Variable length multisection continuum arms are a class of continuum robotic manipulators that generate motion by structural mechanical deformation. Unlike most continuum robots, the sections of these arms do not have (central) supporting flexible backbone, and are actuated by multiple variable length actuators. Because of the constraining nature of actuators, the continuum sections can bend and/or elongate (compress) depending on the elongation/contraction characteristics of the actuators being used. Continuum arms have a number of distinctive differences with respect to traditional rigid arms namely: smooth bending, high inherent compliance, and adaptive whole arm grasping. However, due to numerical instability and the complexity of curve parametric models, there are no spatial dynamic models for multisection continuum arms. This paper introduces novel spatial dynamics and applies these to variable length multisection continuum arms with any number of sections. An efficient recursive computational scheme for deriving the equations of motion is presented. This is applied in a general form based on structurally accurate and numerically well posed modal kinematics that assumes circular arc deformation of continuum sections without torsion. It is shown that the proposed modal dynamics are highly scalable, producing efficient and accurate numerical results. The spatial dynamic simulation results are experimentally validated using a pneumatic muscle actuated multisection prototype continuum arm. For the first time this enables investigation of spatial dynamic effects in this class of continuum arms.

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Biological tentacles, such as octopus arms, have entirely flexible structures and virtually infinite degrees of freedom (DOF) that allow for elongation, shortening and bending at any point along the arm length. The amazing dexterity of biological tentacles has driven the growing implementation of continuum manipulators in robotic systems. This paper presents a pneumatic manipulator inspired by biological continuum structures in some of their key features and functions, such as continuum morphology, intrinsic compliance and stereotyped motions with hyper redundant DOF. The kinematics and dynamics of the manipulator are formulated and identified, and a hierarchical controller taking inspiration from the structure of an octopus nervous system is used to relate desired stereotyped motions to individual actuator inputs. Simulations and experiments are carried out to validate the model and prototype where good agreement was found between the two.

This paper presents a novel spatial kinematic model for multisection continuum arms based on mode shape functions (MSF). Modal methods have been used in many disciplines from finite element methods to structural analysis to approximate complex and nonlinear parametric variations with simple mathematical functions. Given certain constraints and required accuracy, this helps to simplify complex phenomena with numerically efficient implementations leading to fast computations. A successful application of the modal approximation techniques to develop a new modal kinematic model for general variable length multisection continuum arms is discussed. The proposed method solves the limitations associated with previous models and introduces a new approach for readily deriving exact, singularity-free and unique MSF's that simplifies the approach and avoids mode switching. The model is able to simulate spatial bending as well as straight arm motions (i.e., pure elongation/contraction), and introduces inverse position and orientation kinematics for multisection continuum arms. A kinematic decoupling feature, splitting position and orientation inverse kinematics is introduced. This type of decoupling has not been presented for these types of robotic arms before. The model also carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics and impose actuator mechanical limitations onto the kinematics thus generating fully realizable results. The proposed method is easily applicable to a broad spectrum of continuum arm designs.

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Continuum robots exhibit promising adaptability and dexterity for soft manipulation due to their intrinsic compliance. However, this compliance may lead to challenges in modeling as well as positioning and loading. In this paper, a virtual work-based static model is established to describe the deformation and mechanics of continuum robots with a generic rod-driven structure, taking the geometric constraint of the drive rods into account. Following this, this paper presents a novel variable stiffness mechanism powered by a set of embedded Shape Memory Alloy (SMA) springs, which can make the drive rods become ‘locked’ on the body structure with different configurations. The resulting effects of variable stiffness are then presented in the static model by introducing tensions of the SMA and friction on the rods. Compared with conventional models, there is no need to predefine the actuation forces of the drive rods; instead, actuation displacements are used in this new mechanism system with stiffness being regulated. As a result, the phenomenon that the continuum robot can exhibit an S-shaped curve when subject to single-directional forces is observed and analyzed. Simulations and experiments demonstrated that the presented mechanism has stiffness variation of over 287% and further demonstrated that the mechanism and its model are achievable with good accuracy, such that the ratio of positioning error is less than 2.23% at the robot end-effector to the robot length.

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