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We treat the vakonomic dynamics with general constraints within a new geometric framework which will be appropriate to study optimal control problems. We compare our formulation with Vershik-Gershkovich one in the case of linear constraints. We show how nonholonomic mechanics also admits a new geometrical description wich enables us to develop an algorithm of comparison between the solutions of both dynamics. Some examples illustrating the theory are treated.

We treat underactuated mechanical control systems with symmetry taking the viewpoint of the aftinc connection formalism. We first review the appropriate notions and tests of controllability associated with these systems, including that of fiber controllability. Secondly, we present a series expansion describing the evolution of the trajectories of general mechanical control systems starting from non-zero velocity. This series is then used to investigate the behavior of the system under small-amplitude periodic forcing. On this basis, motion control algorithms are designed for systems with symmetry to solve the tasks of point-to-point rcconfiguration, static interpolation and stabilization problems. Several examples are given and the performance of the algorithms is illustrated in the blimp system.

: Motivated by considerations of shape changing propulsion of underwater robotic vehicles, this paper analyses the mechanics of deformable bodies operating in an ideal fluid. The application of methods from geometric mechanics results in a compact and insightful formulation of the problem. We develop an explicit formula for the fluid mechanical connection, in terms of the fluid potential function, for this class of systems. The connection can be used to analyze many issues in motion planning and control. The theory is illustrated by application to an amoeba-like device. 1 Introduction This paper considers the problem of self-propulsion of deformable bodies in an idealized inviscid and irrotational fluid. We are primarily motivated by an interest in robotic underwater vehicles that propel and steer themselves by changes in shape [1, 2]. Aquatic animals propel themselves using a variety of fluid dynamic effects [3]. The analysis presented in this paper is most suited to studying system...

Abstract—This paper describes a series of gaits which we developed for a free crawling snake robot. Snake robots, a class of hyper-redundant mechanisms, can use their many degrees of freedom to achieve a variety of locomotion capabilities. Like their biological counterparts, snake robots locomote using cyclic motions called gaits. These cyclic motions directly control the snake robot’s internal degrees of freedom which causes a net motion (e.g. sining moves the robot forward, strafing moves the robot laterally, and spinning rotates the robot about its center). The gaits described in this paper fall into two categories: differentiable and piecewise differentiable. The differentiable gaits, as their name suggests, can be described by a differentiable function whereas the piecewise cannot. This paper describes the functions we prescribed for gait generation and our experiences in making these robots operate in real experiments. I.

Abstract — Substantial work exists in the undulatory robotics literature on the mechanical design, modeling, gait generation and implementation of robotic prototypes. However, there appears to have been relatively limited work on the use of exteroceptive sensors in control schemes leading to more complex reactive undulatory behaviors. This paper considers a biologically-inspired sensor-based centering behavior for undulatory robots, originally developed for nonholonomic mobile robots. Adaptation to the significantly more complex dynamics of undulatory locomotors highlights a number of issues related to the use of sensors, possibly distributed over the elongated body of the mechanism, for the generation of reactive behaviors, to biomimetic neuromuscular control and to formation control of multi-undulatory swarms. These issues are explored via computational tools specifically geared towards undulatory locomotion in robotics and biology. Index Terms — biomimetic robotics, undulatory locomotion, reactive behaviors, exteroceptive sensors. I.

: This paper addresses the problem of computing reduced equations for mechanical systems with nonholonomic constraints, Lie group symmetries, and dissipative forces. Results are presented for two important cases: the unconstrained case, for both body and spatial representations, and the constrained (mixed kinematic and dynamic) case. In each case, the dynamic equations for these nonholonomic mechanical systems are given, and illustrated by the appropriate calculations for an example system. For unconstrained systems, we show that the structure of the reduced Lagrangian almost transparently reveals two useful components in the reduction process, namely the local forms of the locked inertia tensor and the mechanical connection. For the case where nonholonomic constraints act on the system, we present an extension to the nonholonomic momentum equation developed by Bloch, Krishnaprasad, Marsden, and Murray [4] that includes general forcing functions. We then provide an alternative proof to...

I would like to express my gratitude to the people who made an important difference and played a vital role in the successful completion of my Doctoral studies at the University of Pennsylvania. I am grateful to my advisor Professor Vijay Kumar without whose competence, dedication, generosity, and vision this dissertation would not have been possible. Professor Kumar has been my mentor and an inspiring role model. His energy and relentless support encouraged me towards the completion of my Masters in Mathematics. Professor James Ostrowski, my co-advisor since 1996, provided valuable advice and insight towards my work. I am very thankful for his opinion and guidance during the course of my dissertation. I am very thankful to Professor Joel Burdick (Caltech), Chairman of the committee, Professor G. K. Ananthasuresh, Professor Ruzena Bajcsy, Professor Vijay Kumar and Professor James Ostrowski for agreeing to be the members of my dissertation committee and for taking the time to read my thesis and provide valuable suggestions. This dissertation has allowed me to work with people who are both competent and compassionate. I have been fortunate to receive constant guidance and support from Professor

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Abstract — The polychaete annelid marine worms propel themselves in a variety of challenging locomotion environments by a unique form of tail-to-head body undulations, combined with the synchronized action of numerous parapodial lateral appendages. This combined parapodial and undulatory mode of locomotion is termed pedundulatory in the present work. Robotic analogues of this type of locomotion are being studied, both in simulation, and via experiments with biomimetic robotic prototypes, which combine undulatory movements of their multi-link body with appropriately coordinated parapodial link oscillations. Extensive experimental studies of locomotion on sand demonstrate the potential of the pedundulatory robotic prototypes, especially their rich gait repertoire and their enhanced performance compared to robotic prototypes relying only on body undulations.