This paper describes and discusses the history and state of the art of continuous backbone robot manipulators. Also known as continuum manipulators, these robots, which resemble biological trunks and tentacles, offer capabilities beyond the scope of traditional rigid-link manipulators. They are able to adapt their shape to navigate through complex environments and grasp a wide variety of payloads using their compliant backbones. In this paper, we review the current state of knowledge in the field, focusing particularly on kinematic and dynamic models for continuum robots. We discuss the relationships of these robots and their models to their counterparts in conventional rigid-link robots. Ongoing research and future developments in the field are discussed.

This article provides a tutorial on the dynamic modeling of continuum robots. Continuum robots (CRs) have gained popularity in recent years due to their flexible backbone structure. Modeling and control of CRs motivate accurate and efficient dynamic models. Such models will enable simulation of dynamic behavior, improved structural design, and the development of dynamics-based control systems for CRs. As a unified underlying approach, the Cosserat rod-based modeling of tendon-driven CRs is used as the basis of the modeling techniques discussed in this paper. In addition to conventional continuum robot assemblies, new and emerging assemblies such as tendon-bent concentric tube and co-operative robots are also considered. The governing equations of motion for conventional CRs are first summarized and then extended for other tendon-driven CRs. This tutorial also contributes to developing a MATLAB code package for simulation of the dynamic response of these robots. The presented method and codes provide a useful and compact resource for readers and can be used for further development of tendon-driven continuum robots.

We present a new approach to creating biologically inspired, variable compliance continuum robot sections. Variable compliance is used to great effect in natural continuum structures, such as the arms of octopuses and the tails of kangaroos. We introduce a new approach to variable compliance robots based on mechanical layer jamming. The new design actively tightens and loosens mesh coverings of interleaved surface layers. This mechanical approach to layer jamming avoids problems arising from previously proposed pressure (pneumatic)-based layer jamming implementations. Experiments using a prototype of the new design demonstrate the potential of the approach to produce novel soft and compliant robots.

Despite the rise of development in continuum manipulator technology and application, a model-based feedback closed-loop control appropriate for continuum robot designs has remained a significant challenge. Complicated by the soft and flexible nature of the manipulator body, control of continuum structures with infinite dimensions proves to be difficult due to their complex dynamics. In this paper, a novel strategy is designed for trajectory control of a multi-section continuum robot in three-dimensional (3D) space to achieve accurate orientation, curvature, and section length tracking. The formulation connects the continuum manipulator dynamic behavior to a virtual discrete-jointed robot whose degrees of freedom are directly mapped to those of a continuum robot section under the hypothesis of constant curvature. Based on this connection, a computed torque control architecture is developed for the virtual robot, for which kinematics and dynamic equations are constructed and exploited, with appropriate transformations developed for implementation on the continuum robot. The control algorithm is implemented on a six Degree-of-Freedom two-section OctArm continuum manipulator. Experiments show that the proposed method could manage simultaneous extension/contraction, bending, and torsion actions on multi-section continuum robots with decent performance (arc length and curvature error of ±4mm and ±0.35 m $-1$ ). The designed dynamic controller can reduce the curvature tracking error and rise time by up to 48.1% and 94.8% compared to the traditional PID controller during two-section maneuvers.

Continuous-bodied “trunk and tentacle” robots have increased self-adaptability and obstacle avoidance capabilities, compared with traditional, discrete-jointed, robots with large rigid links. In particular, continuous-bodied robots have obvious advantages in grasping objects across a wide range of external dimensions. Not only can they grasp objects using end effectors like traditional robots, but their bodies can also be regarded as a gripping device, and large objects with respect to the robot’s scale can be captured by the entire structure of the robots themselves. Existing trunk-like robots have distributed multidrive actuation and are often manufactured using soft materials, which leads to a complex actuator system that also limits their potential applications in dangerous and extreme environments. This paper introduces a new type of elephant’s trunk robot with very few driving constraints. The robot consists of a series of novel underactuated linkage units. With a single-motor drive, the robot can achieve stable grasping of objects of different shapes and sizes. The proposed robot simplifies the requirements of the sensing and control systems during the operation process and has the advantage of accomplishing the capture task without determining the exact shape and position of the target object. It is especially suitable for operations such as non-cooperative target capture in extremely dangerous environments, including those in outer space. Based on theoretical analysis and model design, a trunk robot prototype was developed, and a comprehensive experimental study of the bending/extension and grasping operation functions was conducted to verify the validity of the proposed robot design.

We introduce a new class of long and thin continuum robots intended for use in space applications. This ‘cable’ robot is a next-generation version of the current state of the art (NASA’s ‘Tendril’). The article describes the key practical limitations of the mechanical design of ‘Tendril’. We introduce the design specifics of our novel concept for a next-generation device with significantly enhanced performance. Equipped with a light and compact motor-encoder actuation mechanism, the new design has improved compliance and possesses a concentric backbone arrangement which is tendon-actuated and spring-loaded. A new forward kinematic model is developed extending the established models for constant-curvature continuum robots, to account for the new design feature of controllable compression (in the hardware). The model is validated by performing experiments with a three-section prototype of the design. The new model is found to be effective as a baseline to predict the performance of such long and thin continuum ‘cable’ robots. Graphical Abstract