Modeling and frequency domain analysis of nonlinear compliant joints for a passive dynamic swimmer

In this paper we present the study of the mathematical model of a real life joint used in an underwater robotic fish. Fluid-structure interaction is utterly simplified and the motion of the joint is approximated by D\"uffing's equation. We compare the quality of analytical harmonic solutions previously reported, with the input-output relation obtained via truncated Volterra series expansion. Comparisons show a trade-off between accuracy and flexibility of the methods. The methods are discussed in detail in order to facilitate reproduction of our results. The approach presented herein can be used to verify results in nonlinear resonance applications and in the design of bio-inspired compliant robots that exploit passive properties of their dynamics. We focus on the potential use of this type of joint for energy extraction from environmental sources, in this case a K\'arm\'an vortex street shed by an obstacle in a flow. Open challenges and questions are mentioned throughout the document.Comment: 12 p, 5 fig, work in progress, collaborative wor

Energy Based Control System Designs for Underactuated Robot Fish Propulsion

In nature through millions of years of evolution fish and cetaceans have developed fast efficient and highly manoeuvrable methods of marine propulsion. A recent explosion in demand for sub sea robotics, for conducting tasks such as sub sea exploration and survey has left developers desiring to capture some of the novel mechanisms evolved by fish and cetaceans to increase the efficiency of speed and manoeuvrability of sub sea robots. Research has revealed that interactions with vortices and other unsteady fluid effects play a significant role in the efficiency of fish and cetaceans. However attempts to duplicate this with robotic fish have been limited by the difficulty of predicting or sensing such uncertain fluid effects. This study aims to develop a gait generation method for a robotic fish with a degree of passivity which could allow the body to dynamically interact with and potentially synchronise with vortices within the flow without the need to actually sense them. In this study this is achieved through the development of a novel energy based gait generation tactic, where the gait of the robotic fish is determined through regulation of the state energy rather than absolute state position. Rather than treating fluid interactions as undesirable disturbances and `fighting' them to maintain a rigid geometric defined gait, energy based control allows the disturbances to the system generated by vortices in the surrounding flow to contribute to the energy of the system and hence the dynamic motion. Three different energy controllers are presented within this thesis, a deadbeat energy controller equivalent to an analytically optimised model predictive controller, a $H_\infty$ disturbance rejecting controller with a novel gradient decent optimisation and finally a error feedback controller with a novel alternative error metric. The controllers were tested on a robotic fish simulation platform developed within this project. The simulation platform consisted of the solution of a series of ordinary differential equations for solid body dynamics coupled with a finite element incompressible fluid dynamic simulation of the surrounding flow. results demonstrated the effectiveness of the energy based control approach and illustrate the importance of choice of controller in performance

Moving softly : the role of morphological computation in the generation of intelligent behaviour

The central theme of this thesis is ‘morphological computation’, in particular as it pertains to the generation of purposeful and intelligent behaviour. The first part of the thesis covers experiments in simulations, aimed at exploring a previously unasked question: can genuinely computational soft-body reservoirs play a central role in generating behaviour which has previously been described as ‘minimally cognitive’? We conclude in the affirmative, but also note that it remains unclear whether or how they can also exceed such abilities. The main part of this work has been presented at ALIFE 14 and ECAL 15, and published in the Artificial Life journal. In part two, the focus moves to consideration of how morphological computation in soft bodies may collude with the action of nervous systems in the production of adaptive intelligent behaviour. The massive and hypnotic complexity of brains in present day species, and lasting traditions in the design and control of animals’ mechanical analogies (robots), still lead many to perceive bodies in the neuromuscular species as being in service to the goals of their controllers (brains), but in fact the two are of a piece, and work together to the same ends. We hypothesise that this would have been more apparent than now at a time closer to the evolutionary introduction of neuromuscular systems, and introduce our new software framework for the evolution of virtual neuromuscular swimmers, which may be used to study artificial parallels to those distant origins. We begin with a demonstration of the technical innovations which we required in order to simulate soft-bodied swimmers in two-dimensional particle-based fluids, and then proceed to a description of our new concept for mapping arbitrary neural networks to arbitrary body morphologies

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

Physics-based Machine Learning Methods for Control and Sensing in Fish-like Robots

Underwater robots are important for the construction and maintenance of underwater infrastructure, underwater resource extraction, and defense. However, they currently fall far behind biological swimmers such as fish in agility, efficiency, and sensing capabilities. As a result, mimicking the capabilities of biological swimmers has become an area of significant research interest. In this work, we focus specifically on improving the control and sensing capabilities of fish-like robots. Our control work focuses on using the Chaplygin sleigh, a two-dimensional nonholonomic system which has been used to model fish-like swimming, as part of a curriculum to train a reinforcement learning agent to control a fish-like robot to track a prescribed path. The agent is first trained on the Chaplygin sleigh model, which is not an accurate model of the swimming robot but crucially has similar physics; having learned these physics, the agent is then trained on a simulated swimming robot, resulting in faster convergence compared to only training on the simulated swimming robot. Our sensing work separately considers using kinematic data (proprioceptive sensing) and using surface pressure sensors. The effect of a swimming body\u27s internal dynamics on proprioceptive sensing is investigated by collecting time series of kinematic data of both a flexible and rigid body in a water tunnel behind a moving obstacle performing different motions, and using machine learning to classify the motion of the upstream obstacle. This revealed that the flexible body could more effectively classify the motion of the obstacle, even if only one if its internal states is used. We also consider the problem of using time series data from a `lateral line\u27 of pressure sensors on a fish-like body to estimate the position of an upstream obstacle. Feature extraction from the pressure data is attempted with a state-of-the-art convolutional neural network (CNN), and this is compared with using the dominant modes of a Koopman operator constructed on the data as features. It is found that both sets of features achieve similar estimation performance using a dense neural network to perform the estimation. This highlights the potential of the Koopman modes as an interpretable alternative to CNNs for high-dimensional time series. This problem is also extended to inferring the time evolution of the flow field surrounding the body using the same surface measurements, which is performed by first estimating the dominant Koopman modes of the surrounding flow, and using those modes to perform a flow reconstruction. This strategy of mapping from surface to field modes is more interpretable than directly constructing a mapping of unsteady fluid states, and is found to be effective at reconstructing the flow. The sensing frameworks developed as a result of this work allow better awareness of obstacles and flow patterns, knowledge which can inform the generation of paths through the fluid that the developed controller can track, contributing to the autonomy of swimming robots in challenging environments

In silico case studies of compliant robots: AMARSI deliverable 3.3

In the deliverable 3.2 we presented how the morphological computing ap- proach can significantly facilitate the control strategy in several scenarios, e.g. quadruped locomotion, bipedal locomotion and reaching. In particular, the Kitty experimental platform is an example of the use of morphological computation to allow quadruped locomotion. In this deliverable we continue with the simulation studies on the application of the different morphological computation strategies to control a robotic system

Improving Swimming Performance and Flow Sensing by Incorporating Passive Mechanisms

As water makes up approximately 70% of the Earth\u27s surface, humans have expanded operations into aquatic environments out of both necessity and a desire to gain potential innate benefits. This expansion into aquatic environments has consequently developed a need for cost-effective and safe underwater monitoring, surveillance, and inspection, which are missions that autonomous underwater vehicles are particularly well suited for. Current autonomous underwater vehicles vastly underperform when compared to biological swimmers, which has prompted researchers to develop robots inspired by natural swimmers. One such robot is designed, built, tested, and numerically simulated in this thesis to gain insight into the benefits of passive mechanisms and the development of reduced-order models. Using a bio-inspired robot with multiple passive tails I demonstrate herein the relationship between maneuverability and passive appendages. I found that the allowable rotation angle, relative to the main body, of the passive tails corresponds to an increase in maneuverability. Using panel method simulations I determined that the increase in maneuverability was directly related to the change in hydrodynamic moment caused by modulating the circulation sign and location of the shed vortex wake. The identification of this hydrodynamic benefit generalizes the results and applies to a wide range of robots that utilize vortex shedding through tail flapping or body undulations to produce locomotion. Passive appendages are a form of embodied control, which manipulates the fluid-robot interaction and analogously such interaction can be sensed from the dynamics of the body. Body manipulation is a direct result of pressure fluctuations inherent in the surrounding fluid flow. These pressure fluctuations are unique to specific flow conditions, which may produce distinguishable time series kinematics of the appendage. Using a bio-inspired foil tethered in a water tunnel I classified different vortex wakes with the foil\u27s kinematic data. This form of embodied feedback could be used for the development of control algorithms dedicated to obstacle avoidance, tracking, and station holding. Mathematical models of autonomous vehicles are necessary to implement advanced control algorithms such as path planning. Models that accurately and efficiently simulate the coupled fluid-body interaction in freely swimming aquatic robots are difficult to determine due, in part, to the complex nature of fluids. My colleagues and I approach this problem by relating the swimming robot to a terrestrial vehicle known as the Chaplygin sleigh. Using our novel technique we determined an analogous Chaplygin sleigh model that accurately represents the steady-state dynamics of our swimming robot. We additionally used the subsequent model for heading and velocity control in panel method simulations. This work was inspired by the similarities in constraints and velocity space limit cycles of the swimmer and the Chaplygin sleigh, which makes this technique universal enough to be extended to other bio-inspired robots

A framework for design, modeling, and identification of compliant biomimetic swimmers

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 121-126).Research interests in fish-like devices are generally driven by the notion that through eons of evolution fish have developed optimal mechanisms for efficient propulsion and high degrees of maneuverability. Engineered fish-like devices have been developed in hope of mimicking the capabilities of their biological counterparts, but success has been marginal. This thesis considers a unique class of underactuated biomimetic swimmers with compliant bodies that swim by exploiting their structural dynamics. Practical matters surrounding the design and modeling of these swimmers are addressed and explicit references are made to fish morphology and swimming behaviours with the aim of linking biological and engineering design elements, a deficiency in existing literature. A hybrid modeling scheme is presented drawing upon conventional engineering primitives and experimental data. Both a hardware prototype swimmer and a unique motion capture system were developed to demonstrate the described methods. Experimental and simulated results are compared.by Adam Joseph Wahab.S.M