Macro-continuous dynamics for hyper-redundant robots: application to locomotion bio-inspired by elongated animals

International audienceThis article presents a unified dynamic modeling approach of continuum robots. The robot is modeled as a geometrically exact beam continuously actuated through an active strain law. Once included into the geometric mechanics of locomotion, the approach applies to any hyper-redundant or continuous robot devoted to manipulation and/or locomotion. Furthermore, exploiting the nature of the resulting models as being a continuous version of the Newton-Euler models of discrete robots, an algorithm is proposed which is capable of computing the internal control torques (and/or forces) as well as the rigid overall motions of the locomotor robot. The efficiency of the approach is finally illustrated through many examples directly related to the terrestrial locomotion of elongated animals as snakes, worms or caterpillars and their associated bio-mimetic artifacts

Macro-continuous computed torque algorithm for a three-dimensional eel-like robot

International audienceThis paper presents the dynamic modeling of a continuous three-dimensional swimming eel-like robot. The modeling approach is based on the "geometrically exact beam theory" and on that of Newton-Euler, as it is well known within the robotics community. The proposed algorithm allows us to compute the robot's Galilean movement and the control torques as a function of the expected internal deformation of the eel's body

The Mechanics and Control of Undulatory Robotic Locomotion

In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle. We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations. The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations. The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields. The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets

Algebraic Structure and Poisson Integral Method of Snake-Like Robot Systems

The algebraic structure and Poisson's integral of snake-like robot systems are studied. The generalized momentum, Hamiltonian function, generalized Hamilton canonical equations, and their contravariant algebraic forms are obtained for snake-like robot systems. The Lie-admissible algebra structures of the snake-like robot systems are proved and partial Poisson integral methods are applied to the snake-like robot systems. The first integral methods of the snake-like robot systems are given. An example is given to illustrate the results

Design and Analysis of Exaggerated Rectilinear Gait-Based Snake-Inspired Robots

Snake-inspired locomotion is much more maneuverable compared to conventional locomotion concepts and it enables a robot to navigate through rough terrain. A rectilinear gait is quite flexible and has the following benefits: functionality on a wide variety of terrains, enables a highly stable robot platform, and provides pure undulatory motion without passive wheels. These benefits make rectilinear gaits especially suitable for search and rescue applications. However, previous robot designs utilizing rectilinear gaits were slow in speed and required considerable vertical motion. This dissertation will explore the development and implementation of a new exaggerated rectilinear gait that which will enable high speed locomotion and more efficient operation in a snake-inspired robot platform. The exaggerated rectilinear gait will emulate the natural snake's rectilinear gait to gain the benefit a snake's terrain adaptability, but the sequence and range of joint motion will be greatly exaggerated to achieve higher velocities to support robot speeds within the range of human walking speed. The following issues will be investigated in this dissertation. First, this dissertation will address the challenge of developing a snake-inspired robot capable of executing exaggerated rectilinear gaits. To successfully execute the exaggerated rectilinear gait, a snake-inspired robot platform must be able to perform high speed linear expansion/contraction and pivoting motions between segments. In addition to high speed joint motion, the new mechanical architecture much also incorporate a method for providing positive traction during gait execution. Second, a new exaggerated gait dynamics model will be developed using well established kinematics and dynamics analysis techniques. In addition to the exaggerated rectilinear gaits which emphasize high speed, a set of exaggerated rectilinear gaits which emphasize high traction will also be developed for application on difficult terrain types. Finally, an exaggerated rectilinear that emphasizes energy efficiency is defined and analyzed. This dissertation provides the foundations for realizing a high speed limbless locomotion capable of meeting the needs of the search, rescue, and recovery applications

Modular soft pneumatic actuator system design for compliance matching

The future of robotics is personal. Never before has technology been as pervasive as it is today, with advanced mobile electronics hardware and multi-level network connectivity pushing âsmartâ devices deeper into our daily lives through home automation systems, virtual assistants, and wearable activity monitoring. As the suite of personal technology around us continues to grow in this way, augmenting and offloading the burden of routine activities of daily living, the notion that this trend will extend to robotics seems inevitable. Transitioning robots from their current principal domain of industrial factory settings to domestic, workplace, or public environments is not simply a matter of relocation or reprogramming, however. The key differences between âtraditionalâ types of robots and those which would best serve personal, proximal, human interactive applications demand a new approach to their design. Chief among these are requirements for safety, adaptability, reliability, reconfigurability, and to a more practical extent, usability. These properties frame the context and objectives of my thesis work, which seeks to provide solutions and answers to not only how these features might be achieved in personal robotic systems, but as well what benefits they can afford. I approach the investigation of these questions from a perspective of compliance matching of hardware systems to their applications, by providing methods to achieve mechanical attributes complimentary to their environment and end-use. These features are fundamental to the burgeoning field of Soft Robotics, wherein flexible, compliant materials are used as the basis for the structure, actuation, sensing, and control of complete robotic systems. Combined with pressurized air as a power source, soft pneumatic actuator (SPA) based systems offers new and novel methods of exploiting the intrinsic compliance of soft material components in robotic systems. While this strategy seems to answer many of the needs for human-safe robotic applications, it also brings new questions and challenges: What are the needs and applications personal robots may best serve? Are soft pneumatic actuators capable of these tasks, or âusefulâ work output and performance? How can SPA based systems be applied to provide complex functionality needed for operation in diverse, real-world environments? What are the theoretical and practical challenges in implementing scalable, multiple degrees of freedom systems, and how can they be overcome? I present solutions to these problems in my thesis work, elucidated through scientific design, testing and evaluation of robotic prototypes which leverage and demonstrate three key features: 1) Intrinsic compliance: provided by passive elastic and flexible component material properties, 2) Extrinsic compliance: rendered through high number of independent, controllable degrees of freedom, and 3) Complementary design: exhibited by modular, plug and play architectures which combine both attributes to achieve compliant systems. Through these core projects and others listed below I have been engaged in soft robotic technology, its application, and solutions to the challenges which are critical to providing a path forward within the soft robotics field, as well as for the future of personal robotics as a whole toward creating a better society

Data-Driven Methods for Geometric Systems

The tools of geometric mechanics provide a compact representation of locomotion dynamics as ``the reconstruction equation''. We have found this equation yields a convenient form for estimating models directly from observation data. This convenience draws from the method's relatively rare feature of providing high accuracy models with little effort. By little effort, we point to the modeling process's low data requirements and the property that nothing about the implementation changes when substituting robot kinematics, material properties, or environmental conditions, as long as some intuitive baseline features of the dynamics are shared. We have applied data-driven geometric mechanics models toward optimizing robot behaviors both physical and simulated, exploring robots' ability to recover from injury, and efficiently creating libraries of maneuvers to be used as building blocks for higher-level robot tasks. Our methods employed the tools of data-driven Floquet analysis, providing a phase that we used as a means of grouping related measurements, allowing us to estimate a reconstruction equation model as a function of phase in the neighborhood of an observed behavior. This tool allowed us to build models at unanticipated scales of complexity and speed. Our use of a perturbation expansion for the geometric terms led to an improved estimation procedure for highly damped systems containing nontrivial but non-dominating amounts of momentum. Analysis of the role of passivity in dissipative systems led to another extension of the estimation procedure to robots with high degrees of underactuation in their internal shape, such as soft robots. This thesis will cover these findings and results, simulated and physical, and the surprising practicality of data-driven geometric mechanics.PHDRoboticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168033/1/babitt_1.pd

Engineering Dynamics and Life Sciences

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”