From Differential Geometry of Curves to Helical Kinematics of Continuum Robots Using Exponential Mapping

Kinematic modeling of continuum robots is challenging due to the large deflections that these systems usually undergone. In this paper, we derive the kinematics of a continuum robot from the evolution of a three-dimensional curve in space. We obtain the spatial configuration of a continuum robot in terms of exponential coordinates based on Lie group theory. This kinematic framework turns out to handle robotic helical shapes, i.e. spatial configurations with constant curvature and torsion of the arm

Hybrid Mechanical and Data-driven Modeling Improves Inverse Kinematic Control of a Soft Robot

Reinhart F, Steil JJ. Hybrid Mechanical and Data-driven Modeling Improves Inverse Kinematic Control of a Soft Robot. In: Procedia Technology. Vol 26. 2016: 12-19

Artificial neural network for solving the inverse kinematic model of a spatial and planar variable curvature continuum robot

In this paper, neural networks are presented to solve the inverse kinematic models of continuum robots. Firstly, the forward kinematic models are calculated for variable curvature continuum robots. Then, the forward kinematic models are implemented in the neural networks which present the position of the continuum robot’s end effector. After that, the inverse kinematic models are solved through neural networks without setting up any constraints. In the same context, to validate the utility of the developed neural networks, various types of trajectories are proposed to be followed by continuum robots. It is found that the developed neural networks are powerful tool to deal with the high complexity of the non-linear equations, in particular when it comes to solving the inverse kinematics model of variable curvature continuum robots. To have a closer look at the efficiency of the developed neural network models during the follow up of the proposed trajectories, 3D simulation examples through Matlab have been carried out with different configurations. It is noteworthy to say that the developed models are a needed tool for real time application since it does not depend on the complexity of the continuum robots' inverse kinematic models

Software Abstractions for Simulation and Control of a Continuum Robot

Nordmann A, Rolf M, Wrede S. Software Abstractions for Simulation and Control of a Continuum Robot. In: SIMPAR2012 - SIMULATION, MODELING, and PROGRAMMING for AUTONOMOUS ROBOTS. 2012

Finite element method-based kinematics and closed-loop control of soft, continuum manipulators

International audienceThis paper presents a modeling methodology and experimental validation for soft 1 manipulators to obtain forward and inverse kinematic models under quasistatic conditions. It offers a way to obtain the kinematic characteristics of this type of soft robots that is suitable for offline path planning and position control. The modeling methodology presented relies on continuum mechanics which does not provide analytic solutions in the general case. Our approach proposes a real-time numerical integration strategy based on Finite Element Method (FEM) with a numerical optimization based on Lagrangian Multipliers to obtain forward and inverse models. To reduce the dimension of the problem, at each step, a projection of the model to the constraint space (gathering actuators, sensors and end-effector) is performed to obtain the smallest number possible of mathematical equations to be solved. This methodology is applied to obtain the kinematics of two different manipulators with complex structural geometry. An experimental comparison is also performed in one of the robots, between two other geometric approaches and the approach that is showcased in this paper. A closed-loop controller based on a state estimator is proposed. The controller is experimentally validated and its robustness is evaluated using Lypunov stability method

Dynamic modelling and visco-elastic parameter identification of a fibre-reinforced soft fluidic elastomer manipulator

A dynamic model of a soft fibre-reinforced fluidic elastomer is presented and experimentally verified, which can be used for model-based controller design. Due to the inherent visco-(hyper)elastic characteristics and nonlinear timedependent behaviour of soft fluidic elastomer robots, analytic dynamic modelling is challenging. The fibre reinforced noninflatable soft fluidic elastomer robot used in this paper can produce both planar and spatial movements. Dynamic equations are developed for both cases. Parameters, related to the viscoelastic behaviour of the robot during elongation and bending motion, are identified experimentally and incorporated into our model. The modified dynamic model is then validated in experiments comparing the time responses of the physical robot with the corresponding outputs of the simulation model. The results validate the accuracy of the proposed dynamic model

Multi-Segment Parallel Continuum Manipulator

Continuum manipulators are a type of robot arm that resemble biological tentacles and trunks. They have a flexible and compliant structure, which may allow them to out-perform rigid-link designs in cluttered workspaces or in environments that contain people. While most continuum manipulators are required to have constant curvature along the length of each segment, a new design known as a parallel continuum manipulator removes this restriction and inherits some properties of parallel rigid-link robots such as greater stability, precision, strength, and maneuverability. Until now, only single segment forms of these manipulators have been created. This project expands this manipulator design concept by creating the first multi-segment parallel continuum manipulator