In this thesis, we present a dynamical systems approach to adaptive controllers for locomotion control. The approach is based on a rigorous mathematical framework using nonlinear dynamical systems and is inspired by theories of self-organization. Nonlinear dynamical systems such as coupled oscillators are an interesting approach for the on-line generation of trajectories for robots with many degrees of freedom (e.g. legged locomotion). However, designing a nonlinear dynamical system to satisfy a given specification and goal is not an easy task, and, hitherto no methodology exists to approach this problem in a unified way. Nature presents us with satisfactory solutions for the coordination of many degrees of freedom. One central feature observed in biological subjects is the ability of the neural systems to exploit natural dynamics of the body to achieve efficient locomotion. In order to be able to exploit the body properties, adaptive mechanisms must be at work. Recent work has pointed out the importance of the mechanical system for efficient locomotion. Even more interestingly, such well suited mechanical systems do not need complicated control. Yet, in robotics, in most approaches, adaptive mechanisms are either missing or they are not based on a rigorous framework, i.e. they are based on heuristics and ad-hoc approaches. Over the last three decades there has been enormous progress in describing movement coordination with the help of Synergetic approaches. This has led to the formulation of a theoretical framework: the theory of dynamic patterns. This framework is mathematically rigorous and at the same time fully operational. However, it does not provide any guidelines for synthetic approaches as needed for the engineering of robots with many degrees of freedom, nor does it directly help to explain adaptive systems. We will show how we can extend the theoretical framework to build adaptive systems. For this purpose, we propose the use of multi-scale dynamical systems. The basic idea behind multi-scale dynamical systems is that a given dynamical system gets extended by additional slow dynamics of its parameters, i.e. some of the parameters become state variables. The advantages of the framework of multi-scale dynamical systems for adaptive controllers are 1) fully dynamic description, 2) no separation of learning algorithm and learning substrate, 3) no separation of learning trials or time windows, 4) mathematically rigorous, 5) low dimensional systems. However, in order to fully exploit the framework important questions have to be solved. Most importantly, methodologies for designing the feedback loops have to be found and important theoretical questions about stability and convergence properties of the devised systems have to be answered. In order to tackle this challenge, we first introduce an engineering view on designing nonlinear dynamical systems and especially oscillators. We will highlight the important differences and freedom that this engineering view introduces as opposed to a modeling one. We then apply this approach by first proposing a very simple adaptive toy-system, consisting of a dynamical system coupled to a spring-mass system. Due to its spring-mass dynamics, this system contains clear natural dynamics in the form of resonant frequencies. We propose a prototype adaptive multi-scale system, the adaptive frequency oscillator, which is able to adapt its intrinsic frequency to the resonant frequency of the body dynamics. After a small sidetrack to show that we can use adaptive frequency oscillators also for other applications than for adaptive controllers, namely for frequency analysis, we then come back to further investigation of the adaptive controller. We apply the same controller concept to a simple spring-mass hopper system. The spring-mass system consists of a body with two legs attached by rotational joints. The legs contain spring-damper elements. Finally, we present results of the implementation of the controller on a real robot, the experimental robot PUPPY II. This robot is a under-actuated robot with spring dynamics in the knee joints. It will be shown, that due to the appropriate simplification and concentration on relevant features in the toy-system the controller concepts works without a fundamental change on all systems from the toy system up to the real robot.
8Modeling of Microblogging Social Networks: Dynamical System vs. Random Dynamical System
Modeling of Microblogging Social Networks: Dynamical System vs. Random Dynamical System
3Extracting Phase Coupling Functions between Collectively Oscillating Networks from Time-Series Data
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical methods for investigating the synchronization properties of such a rhythmic system is to statistically extract phase coupling functions between limit-cycle oscillators directly from observed time-series data. In Particular, using a method that combines phase reduction theory and Bayesian inference, the phase coupling functions can be extracted from the time-series data of even just one variable in each oscillatory dynamical system with many degrees of freedom. However, it remains unclear how the choice of the observed variables affects the statistical inference for the phase coupling functions. In this study, we examine the influence of observed variable types on the extraction of phase coupling functions using some typical dynamical elements under various conditions. We demonstrate that our method can consistently extract the macroscopic phase coupling functions between two phases representing collective oscillations in a fully locked state, regardless of the observed variable types; for example, even using one variable of any element in one system and the mean-field value over all the elements in another system. We also study the case of globally coupled phase oscillators in a partially locked state. Our results reveal directional asymmetry in the robustness of extracting the macroscopic phase coupling function between two networks. For instance, when an asynchronous oscillator in network $A$ and the macroscopic collective oscillation of network $B$ is observed, the macroscopic phase coupling function from network $A$ to network $B$ can be extracted more robustly than in the opposite direction.
Read more28Elements of mathematical phenomenology of self-organization nonlinear dynamical systems: Synergetics and fractional calculus approach
Elements of mathematical phenomenology of self-organization nonlinear dynamical systems: Synergetics and fractional calculus approach
Read more624The behavior of adaptive bone-remodeling simulation models
The behavior of adaptive bone-remodeling simulation models
20216 多リンクマニピュレータにおける冗長関節を利用した運動量軌道生成(ロボット(1),一般講演)
Recently, the robot with many links and degrees of freedoms is actively produced. Generally, the robot that has many degrees of freedoms owns many redundant joints. So we make a suggestion for using redundant joints effectively. The paper proposes using redundant joint as a counter weight. We make a trajectory in momentum space, and we use Fourier Basis Algorism as the method for an optimization. This trajectory generating method has an effect on reducing a driving energy for throwing motion.
Read more9Control synthesis in a non-linear dynamical system
Control synthesis in a non-linear dynamical system
Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement
While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution. Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.
Read moreQuantitative analysis of non-linear probabilistic state estimation filters for deployment on dynamic unmanned systems
The work conducted in this thesis is a part of an EU Horizon 2020 research initiative project known as DigiArt. This part of the DigiArt project presents and explores the design, formulation and implementation of probabilistically orientated state estimation algorithms with focus towards unmanned system positioning and three-dimensional (3D) mapping. State estimation algorithms are considered an influential aspect of any dynamic system with autonomous capabilities. Possessing the ability to predictively estimate future conditions enables effective decision making and anticipating any possible changes in the environment. Initial experimental procedures utilised a wireless ultra-wide band (UWB) based communication network. This system functioned through statically situated beacon nodes used to localise a dynamically operating node. The simultaneous deployment of this UWB network, an unmanned system and a Robotic Total Station (RTS) with active and remote tracking features enabled the characterisation of the range measurement errors associated with the UWB network. These range error metrics were then integrated into an Range based Extended Kalman Filter (R-EKF) state estimation algorithm with active outlier identification to outperform the native approach used by the UWB system for two-dimensional (2D) pose estimation.The study was then expanded to focus on state estimation in 3D, where a Six Degreeof-Freedom EKF (6DOF-EKF) was designed using Light Detection and Ranging (LiDAR) as its primary observation source. A two step method was proposed which extracted information between consecutive LiDAR scans. Firstly, motion estimation concerning Cartesian states x, y and the unmanned system’s heading (ψ) was achieved through a 2D feature matching process. Secondly, the extraction and alignment of ground planes from the LiDAR scan enabled motion extraction for Cartesian position z and attitude angles roll (θ) and pitch (φ). Results showed that the ground plane alignment failed when two scans were at 10.5◦ offset. Therefore, to overcome this limitation an Error State Kalman Filter (ES-KF) was formulated and deployed as a sub-system within the 6DOF-EKF. This enabled the successful tracking of roll, pitch and the calculation of z. The 6DOF-EKF was seen to outperform the R-EKF and the native UWB approach, as it was much more stable, produced less noise in its position estimations and provided 3D pose estimation.
Read more7Modular Robot Control Environment – Testing Neural Control on Simulated and Real Robots
Event Abstract Back to Event Modular Robot Control Environment – Testing Neural Control on Simulated and Real Robots Frank Hesse1, 2*, Georg Martius3, Poramate Manoonpong1, 4, Martin Biehl1, 4 and Florentin Wörgötter1, 4 1 Georg-August-Universität Göttingen, Third Institute of Physics - Biophysics, Germany 2 Bernstein Focus Neurotechnology, Germany 3 Max Planck Institute for Mathematics in the Sciences, Germany 4 Bernstein Center for Computational Neuroscience, Germany To develop new control approaches for robotic devices and evaluate their results it is important to be able to efficiently test them not only in simulated but also real environments. This means switching between simulated and real systems should be easily possible using the same controller code (without reprogramming). Furthermore, the development process should be able to continuously increase robot functionality in order to solve more complex tasks. This can be achieved based on modularity. A modular structure is considered as a major advantage, compared to many other approaches due to the following aspects: 1) It is flexible, allowing to simply rearrange, add, and/or remove modules for controlling different types of robots. 2) Each module is typically independent of other modules in its functioning and does not influence or become influenced by other modules. Taking this into account, here we present a modular robot control environment relying on the C++ programming language and providing an artificial neural network library. It is used to develop neurocontrollers for different robots. The very same controller code can now be tested in simulation and on real hardware, which allows speeding up the development process. The modular robot control environment also allows to exchange robots and controller in a plug-and-play manner where parameters of the simulation and real robot can be observed and changed online. We have applied the modular robot control environment to develop neural control of hexapod walking robots AMOSII. They are biologically inspired hardware platforms developed in collaboration with the Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS. They are used to study the coordination of many degrees of freedom, to perform experiments with neural control, memory, and learning. The robots were modeled using LPZRobots [1], a physically realistic simulation toolkit (freely available under GNU General Public License). Employing iterated development cycles, including progression of a neural controller and tests on the simulated and real hexapod platform, a variety of biologically inspired walking gaits as well as orienting, taxis and their combinations have been successfully achieved. By recently developing another module for adaptive climbing behavior, the hexapod can now overcome obstacles of various heights (e.g., ~ 75% of its leg length, which is higher than those that other comparable legged robots have achieved so far). The presented modular robot control environment can also be applied to different types of robotic systems, like wheeled robots and manipulators (e.g., integration of the E-puck mobile robot and the KUKA-DLR Lightweight Robot arm in preparation). Figure 1: Modular Robot Control Environment: The developed neural controllers can easily be transferred to and tested on real and simulated hardware platforms. Here a neural control for hexapod locomotion is depicted. Figure 1 Acknowledgements This research was supported by the BMBF-funded BFNT Göttingen with grant number 01GQ0811 (project 3B) and BCCN Göttingen with grant number 01GQ1005A (project D1), and the Emmy Noether Program (DFG, MA4464/3-1).
Read more130Scaling and universality in statistical physics
Scaling and universality in statistical physics
7Dissipative effects in a linear Lagrangian system with infinitely many degrees of freedom
We consider the problem of potential interaction between a finite-dimensional linear Lagrangian system and an infinite-dimensional one (a system of linear oscillators and a thermostat). We study the final dynamics of the system. Under natural assumptions, this dynamics turns out to be very simple and admits an explicit description because the thermostat produces an effective dissipation despite the energy conservation and the Lagrangian nature of the system. We use the methods of [1], where the final dynamics of the finite-dimensional subsystem is studied in the case when it has one degree of freedom and a linear potential or (under additional assumptions) polynomial potential. We consider the case of finite-dimensional subsystems with arbitrarily many degrees of freedom and a linear potential and study the final dynamics of the system of oscillators and the thermostat. The necessary assertions from [1] are given with proofs adapted to the present situation.
Read more2Collapses and avoiding wave function spreading
We address the impossibility of achieving exact time reversal in a system with many degrees of freedom. This is a particular example of the difficult task of “aiming” an initial classical state so as to become a specific final state. We also comment on the classical-to-quantum transition in any non-separable closed system of \(n \ge 2\) degrees of freedom. Even if the system is initially in a well-defined WKB, semi-classical state, quantum evolution and, in particular, multiple reflections at classical turning points make it completely quantum mechanical with each particle smeared almost uniformly over all the configuration space. The argument, which is presented in the context of \(n\) hard discs, is quite general. Finally, we briefly address more complex quantum systems with many degrees of freedom and ask when can they provide an appropriate environment to the above simpler systems so that quantum spreading is avoided by continuously leaving “imprints” in the environment. We also discuss the possible connections with the pointer systems that are needed in the quantum-to-classical “collapse” transitions.
Read more21Training ANFIS using artificial bee colony algorithm for nonlinear dynamic systems identification
In this study, nonlinear dynamic systems are identified by using artificial bee colony (ABC) algorithm and adaptive neuro fuzzy inference system (ANFIS). ABC algorithm is used in training and updating of ANFIS. The most appropriate model is formed by optimizing the antecedent and conclusion parameters that are found in the structure of ANFIS. The dynamic systems that consist of one input and one output (SISO) are used for the identification of nonlinear dynamic systems. The obtained results are compared with fuzzy neural network, neural network and ANFIS-based methods such as RSONFIN, DFNN, RSEFNN-LF, WRFNN and RFNN. The simulation results show that the proposed method is successful in the identification of considered nonlinear dynamic systems.
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4Determining the influence of higher harmonics of nonlinear technological load in dynamic action systems
This paper considers the influence of higher harmonics in dynamic action systems due to their complex movement in the process of interaction with the technological load. The object of research is the process of propagation of oscillations in complex dynamic systems. One of the problems in the application of oscillatory processes is the consideration of higher harmonics in the overall movement of systems. To solve the problem, the idea of using a hybrid model that takes into account both discrete and distributed parameters was proposed. The resulting mathematical discrete model in the analytical equations of motion of the dynamic system preserves continuous properties in the form of wave coefficients. These coefficients in their analytical form take into account the contribution of higher harmonics of both the reactive (elastic-inertial) and active (dissipative) components of the resistance force. The studies were carried out on a model of a plant with a multimode spectrum of oscillations and a nonlinear dynamic system, which is a system with piecewise linear characteristics.A series of experimental studies with a wide variation of the change in the frequency of oscillations was carried out on the installation with a multimode spectrum of oscillations. Zones of manifestation of higher harmonics along the vertical axis of force action were revealed. The given spectrum at the exciter frequency of 35 Hz showed the manifestation of the spectrum component (around 70 Hz) along the X axis, which is an important result for practical application. For a system with piecewise linear characteristics, the manifestation of multimode, which manifests itself in the form of subharmonic and superharmonic oscillations, was determined. The contribution of each harmonic is determined by applying the obtained dependences. The results were used in the development of algorithms and calculation methods of a new class of dynamic action systems taking into account the contribution of higher harmonics
Read more11Numerical solution of dynamical systems by direct application of Hamilton's principle
In this paper, a method is described which allows a direct derivation of a set of first‐order finite difference equations to numerically compute the motion of any conservative or non‐conservative dynamic system with a finite number of degrees of freedom. The derivation of the method is based on an application of Lagrangian multipliers to a functional form of Hamilton's equations, and reduces the work required to obtain the most desirable form for numerical integration from the standpoint of computational efficiency and accuracy. For systems with many degrees of freedom, the required matrix inversions produce first derivatives of the co‐ordinates, instead of second derivatives, thus eliminating a potential source of error in numerical integration. Two examples are given to illustrate the method.
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