Discrete Cosserat Approach for Multi-Section Soft Robots Dynamics

In spite of recent progress, soft robotics still suffers from a lack of unified modeling framework. Nowadays, the most adopted model for the design and control of soft robots is the piece-wise constant curvature model, with its consolidated benefits and drawbacks. In this work, an alternative model for multisection soft robots dynamics is presented based on a discrete Cosserat approach, which, not only takes into account shear and torsional deformations, essentials to cope with out-of-plane external loads, but also inherits the geometrical and mechanical properties of the continuous Cosserat model, making it the natural soft robotics counterpart of the traditional rigid robotics dynamics model. The soundness of the model is demonstrated through extensive simulation and experimental results for both plane and out-of-plane motions.Comment: 13 pages, 9 figure

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multisegment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic methods. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6%-8% (4-6 mm) mean error for the Ritz-Galerkin method in static cases and 16%-20% (12-14 mm) mean error for the Ritz method in dynamic cases, in planar and general three-dimensional motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation, and control applications

Static kinematics for an antagonistically actuated robot based on a beam-mechanics-based model

Soft robotic structures might play a major role in the 4th industrial revolution. Researchers have successfully demonstrated advantages of soft robotics over traditional robots made of rigid links and joints in several application areas including manufacturing, healthcare and surgical interventions. However, soft robots have limited ability to exert higher forces when it comes to interaction with the environment, hence, change their stiffness on demand over a wide range. One stiffness mechanism embodies tendon-driven and pneumatic air actuation in an antagonistic way achieving variable stiffness values. In this paper, we apply a beammechanics-based model to this type of soft stiffness controllable robot. This mathematical model takes into account the various stiffness levels of the soft robotic manipulator as well as interaction forces with the environment at the tip of the manipulator. The analytical model is implemented into a robotic actuation system made of motorised linear rails with load cells (obtaining applied forces to the tendons) and a pressure regulator. Here, we present and analyse the performance and limitations of our model

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multi-segment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic method. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6-8% (4-6 [mm]) mean error for the Ritz-Galerkin method in static cases and 16-20% (12-14 [mm]) mean error for the Ritz method in dynamic cases, in planar and general 3D motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation and control applications

First-Order Dynamic Modeling and Control of Soft Robots

Modeling of soft robots is typically performed at the static level or at a second-order fully dynamic level. Controllers developed upon these models have several advantages and disadvantages. Static controllers, based on the kinematic relations tend to be the easiest to develop, but by sacrificing accuracy, efficiency and the natural dynamics. Controllers developed using second-order dynamic models tend to be computationally expensive, but allow optimal control. Here we propose that the dynamic model of a soft robot can be reduced to first-order dynamical equation owing to their high damping and low inertial properties, as typically observed in nature, with minimal loss in accuracy. This paper investigates the validity of this assumption and the advantages it provides to the modeling and control of soft robots. Our results demonstrate that this model approximation is a powerful tool for developing closed-loop task-space dynamic controllers for soft robots by simplifying the planning and sensory feedback process with minimal effects on the controller accuracy

Towards a Modular Framework for Visco-Hyperelastic Simulations of Soft Material Manipulators with Well-Parameterised Material

Controller design for continuum robots maintains to be a difficult task. Testing controllers requires dedicated work in manufacturing and investment into hardware as well as software, to acquire a test bench capable of performing dynamic control tasks. Typically, proprietary software for practical controller design such as Matlab/Simulink is used but lacks specific implementations of soft material robots. This intermediate work presents the results of a toolchain to derive well-identified rod simulations. State-of-the-art methods to simulate the dynamics of continuum robots are integrated into an object-oriented implementation and wrapped into the Simulink framework. The generated S-function is capable of handling arbitrary, user-defined input such as pressure actuation or external tip forces as demonstrated in numerical examples. With application to a soft pneumatic actuator, stiffness parameters of a nonlinear hyperelastic material law are identified via finite element simulation and paired with heuristically identified damping parameters to perform dynamic simulation. To prove the general functionality of the simulation, a numerical example as well as a benchmark from literature is implemented and shown. A soft pneumatic actuator is used to generate validation data, which is in good accordance with the respective simulation output. The tool is provided as an open-source project. Code is available under https://gitlab.com/soft_material_robotics/cosserat-rod-simulink-sfunction.© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

Forward dynamics of continuum and soft robots: a strain parametrization based approach

soumis à IEEE TROIn this article we propose a new solution to the forward dynamics of Cosserat beams with in perspective, its application to continuum and soft robotics manipulation and locomotion. In contrast to usual approaches, it is based on the non-linear parametrization of the beam shape by its strain fields and their discretization on a functional basis of strain modes. While remaining geometrically exact, the approach provides a minimal set of ordinary differential equations in the usual Lagrange matrix form that can be solved with standard explicit time-integrators. Inspired from rigid robotics, the calculation of the matrices of the Lagrange model is performed with a continuous inverse Newton-Euler algorithm. The approach is tested on several numerical benches of non-linear structural statics, as well as further examples illustrating its capabilities for dynamics

Modeling, simulation, and control of soft robots

2019 Fall.Includes bibliographical references.Soft robots are a new type of robot with deformable bodies and muscle-like actuations, which are fundamentally different from traditional robots with rigid links and motor-based actuators. Owing to their elasticity, soft robots outperform rigid ones in safety, maneuverability, and adaptability. With their advantages, many soft robots have been developed for manipulation and locomotion in recent years. However, the current state of soft robotics has significant design and development work, but lags behind in modeling and control due to the complex dynamic behavior of the soft bodies. This complexity prevents a unified dynamics model that captures the dynamic behavior, computationally-efficient algorithms to simulate the dynamics in real-time, and closed-loop control algorithms to accomplish desired dynamic responses. In this thesis, we address the three problems of modeling, simulation, and control of soft robots. For the modeling, we establish a general modeling framework for the dynamics by integrating Cosserat theory with Hamilton's principle. Such a framework can accommodate different actuation methods (e.g., pneumatic, cable-driven, artificial muscles, etc.). To simulate the proposed models, we develop efficient numerical algorithms and implement them in C++ to simulate the dynamics of soft robots in real-time. These algorithms consider qualities of the dynamics that are typically neglected (e.g., numerical damping, group structure). Using the developed numerical algorithms, we investigate the control of soft robots with the goal of achieving real-time and closed-loop control policies. Several control approaches are tested (e.g., model predictive control, reinforcement learning) for a few key tasks: reaching various points in a soft manipulator's workspace and tracking a given trajectory. The results show that model predictive control is possible but is computationally demanding, while reinforcement learning techniques are more computationally effective but require a substantial number of training samples. The modeling, simulation, and control framework developed in this thesis will lay a solid foundation to unleash the potential of soft robots for various applications, such as manipulation and locomotion