111 research outputs found
Efficient Learning and Inference for High-dimensional Lagrangian Systems
Learning the nature of a physical system is a problem that presents many challenges and opportunities owing to the unique structure associated with such systems. Many physical systems of practical interest in engineering are high-dimensional, which prohibits the application of standard learning methods to such problems. This first part of this work proposes therefore to solve learning problems associated with physical systems by identifying their low-dimensional Lagrangian structure. Algorithms are given to learn this structure in the case that it is obscured by a change of coordinates. The associated inference problem corresponds to solving a high-dimensional minimum-cost path problem, which can be solved by exploiting the symmetry of the problem. These techniques are demonstrated via an application to learning from high-dimensional human motion capture data. The second part of this work is concerned with the application of these methods to high-dimensional motion planning. Algorithms are given to learn and exploit the struc- ture of holonomic motion planning problems effectively via spectral analysis and iterative dynamic programming, admitting solutions to problems of unprecedented dimension com- pared to known methods for optimal motion planning. The quality of solutions found is also demonstrated to be much superior in practice to those obtained via sampling-based planning and smoothing, in both simulated problems and experiments with a robot arm. This work therefore provides strong validation of the idea that learning low-dimensional structure is the key to future advances in this field
ALADIN-α—An open-source MATLAB toolbox for distributed non-convex optimization
This article introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-α. ALADIN-α is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. It is user interface is convenient for rapid prototyping of non-convex distributed optimization algorithms. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization with reduced information exchange. A collection of examples from different applications fields including chemical engineering, robotics, and power systems underpins the potential of ALADIN-α
Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control
Recent approaches for modelling dynamics of physical systems with neural
networks enforce Lagrangian or Hamiltonian structure to improve prediction and
generalization. However, these approaches fail to handle the case when
coordinates are embedded in high-dimensional data such as images. We introduce
a new unsupervised neural network model that learns Lagrangian dynamics from
images, with interpretability that benefits prediction and control. The model
infers Lagrangian dynamics on generalized coordinates that are simultaneously
learned with a coordinate-aware variational autoencoder (VAE). The VAE is
designed to account for the geometry of physical systems composed of multiple
rigid bodies in the plane. By inferring interpretable Lagrangian dynamics, the
model learns physical system properties, such as kinetic and potential energy,
which enables long-term prediction of dynamics in the image space and synthesis
of energy-based controllers
ALADIN- -- An open-source MATLAB toolbox for distributed non-convex optimization
This paper introduces an open-source software for distributed and
decentralized non-convex optimization named ALADIN-. ALADIN- is
a MATLAB implementation of the Augmented Lagrangian Alternating Direction
Inexact Newton (ALADIN) algorithm, which is tailored towards rapid prototyping
for non-convex distributed optimization. An improved version of the recently
proposed bi-level variant of ALADIN is included enabling decentralized
non-convex optimization. A collection of application examples from different
applications fields including chemical engineering, robotics, and power systems
underpins the application potential of ALADIN-
Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes
The identification of the constrained dynamics of mechanical systems is often
challenging. Learning methods promise to ease an analytical analysis, but
require considerable amounts of data for training. We propose to combine
insights from analytical mechanics with Gaussian process regression to improve
the model's data efficiency and constraint integrity. The result is a Gaussian
process model that incorporates a priori constraint knowledge such that its
predictions adhere to Gauss' principle of least constraint. In return,
predictions of the system's acceleration naturally respect potentially
non-ideal (non-)holonomic equality constraints. As corollary results, our model
enables to infer the acceleration of the unconstrained system from data of the
constrained system and enables knowledge transfer between differing constraint
configurations.Comment: To be published in 2nd Annual Conference on Learning for Dynamics and
Control (L4DC), Proceedings of Machine Learning Research 202
Physics-Informed Multi-Agent Reinforcement Learning for Distributed Multi-Robot Problems
The networked nature of multi-robot systems presents challenges in the
context of multi-agent reinforcement learning. Centralized control policies do
not scale with increasing numbers of robots, whereas independent control
policies do not exploit the information provided by other robots, exhibiting
poor performance in cooperative-competitive tasks. In this work we propose a
physics-informed reinforcement learning approach able to learn distributed
multi-robot control policies that are both scalable and make use of all the
available information to each robot. Our approach has three key
characteristics. First, it imposes a port-Hamiltonian structure on the policy
representation, respecting energy conservation properties of physical robot
systems and the networked nature of robot team interactions. Second, it uses
self-attention to ensure a sparse policy representation able to handle
time-varying information at each robot from the interaction graph. Third, we
present a soft actor-critic reinforcement learning algorithm parameterized by
our self-attention port-Hamiltonian control policy, which accounts for the
correlation among robots during training while overcoming the need of value
function factorization. Extensive simulations in different multi-robot
scenarios demonstrate the success of the proposed approach, surpassing previous
multi-robot reinforcement learning solutions in scalability, while achieving
similar or superior performance (with averaged cumulative reward up to x2
greater than the state-of-the-art with robot teams x6 larger than the number of
robots at training time).Comment: This paper is under review at IEEE T-R
Constructing Neural Network-Based Models for Simulating Dynamical Systems
Dynamical systems see widespread use in natural sciences like physics,
biology, chemistry, as well as engineering disciplines such as circuit
analysis, computational fluid dynamics, and control. For simple systems, the
differential equations governing the dynamics can be derived by applying
fundamental physical laws. However, for more complex systems, this approach
becomes exceedingly difficult. Data-driven modeling is an alternative paradigm
that seeks to learn an approximation of the dynamics of a system using
observations of the true system. In recent years, there has been an increased
interest in data-driven modeling techniques, in particular neural networks have
proven to provide an effective framework for solving a wide range of tasks.
This paper provides a survey of the different ways to construct models of
dynamical systems using neural networks. In addition to the basic overview, we
review the related literature and outline the most significant challenges from
numerical simulations that this modeling paradigm must overcome. Based on the
reviewed literature and identified challenges, we provide a discussion on
promising research areas
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