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     

Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots

Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model.     

A Neural Network Controller for Continuum Robots

Continuum or hyper-redundant robot manipulators can exhibit behavior similar to biological trunks, tentacles, or snakes. Unlike traditional rigid-link robot manipulators, continuum robot manipulators do not have rigid joints, hence these manipulators are extremely dexterous, compliant, and are capable of dynamic adaptive manipulation in unstructured environments. However, the development of high-performance control algorithms for these manipulators is quite a challenge, due to their unique design and the high degree of uncertainty in their dynamic models. In this paper, a controller for continuum robots, which utilizes a neural network feedforward component to compensate for dynamic uncertainties is presented. Experimental results using the OCTARM, which is a soft extensible continuum manipulator, are provided to illustrate that the addition of the neural network feedforward component to the controller provides improved performance.     

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.     

连续软体机器人的结构范型与形态复现

为提出连续软体机器人的设计与分析通用理论,根据当前连续软体机器人的运动特征和细长软体生物纵肌结构抽象出通用的结构范型（GSP）,并由此建立了连续软体机器人在驱动空间、构型空间和任务空间中的一般运动学．针对这类机器人在构型空间中灵活运动或操作的需求,提出一种细长软体机器人对任意目标曲线的形态复现算法,并采用离散Fréchet距离评价形态复现的相似性．通过仿真和实验,以形状记忆合金（SMA）弹簧驱动的双软体模块机器人为例验证了结构范型与一般运动学的正确性．此外,以仿生运动曲线等为目标曲线,以组合案例分析曲线形状、关节数量和关节参数对复现效果的影响．结果表明,软体单元模块数量越多或其最大弯曲角越大,形态复现的相似性越高．     

模块化可重构机器人动力学研究进展

模块化可重构机器人由于其构型多变,运动形式丰富等特点,可以在非结构化环境或未知环境中执行任务,在最近几年迅速成为机器人研究领域的前沿和热点. 模块化可重构机器人在军事、医疗、教育等众多工程领域具有广泛的应用前景,其典型代表包括仿生多足模块化机器人、模块化可重构机械臂、晶格式模块化机器人等. 模块化可重构机器人丰富的构型设计、多样的连接特征、不断拓展的应用范围,给动力学建模与控制带来了很多挑战和机遇. 本文首先阐述了模块化可重构机器人的研究背景和意义,并概述了其构型分类与设计、构型描述与运动学建模方法.随后,本文系统回顾了模块化可重构机器人动力学研究中相关问题的最新进展,包括：(1)系统整体动力学建模;(2)结合面以及对接机构动力学建模;(3)基于动力学模型的控制方法. 本文最后提出了模块化可重构机器人动力学研究中若干值得关注的问题.     

Euler Spiral for Shape Completion

In this paper we address the curve completion problem, e.g., the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion. Also known as the gap completion or shape completion problem, this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared (elastica), as motivated by a physical analogy. Our approach is motivated by railroad design methods of the early 1900's which connect two rail segments by transition curves, and by the work of Knuth on mathematical typography. We propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation. The minimization of total curvature variation leads to an Euler Spiral solution, a curve whose curvature varies linearly with arclength. We reduce the construction of this curve from a pair of points and tangents at these points to solving a nonlinear system of equations involving Fresnel Integrals, whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions. Since the choice of an appropriate initial curve is critical in this optimization, we analytically derive an optimal solution in the class of biarc curves, which is then used as the initial curve. The resulting interpolations yield intuitive interpolation across gaps and occlusions, and are extensible, in contrast to the scale-invariant version of elastica. In addition, Euler Spiral segments can be used in other applications of curve completions, e.g., modeling boundary segments between curvature extrema or modeling skeletal branch geometry.     

Dynamics and Cooperative Object Manipulation Control of Suspended Mobile Manipulators

Dynamics and control of mobile manipulators is obviously a more challenging problem compared to fixed-base robots. Including a suspension system for these mobile platforms increases their maneuverability, but considerably adds to their complexity. In this paper, a suspended wheeled mobile platform with two 6-DOF Puma-type manipulators is used to manipulate an object along a given path. To apply a model-based control algorithm, it is required to have an explicit dynamics model for such highly nonlinear system. This model should be as concise as possible to include fewer mathematical calculations for online computations. Therefore in this paper, a detailed set of dynamics equations for a multiple arm wheeled mobile platform equipped with an effective suspension system is presented. The method is based on the concept of Direct Path Method (DPM), which is extended here for such challenging type of robots. The obtained dynamics model is then verified with a dynamical analysis study using software ADAMS. Then, Natural Orthogonal Complement Method is used to include the non-holonomic constraint of the wheeled platform in a more concise dynamics model. Next, an impedance control law is applied for cooperative manipulation of an object by the two manipulators. The obtained results for a suspended wheeled platform equipped with two 6-DOF Puma-type manipulators reveal a successful performance for moving an object along a mixed circular-straight path, even in the presence of unexpected disturbing forces, system/end-effector flexibility and impacts due to contact with an obstacle.     

Real-Time Kinematics of Continuum Robots: Modelling and Validation

Kinematics of flexible backbone continuum robots is highly non linear and its complexity quickly escalates with the number of sections of the robot, which is usually more than three. This paper introduces a kinematic modelling of actuation and configuration spaces that greatly simplifies the computational requirements compared to the commonly used Piecewise Constant Curvature Kinematics which results in a faster algorithm at a rate proportional to the number of sections. This new algorithm is firstly developed for Twin Pivot Compliant Joint continuum robots but then extended to a general single neutral axis backbone configuration, both achieving a very low error of approximation (0.7% for the prototype developed), which results in several advantages such as the avoidance of highly non-linear functions and singularities, great reduction of computational complexity and an user-friendly graphical representation to help operation and status monitoring of this kind of robots. Moreover, a slender, small diameter and hyper-redundant (175 mm length, 6 mm diameter, 10 Degrees of Freedom) continuum robot prototype is developed and tested in a real-case industrial application for inspection and repair of aero engines in order to validate the proposed model.     

柔性机器人的动力学建模及其控制*

本文首先综述了近年来在柔性机器人动力学建模方面所取得的进展，着重介绍了目前较常见的几种建模方法和模型，同时对柔性机器人的控制问题进行了评述，指出了今后研究的方向。     

Editorial

A fundamental physical understanding of the properties and structure of dynamic robot models is the basis of controller design for robotic manipulators. This paper focuses on the estimation of different parameters which appear in the dynamics models of robots. By introducing candidate functions and a statistical approach to analyze these functions it is possible to identify the significant parameters in the dynamics model of the manipulator. This generalized method is also capable of considering Coloumb and viscous friction effects. Modeling based on candidate functions does not require symbolic calculation for the dynamics of the manipulator and can easily be applied to manipulators with more than 6 d.o.f. Parameter estimation is especially appropriate for modeling manipulators with many degrees of freedom prior to developing control algorithms, where otherwise the computation of such models is overwhelming. It is also demonstrated that this type of modeling is equivalent to the conventional symbolic calculation of dynamics of manipulators.     

Geometric phases and robotic locomotion

Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallel parking. In this article we explore the use of tools from differential geometry to model and analyze this class of locomotion mechanisms in a unified way. In particular, we describe locomotion in terms of the geometric phase associated with a connection on a principal bundle, and address issues such as controllability and choice of gait. We also provide an introduction to the basic mathematical concepts that we require and apply the theory to numerous example systems. © 1995 John Wiley & Sons, Inc.     

Geometrically Exact Models for Soft Robotic Manipulators

Unlike traditional rigid linked robots, soft robotic manipulators can bend into a wide variety of complex shapes due to control inputs and gravitational loading. This paper presents a new approach for modeling soft robotic manipulators that incorporates the effect of material nonlinearities and distributed weight and payload. The model is geometrically exact for the large curvature, shear, torsion, and extension that often occur in these manipulators. The model is based on the geometrically exact Cosserat rod theory and a fiber reinforced model of the air muscle actuators. The model is validated experimentally on the OctArm V manipulator, showing less than 5% average error for a wide range of actuation pressures and base orientations as compared to almost 50% average error for the constant-curvature model previously used by researchers. Workspace plots generated from the model show the significant effects of self-weight on OctArm V.      

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.     

Markerless human–robot interface for dual robot manipulators using Kinect sensor

Remote teleoperation of robot manipulators is often necessary in unstructured, dynamic, and dangerous environments. However, the existing mechanical and other contacting interfaces require unnatural, or hinder natural, human motions. At present, the contacting interfaces used in teleoperation for multiple robot manipulators often require multiple operators. Previous vision-based approaches have only been used in the remote teleoperation for one robot manipulator as well as require the special quantity of illumination and visual angle that limit the field of application. This paper presents a noncontacting Kinect-based method that allows a human operator to communicate his motions to the dual robot manipulators by performing double hand–arm movements that would naturally carry out an object manipulation task. This paper also proposes an innovative algorithm of over damping to solve the problem of error extracting and dithering due to the noncontact measure. By making full use of the human hand–arm motion, the operator would feel immersive. This human–robot interface allows the flexible implementation of the object manipulation task done in collaboration by dual robots through the double hand–arm motion by one operator.     

Introduction to the special issue on Advances in intelligent nonlinear control for robotic systems

In the last two decades, robotic systems have achieved wide applications in every aspect of human society, including industrial manufacturing, automotive production, medical devices, and social lives. With the     

多关节机器人的运动学动态仿真研究

机器人运动学是机器人学的一个重要分支，是实现机器人运动控制的基础。文中主要针对PUMA560机器人运动学正问题分析，以D-H坐标系理论为基础并建模，利用MATLAB／ROBOTICS工具，实现了简单的运动学动态仿真，有助于对机器人关节运动角度的深入理解，并为工程人员提供一种有效的分析手段。     

Kinematic modeling of mobile robots by transfer method of augmented generalized coordinates

A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc.     

Kinematics of a parallel-serial (Hybrid) manipulator

Hybrid manipulators are parallel-serial connection robots that give rise to a multitude of highly articulate robotic manipulators. These manipulators are modular and can be extended by additional modules over large distances. Every module has a hemispherical work space and collective modules give rise to highly dexterous symmetrical work space. In this article, some basic designs and kinematical structures of these robot manipulators are discussed, the associated direct and the inverse kinematics formulations are presented, and solutions to the inverse kinematic problem are obtained explicitly and elaborated upon. These robot manipulators are shown to have a strength-to-weight ratio many times larger than the value currently available with industrial or research manipulators. This is due to the fact that these hybrid manipulators are stress compensated and have an ultralight weight, yet are extremely stiff due to the fact that the force distribution in their structure is mostly axial. The means of actuation in these manipulators are entirely prismatic and can be provided by ball-screws with antibacklash nuts or linear induction motors for maximum precision.