anisotropic: bending and extension are reduced by about one order of magnitude, whereas torsion remains close to the effective backbone stiffness. The resulting sectional law is embedded in a geometrically exact dynamic Cosserat model with GVS discretization and routed-tendon actuation. Across 103 measured configurations, the three datasets give pooled normalized position errors of \SI{7.7}{\percent}, \SI{6.7}{\percent}, and \SI{7.8}{\percent}, while each full-arm solve requires approximately \SI{0.3}{s} on one CPU core (Intel Xeon, Cascade Lake, \SI{2.8}{GHz}), enabling rapid model-based planning, state and load estimation, and morphology--control co-design for architected soft robots.