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Stefano Stramigioli

Publications and source records attributed to Stefano Stramigioli.

32 records · Page 2Linked to original sources
arXiv2022

A differential geometric description of thermodynamics in continuum mechanics with application to Fourier-Navier-Stokes fluids

A description of thermodynamics for continuum mechanical systems is presented in the coordinate-free language of exterior calculus. First, a careful description of the mathematical tools that are needed to formulate the relevant conservation laws is given. Second, following an axiomatic approach, the two thermodynamic principles will be described, leading to a consistent description of entropy creation mechanisms on manifolds. Third, a specialisation to Fourier-Navier-Stokes fluids will be carried through.

physics.flu-dyn↗
arXiv2022

Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation laws and cope with mixed open boundary conditions using a single computational mesh. The possibility of including open boundary conditions allows for modular composition of complex multi-physical systems whereas the exterior calculus formulation provides a coordinate-free treatment. Our approach relies on a dual-field representation of the physical system that is redundant at the continuous level but eliminates the need of mimicking the Hodge star operator at the discrete level. By considering the Stokes-Dirac structure representing the system together with its adjoint, which embeds the metric information directly in the codifferential, the need for an explicit discrete Hodge star is avoided altogether. By imposing the boundary conditions in a strong manner, the power balance characterizing the Stokes-Dirac structure is then retrieved at the discrete level via symplectic Runge-Kutta integrators based on Gauss-Legendre collocation points. Numerical experiments validate the convergence of the method and the conservation properties in terms of energy balance both for the wave and Maxwell equations in a three dimensional domain. For the latter example, the magnetic and electric fields preserve their divergence free nature at the discrete level.

math.NA↗
arXiv2021

Towards Autonomous Pipeline Inspection with Hierarchical Reinforcement Learning

Inspection and maintenance are two crucial aspects of industrial pipeline plants. While robotics has made tremendous progress in the mechanic design of in-pipe inspection robots, the autonomous control of such robots is still a big open challenge due to the high number of actuators and the complex manoeuvres required. To address this problem, we investigate the usage of Deep Reinforcement Learning for achieving autonomous navigation of in-pipe robots in pipeline networks with complex topologies. Moreover, we introduce a hierarchical policy decomposition based on Hierarchical Reinforcement Learning to learn robust high-level navigation skills. We show that the hierarchical structure introduced in the policy is fundamental for solving the navigation task through pipes and necessary for achieving navigation performances superior to human-level control.

cs.RO↗
arXiv2021

Low Dimensional State Representation Learning with Robotics Priors in Continuous Action Spaces

Autonomous robots require high degrees of cognitive and motoric intelligence to come into our everyday life. In non-structured environments and in the presence of uncertainties, such degrees of intelligence are not easy to obtain. Reinforcement learning algorithms have proven to be capable of solving complicated robotics tasks in an end-to-end fashion without any need for hand-crafted features or policies. Especially in the context of robotics, in which the cost of real-world data is usually extremely high, reinforcement learning solutions achieving high sample efficiency are needed. In this paper, we propose a framework combining the learning of a low-dimensional state representation, from high-dimensional observations coming from the robot's raw sensory readings, with the learning of the optimal policy, given the learned state representation. We evaluate our framework in the context of mobile robot navigation in the case of continuous state and action spaces. Moreover, we study the problem of transferring what learned in the simulated virtual environment to the real robot without further retraining using real-world data in the presence of visual and depth distractors, such as lighting changes and moving obstacles.

cs.RO↗
arXiv2021

Image-guided Breast Biopsy of MRI-visible Lesions with a Hand-mounted Motorised Needle Steering Tool

A biopsy is the only diagnostic procedure for accurate histological confirmation of breast cancer. When sonographic placement is not feasible, a Magnetic Resonance Imaging(MRI)-guided biopsy is often preferred. The lack of real-time imaging information and the deformations of the breast make it challenging to bring the needle precisely towards the tumour detected in pre-interventional Magnetic Resonance (MR) images. The current manual MRI-guided biopsy workflow is inaccurate and would benefit from a technique that allows real-time tracking and localisation of the tumour lesion during needle insertion. This paper proposes a robotic setup and software architecture to assist the radiologist in targeting MR-detected suspicious tumours. The approach benefits from image fusion of preoperative images with intraoperative optical tracking of markers attached to the patient's skin. A hand-mounted biopsy device has been constructed with an actuated needle base to drive the tip toward the desired direction. The steering commands may be provided both by user input and by computer guidance. The workflow is validated through phantom experiments. On average, the suspicious breast lesion is targeted with a radius down to 2.3 mm. The results suggest that robotic systems taking into account breast deformations have the potentials to tackle this clinical challenge.

cs.RO↗
arXiv2021

Geometric and energy-aware decomposition of the Navier-Stokes equations: A port-Hamiltonian approach

A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the interconnection of the power preserving structure which underlies the motion of perfect fluids to a dissipative port which encodes Newtonian constitutive relations of shear and bulk stresses. The relevant diffusion and the boundary terms characterizing the Navier-Stokes equations on a general Riemannian manifold arise naturally from the proposed construction.

physics.flu-dyn↗
arXiv2021

Low Dimensional State Representation Learning with Reward-shaped Priors

Reinforcement Learning has been able to solve many complicated robotics tasks without any need for feature engineering in an end-to-end fashion. However, learning the optimal policy directly from the sensory inputs, i.e the observations, often requires processing and storage of a huge amount of data. In the context of robotics, the cost of data from real robotics hardware is usually very high, thus solutions that achieve high sample-efficiency are needed. We propose a method that aims at learning a mapping from the observations into a lower-dimensional state space. This mapping is learned with unsupervised learning using loss functions shaped to incorporate prior knowledge of the environment and the task. Using the samples from the state space, the optimal policy is quickly and efficiently learned. We test the method on several mobile robot navigation tasks in a simulation environment and also on a real robot.

cs.LG↗
arXiv2020

Port-Hamiltonian Modeling of Ideal Fluid Flow: Part II. Compressible and Incompressible Flow

Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for the fluid, the Stokes Dirac structure is derived by Poisson reduction and then augmented by boundary ports and distributed ports. The additional boundary ports have been shown to appear naturally as surface terms in the pairings of dual maps, always neglected in standard Hamiltonian theory. The port-Hamiltonian model presented in Part I corresponded only to the kinetic energy of the fluid and how its energy variables evolve such that the energy is conserved. In Part II, we utilize the distributed port of the kinetic energy port-Hamiltonian system for representing a number of fluid-dynamical systems. By adding internal energy we model compressible flow, both adiabatic and isentropic, and by adding constraint forces we model incompressible flow. The key tools used are the interconnection maps relating the dynamics of fluid motion to the dynamics of advected quantities.

physics.flu-dyn↗
arXiv2020

Port-Hamiltonian Modeling of Ideal Fluid Flow: Part I. Foundations and Kinetic Energy

In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac structures. The first novelty of the presented model is the inclusion of non-zero energy exchange through, and within, the spatial boundaries of the domain containing the fluid. The second novelty is that the port-Hamiltonian model is constructed as the interconnection of a small set of building blocks of open energetic subsystems. Depending only on the choice of subsystems one composes and their energy-aware interconnection, the geometric description of a wide range of fluid dynamical systems can be achieved. The constructed port-Hamiltonian models include a number of inviscid fluid dynamical systems with variable boundary conditions. Namely, compressible isentropic flow, compressible adiabatic flow, and incompressible flow. Furthermore, all the derived fluid flow models are valid covariantly and globally on n-dimensional Riemannian manifolds using differential geometric tools of exterior calculus.

math.DG↗
arXiv2020

On Reward Shaping for Mobile Robot Navigation: A Reinforcement Learning and SLAM Based Approach

We present a map-less path planning algorithm based on Deep Reinforcement Learning (DRL) for mobile robots navigating in unknown environment that only relies on 40-dimensional raw laser data and odometry information. The planner is trained using a reward function shaped based on the online knowledge of the map of the training environment, obtained using grid-based Rao-Blackwellized particle filter, in an attempt to enhance the obstacle awareness of the agent. The agent is trained in a complex simulated environment and evaluated in two unseen ones. We show that the policy trained using the introduced reward function not only outperforms standard reward functions in terms of convergence speed, by a reduction of 36.9\% of the iteration steps, and reduction of the collision samples, but it also drastically improves the behaviour of the agent in unseen environments, respectively by 23\% in a simpler workspace and by 45\% in a more clustered one. Furthermore, the policy trained in the simulation environment can be directly and successfully transferred to the real robot. A video of our experiments can be found at: https://youtu.be/UEV7W6e6ZqI

cs.RO↗
arXiv2019

One-Dimensional Solution Families of Nonlinear Systems Characterized by Scalar Functions on Riemannian Manifolds

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of low-dimensional invariant manifolds in the form of nonlinear normal modes is rather a niche topic, treated mainly in the context of structural mechanics for systems with Euclidean metrics, i.e., for point masses connected by nonlinear springs. Newest results emphasize, however, that a very rich structure of periodic and low-dimensional solutions exist also within nonlinear systems such as elastic multi-body systems encountered in the biomechanics of humans and animals or of humanoid and quadruped robots, which are characterized by a non-constant metric tensor. This paper discusses different generalizations of linear oscillation modes to nonlinear systems and proposes a definition of strict nonlinear normal modes, which matches most of the relevant properties of the linear modes. The main contributions are a theorem providing necessary and sufficient conditions for the existence of strict oscillation modes on systems endowed with a Riemannian metric and a potential field as well as a constructive example of designing such modes in the case of an elastic double pendulum.

eess.SY↗
arXiv2017

Design, Modeling, and Geometric Control on SE(3) of a Fully-Actuated Hexarotor for Aerial Interaction

In this work we present the optimization-based design and control of a fully-actuated omnidirectional hexarotor. The tilt angles of the propellers are designed by maximizing the control wrench applied by the propellers. This maximizes (a) the agility of the UAV, (b) the maximum payload the UAV can hover with at any orientation, and (c) the interaction wrench that the UAV can apply to the environment in physical contact. It is shown that only axial tilting of the propellers with respect to the UAV's body yields optimal results. Unlike the conventional hexarotor, the proposed hexarotor can generate at least 1.9 times the maximum thrust of one rotor in any direction, in addition to the higher control torque around the vehicle's upward axis. A geometric controller on SE(3) is proposed for the trajectory tracking problem for the class of fully actuated UAVs. The proposed controller avoids singularities and complexities that arise when using local parametrizations, in addition to being invariant to a change of inertial coordinate frame. The performance of the controller is validated in simulation.

math.OC↗
arXiv2017

Bipedal locomotion using variable stiffness actuation

Robust and energy-efficient bipedal locomotion in robotics is still a challenging topic. In order to address issues in this field, we can take inspiration from nature, by studying human locomotion. The Spring-Loaded Inverted Pendulum (SLIP) model has shown to be a good model for this purpose. However, the human musculoskeletal system enables us to actively modulate leg stiffness, for example when walking in rough terrain with irregular and unexpected height variations of the walking surface. This ability of varying leg stiffness is not considered in conventional SLIP-based models, and therefore this paper explores the potential role of active leg stiffness variation in bipedal locomotion. It is shown that the conceptual SLIP model can be iteratively extended to more closely resemble a realistic (i.e., non-ideal) walker, and that feedback control strategies can be designed that reproduce the SLIP behavior in these extended models. We show that these extended models realize a cost of transport comparable to human walking, which indicates that active leg stiffness variation plays an important role in human locomotion that was previously not captured by the SLIP model. The results of this study show that active leg stiffness adaptation is a promising approach for realizing more energy-efficient and robust bipedal walking robots.

cs.RO↗