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1. The dynamics of a two link Chaplygin sleigh driven by an internal momentum wheel

   https://doi.org/10.23919/ACC.2017.7963274  

   Fedonyuk, Vitaliy; Tallapragada, Phanindra (May 2017, American Control Conference)

   A class of aquatic robots have been shown to have a correspondence to terrestrial nonholonomic systems. In particular bodies shaped as a Joukowski foil have been shown to have dynamics similar to a well known nonholonomic system, the Chaplygin sleigh. This inspires several related rigid body nonholonomic systems whose behavior is similar to other aquatic robots with other morphologies. In this paper we investigate the dynamics of one such nonholonomic system, a two-link Chaplygin sleigh that is controlled by an internal momentum wheel. This system is analogous to a similar aquatic robot with a passive tail. We also discuss results related to the accessibility and controllability of the two-link Chaplygin sleigh. 

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2. Limit Cycle Analysis and Control of the Dissipative Chaplygin Sleigh

   https://doi.org/10.1115/DSCC2017-5193  

   Fedonyuk, Vitaliy; Tallapragada, Phanindra; Wang, Yongqiang (October 2017, ASME Dynamic Systems and Control Conference)

   There are many types of systems in both nature and technology that exhibit limit cycles under periodic forcing. Sometimes, especially in swimming robots, such forcing is used to propel a body forward in a plane. Due to the complexity in studying a fluid system it is often useful to investigate the dynamics of an analogous land model. Such analysis can then be useful in gaining insight about and controlling the original fluid system. In this paper we investigate the behavior of the Chaplygin sleigh under the effect of viscous dissipation and sinusoidal forcing. This is shown to behave in a similar manner as certain robotic fish models. We then apply limit cycle analysis techniques to predict the behavior and control the net translational velocity of the sleigh in a horizontal plane. 

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3. Prediction of the behavior of a pneumatic soft robot based on Koopman operator theory

   https://doi.org/10.23919/MIPRO48935.2020.9245155  

   Kamenar, E.; Crnjaric-Zic, N.; Haggerty, D.; Zelenika, S.; Hawkes, E. W.; Mezic, I. (September 2020, MIPRO)

   null (Ed.)

   Thanks to their flexibility, soft robotic devices offer critical advantages over rigid robots, allowing adaptation to uncertainties in the environment. As such, soft robots enable various intriguing applications, including human-safe interaction devices, soft active rehabilitation devices, and soft grippers for pick-and-place tasks in industrial environments. In most cases, soft robots use pneumatic actuation to inflate the channels in a compliant material to obtain the movement of the structure. However, due to their flexibility and nonlinear behavior, as well as the compressibility of air, controlled movements of the soft robotic structure are difficult to attain. Obtaining physically-based mathematical models, which would enable the development of suitable control approaches for soft robots, constitutes thus a critical challenge in the field. The aim of this work is, therefore, to predict the movement of a pneumatic soft robot by using a data-driven approach based on the Koopman operator framework. The Koopman operator allows simplifying a nonlinear system by“lifting” its dynamics into a higher dimensional space, where its behavior can be accurately approximated by a linear model, thus allowing a significant reduction of the complexity of the design of the resulting controllers. 

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4. Localized Motion Dynamics Modeling of A Soft Robot: A Data-Driven Adaptive Learning Approach

   https://doi.org/10.23919/ACC53348.2022.9867191  

   Chen, Xiaotian; Stegagno, Paolo; Zeng, Wei; Yuan, Chengzhi (June 2022, Proceedings of the American Control Conference)

   Soft robots have recently drawn extensive attention thanks to their unique ability of adapting to complicated environments. Soft robots are designed in a variety of shapes of aiming for many different applications. However, accurate modelling and control of soft robots is still an open problem due to the complex robot structure and uncertain interaction with the environment. In fact, there is no unified framework for the modeling and control of generic soft robots. In this paper, we present a novel data-driven machine learning method for modeling a cable-driven soft robot. This machine learning algorithm, named deterministic learning (DL), uses soft robot motion data to train a radial basis function neural network (RBFNN). The soft robot motion dynamics are then guaranteed to be accurately identified, represented, and stored as an RBFNN model with converged constant neural network weights. To validate our method, We have built a simulated soft robot almost identical to our real inchworm soft robot, and we have tested the DL algorithm in simulation. Furthermore, a neural network weight combining technique is used which can extract and combine useful dynamics information from multiple robot motion trajectories. 

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5. On the Mathematical Modeling of Slender Biomedical Continuum Robots

   https://doi.org/10.3389/frobt.2021.732643  

   Gilbert, Hunter B. (October 2021, Frontiers in Robotics and AI)

   The passive, mechanical adaptation of slender, deformable robots to their environment, whether the robot be made of hard materials or soft ones, makes them desirable as tools for medical procedures. Their reduced physical compliance can provide a form of embodied intelligence that allows the natural dynamics of interaction between the robot and its environment to guide the evolution of the combined robot-environment system. To design these systems, the problems of analysis, design optimization, control, and motion planning remain of great importance because, in general, the advantages afforded by increased mechanical compliance must be balanced against penalties such as slower dynamics, increased difficulty in the design of control systems, and greater kinematic uncertainty. The models that form the basis of these problems should be reasonably accurate yet not prohibitively expensive to formulate and solve. In this article, the state-of-the-art modeling techniques for continuum robots are reviewed and cast in a common language. Classical theories of mechanics are used to outline formal guidelines for the selection of appropriate degrees of freedom in models of continuum robots, both in terms of number and of quality, for geometrically nonlinear models built from the general family of one-dimensional rod models of continuum mechanics. Consideration is also given to the variety of actuators found in existing designs, the types of interaction that occur between continuum robots and their biomedical environments, the imposition of constraints on degrees of freedom, and to the numerical solution of the family of models under study. Finally, some open problems of modeling are discussed and future challenges are identified. 

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