The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Modelling and simulation of a biomimetic underwater vehicle

This paper describes work carried out at the University of Glasgow investigating biomimetic fish-like propulsion systems for underwater vehicles. The development of a simple mathematical model is described for a biomimetic fish like vehicle which utilizes a tendon drive propulsion system. This model is then compared with a model of a vehicle of similar size but with a propeller for main propulsion. Simulation results for both models are shown and compared

Improving the energy efficiency of autonomous underwater vehicles by learning to model disturbances

Energy efficiency is one of the main challenges for long-term autonomy of AUVs (Autonomous Underwater Vehicles). We propose a novel approach for improving the energy efficiency of AUV controllers based on the ability to learn which external disturbances can safely be ignored. The proposed learning approach uses adaptive oscillators that are able to learn online the frequency, amplitude and phase of zero-mean periodic external disturbances. Such disturbances occur naturally in open water due to waves, currents, and gravity, but also can be caused by the dynamics and hydrodynamics of the AUV itself. We formulate the theoretical basis of the approach, and demonstrate its abilities on a number of input signals. Further experimental evaluation is conducted using a dynamic model of the Girona 500 AUV in simulation on two important underwater scenarios: hovering and trajectory tracking. The proposed approach shows significant energy-saving capabilities while at the same time maintaining high controller gains. The approach is generic and applicable not only for AUV control, but also for other type of control where periodic disturbances exist and could be accounted for by the controller. © 2013 IEEE

Dissipation and Controlled Euler-Poincaré Systems

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor

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

Ultra-fast escape maneuver of an octopus-inspired robot

We design and test an octopus-inspired flexible hull robot that demonstrates outstanding fast-starting performance. The robot is hyper-inflated with water, and then rapidly deflates to expel the fluid so as to power the escape maneuver. Using this robot we verify for the first time in laboratory testing that rapid size-change can substantially reduce separation in bluff bodies traveling several body lengths, and recover fluid energy which can be employed to improve the propulsive performance. The robot is found to experience speeds over ten body lengths per second, exceeding that of a similarly propelled optimally streamlined rigid rocket. The peak net thrust force on the robot is more than 2.6 times that on an optimal rigid body performing the same maneuver, experimentally demonstrating large energy recovery and enabling acceleration greater than 14 body lengths per second squared. Finally, over 53% of the available energy is converted into payload kinetic energy, a performance that exceeds the estimated energy conversion efficiency of fast-starting fish. The Reynolds number based on final speed and robot length is $Re \approx 700,000$. We use the experimental data to establish a fundamental deflation scaling parameter $\sigma^*$ which characterizes the mechanisms of flow control via shape change. Based on this scaling parameter, we find that the fast-starting performance improves with increasing size.Comment: Submitted July 10th to Bioinspiration & Biomimetic

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue