Continuum robotics has rapidly become a rich and diverse area of research, with many designs and applications demonstrated. Despite this diversity in form and purpose, there exists remarkable similarity in the fundamental simplified kinematic models that have been applied to continuum robots. However, this can easily be obscured, especially to a newcomer to the field, by the different applications, coordinate frame choices, and analytical formalisms employed. In this paper we review several modeling approaches in a common frame and notational convention, illustrating that for piecewise constant curvature, they produce identical results. This discussion elucidates what has been articulated in different ways by a number of researchers in the past several years, namely that constant-curvature kinematics can be considered as consisting of two separate submappings: one that is general and applies to all continuum robots, and another that is robot-specific. These mappings are then developed both for the singlesection and for the multi-section case. Similarly, we discuss the decomposition of differential kinematics (the robot's Jacobian) into robot-specific and robot-independent portions. The paper concludes with a perspective on several of the themes of current research that are shaping the future of continuum robotics.

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Continuum robots, which are composed of multiple concentric, precurved elastic tubes, can provide dexterity at diameters equivalent to standard surgical needles. Recent mechanics-based models of these “active cannulas” are able to accurately describe the curve of the robot in free space, given the preformed tube curves and the linear and angular positions of the tube bases. However, in practical applications, where the active cannula must interact with its environment or apply controlled forces, a model that accounts for deformation under external loading is required. In this paper, we apply geometrically exact rod theory to produce a forward kinematic model that accurately describes large deflections due to a general collection of externally applied point and/or distributed wrench loads. This model accommodates arbitrarily many tubes, with each having a general preshaped curve. It also describes the independent torsional deformation of the individual tubes. Experimental results are provided for both point and distributed loads. Average tip error under load was 2.91 mm (1.5%–3% of total robot length), which is similar to the accuracy of existing free-space models.

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We present design and experimental performance results for a novel mechanism for robotic legged locomotion at the mesoscale (from hundreds of microns to tens of centimeters). The new mechanism is compact and strikes a balance between conflicting design objectives, exhibiting high foot forces and low power consumption. It enables a small robot to traverse a compliant, slippery, tubular environment, even while climbing against gravity. This mechanism is useful for many mesoscale locomotion tasks, including endoscopic capsule robot locomotion in the gastrointestinal tract. It has enabled fabrication of the first legged endoscopic capsule robot whose mechanical components match the dimensions of commercial pill cameras (11 mm diameter by 25 mm long). A novel slot-follower mechanism driven via lead screw enables the mechanical components of the capsule robot to be as small while simultaneously generating 0.63 N average propulsive force at each leg tip. In this paper, we describe kinematic and static analyses of the lead screw and slot-follower mechanisms, optimization of design parameters, and experimental design and tuning of a gait suitable for locomotion. A series of ex vivo experiments demonstrate capsule performance and ability to traverse the intestine in a manner suitable for inspection of the colon in a time period equivalent to standard colonoscopy.

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Mechanics-based models of concentric tube continuum robots have recently achieved a level of sophistication that makes it possible to begin to apply these robots to a variety of real-world clinical scenarios. Endonasal skull base surgery is one such application, where their small diameter and tentacle like dexterity are particularly advantageous. In this paper we provide the medical motivation for an endonasal surgical robot featuring concentric tube manipulators, and describe our model-based design and teleoperation methods, as well as a complete system incorporating image-guidance. Experimental demonstrations using a laparoscopic training task, a cadaver reachability study, and a phantom tumor resection experiment illustrate that both novice and expert users can effectively teleoperate the system, and that skull base surgeons can use the robot to achieve their objectives in a realistic surgical scenario.