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 ηc(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.
In this paper, we design feedback control laws for soft robots modelled using the Cosserat rod, which is spatially discretised using the Piecewise Constant Strain (PCS) approach. The PCS approach transforms the nonlinear PDEs describing the Cosserat rod to a system of nonlinear ODEs. This simplification results in a model describing soft robots which is similar to the serial rigid-link manipulators. We design feedback control laws for the quasi-static PCS model by using external wrenches as control inputs. The control laws are designed based on state-feedback linearisation in strain and task spaces. An extensive set of numerical results demonstrates the performance of the control laws for end-effector trajectory tracking and shape control of soft robots.
Modeling soft robot dynamics is challenging due to their continuum structure and typically nonlinear dynamics. Creating models based on first-order principles is typically time-demanding, and their expressiveness is limited, whereas data-driven models lack interpretability and physical consistency. This work aims to overcome these challenges by introducing a port-Hamiltonian Gaussian Process Regression framework for learning and simulating the dynamics of planar, rod-like soft robots. In detail, the proposed model integrates Cosserat rod theory and Hamiltonian physics with data-driven inference to preserve the system's energy structure while accurately learning the rod dynamics. Numerical simulations show that we can achieve accurate and energy-consistent representations of a rod-like soft robot, showing the potential for a robust and interpretable pathway for modeling complex continuum mechanics.
Mohammad Ali, Nithin Senthur Kumar, Eric J. Barth +1
Soft continuum robots require embedded sensing for proprioception and contact detection, yet integrating sensors into sparse, highly deformable architected structures remains challenging. We present a model-based strategy that decouples proprioceptive and contact signals from a common set of fluidic pressure sensors embedded in a soft architected segment. Each segment of the Innervated Trimmed Helicoid (ITH) contains six air channels routed in a localized zigzag pattern along the circumference. With only three principal kinematic degrees of freedom (axial compression, bending in x, bending in y), the six pressure readings form an overdetermined system. A piecewise constant curvature model maps pressures to shape, and Huber regression identifies outlier channels whose residuals indicate external contact. On a single ITH segment, this approach achieves proprioceptive shape estimation with a relative bending error of 0.11 +/- 0.02 and a contact detection rate of 97% across 178 trials. We integrate eight ITH segments into Air-Helix, a tendon-driven soft continuum manipulator, and present exploratory whole-arm demonstrations that include tactile teaching by demonstration, admittance-controlled force regulation, and tactile object reconstruction. The results suggest that localized fluidic innervation combined with model-based redundancy resolution is a practical path toward concurrent proprioception and contact sensing in architected soft robots.
Francesco Stella, Annan Zhang, Cosimo Della Santina +2