Buckling of chiral rods due to coupled axial and rotational growth

We present a growth model for special Cosserat rods that allows for induced rotation of cross-sections. The growth law considers two controls, one for lengthwise growth and another for rotations. This is explored in greater detail for straight rods with helical and hemitropic material symmetries by introduction of symmetry-preserving growth to account for the microstructure. The example of a guided-guided rod possessing a chiral microstructure is considered to study its deformation due to growth. We show the occurrence of growth-induced out-of-plane buckling in such rods.

Low-Mach-number and slenderness limit for elastic Cosserat rods and its numerical investigation

This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e., low-Mach-number–slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a Gauss–Legendre collocation in space and an α-method in time.

Modeling and simulation of complex dynamic musculoskeletal architectures

Natural creatures, from fish and cephalopods to snakes and birds, combine neural control, sensory feedback and compliant mechanics to effectively operate across dynamic, uncertain environments. In order to facilitate the understanding of the biophysical mechanisms at play and to streamline their potential use in engineering applications, we present here a versatile numerical approach to the simulation of musculoskeletal architectures. It relies on the assembly of heterogenous, active and passive Cosserat rods into dynamic structures that model bones, tendons, ligaments, fibers and muscle connectivity. We demonstrate its utility in a range of problems involving biological and soft robotic scenarios across scales and environments: from the engineering of millimeter-long bio-hybrid robots to the synthesis and reconstruction of complex musculoskeletal systems. The versatility of this methodology offers a framework to aid forward and inverse bioengineering designs as well as fundamental discovery in the functioning of living organisms.

Stiffness Control of Parallel Continuum Robots

Parallel continuum robots can provide compact, compliant manipulation of tools in robotic surgery and larger-scale human robot interaction. In this paper we address stiffness control of parallel continuum robots using a general nonlinear kinetostatic modeling framework based on Cosserat rods. We use a model formulation that estimates the applied end-effector force and pose using actuator force measurements. An integral control approach then modifies the commanded target position based on the desired stiffness behavior and the estimated force and position. We then use low-level position control of the actuators to achieve the modified target position. Experimental results show that after calibration of a single model parameter, the proposed approach achieves accurate stiffness control in various directions and poses.