Bryan A. Jones

Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review

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 single-section 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.

Kinematics for multisection continuum robots

We introduce a new method for synthesizing kinematic relationships for a general class of continuous backbone, or continuum , robots. The resulting kinematics enable real-time task and shape control by relating workspace (Cartesian) coordinates to actuator inputs, such as tendon lengths or pneumatic pressures, via robot shape coordinates. This novel approach, which carefully considers physical manipulator constraints, avoids artifacts of simplifying assumptions associated with previous approaches, such as the need to fit the resulting solutions to the physical robot. It is applicable to a wide class of existing continuum robots and models extension, as well as bending, of individual sections. In addition, this approach produces correct results for orientation, in contrast to some previously published approaches. Results of real-time implementations on two types of spatial multisection continuum manipulators are reported.

A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots

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.

Three dimensional statics for continuum robotics

This paper introduces a method for computing the shape of a continuously-flexible (continuum) robot in 3-D space which includes gravity loading by applying Cosserat rod theory to a continuum robot. With this theory, the shape of the rod can be determined using force-torque balance equations obtained from a simple free body diagram that represents the continuum robot. Real-time performance of 125 Hz makes this approach viable for the control of a continuum robot, enabled by avoiding boundary-value conditions in the solution.

Closed-Form Inverse Kinematics for Continuum Manipulators

This paper presents a novel, analytical approach to solving inverse kinematics for multi-section continuum robots, defined as robots composed of a continuously bendable backbone. The problem is decomposed into several simpler subproblems. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming endpoints for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for the resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a prototype continuum robot are presented and possible applications discussed.

Design and experimental testing of the OctArm soft robot manipulator

This paper describes the development of the octopus biology inspired OctArm series of soft robot manipulators. Each OctArm is constructed using air muscle extensors with three control channels per section that provide two axis bending and extension. Within each section, mesh and plastic coupler constraints prevent extensor buckling. OctArm IV is comprised of four sections connected by endplates, providing twelve degrees of freedom. Performance of OctArm IV is characterized in a lab environment. Using only 4.13 bar of air pressure, the dexterous distal section provides 66% extension and 380° of rotation in less than .5 seconds. OctArm V has three sections and, using 8.27 bar of air pressure, the strong proximal section provides 890 N and 250 N of vertical and transverse load capacity, respectively. In addition to the in-lab testing, OctArm V underwent a series of field trials including open-air and in-water field tests. Outcomes of the trials, in which the manipulator demonstrated the ability for adaptive and novel manipulation in challenging environments, are described. OctArm VI is designed and constructed based on the in-lab performance, and the field testing of its predecessors. Implications for the deployment of soft robots in military environments are discussed.

Design and Analysis of a Novel Pneumatic Manipulator

Abstract This paper discusses the design and analysis of a novel “continuum” robot manipulator. The design features two concentric flexible cylinders, with a pneumatically actuated inner tube and with tendons fixed to an outer cylinder. The tendons control bending of the (continuous) structure. Variation of pneumatic pressure allows both extension and the presentation of variable compliance to the environment. Details of the design and implementation of the robot are discussed. Additionally, a novel kinematic model, relating robot shape to tendon lengths, is presented. The design is highly scalable, with a wide range of potential applications.

A model for concentric tube continuum robots under applied wrenches

Continuum robots made from telescoping precurved elastic tubes enable base-mounted actuators to specify the curved shapes of robots as thin as standard surgical needles. While free space beam mechanics-based models of the shape of these ‘active cannulas’ exist, current models cannot account for external forces and torques applied to the cannula by the environment. In this paper we apply geometrically exact beam theory to solve the statics problem for concentric-tube continuum robots. This yields the equivalent of forward kinematics for an active cannula with general tube precurvature functions and arbitrarily many tubes, under loading from a general wrench distribution. The model achieves average experimental tip errors of less than 3 mm over the workspace of a prototype active cannula subject to various tip forces.

Practical kinematics for real-time implementation of continuum robots

This paper introduces three algorithms which are essential for the practical, real-time implementation of continuum robots. Continuum robots lack the joints and links which compose traditional and high-degree-of-freedom robots, instead relying on finite actuation mechanisms to shape the robot into a smooth curve. Actuator length limits shape the configuration or joint space of continuum manipulators, introducing couplings analyzed in this paper which must be understood to make effective use of continuum robot hardware. Based on the new understanding of the configuration space uncovered, this paper then derives the workspace of continuum robots when constrained by actuator length limits. Finally, a tangle/untangle algorithm correctly computes the shape of the distal segments of multisection tendon-actuated continuum robots. These contributions are essential for effective use of a wide range of continuum robots, and have been implemented and tested on two different types of continuum robots. Results and insight gained from this implementation are presented

A geometrical approach to inverse kinematics for continuum manipulators

We present a new geometrical approach to solving inverse kinematics for continuous backbone (continuum) robot manipulators. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming end-points for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a physical continuum robot are presented and possible applications are discussed.