arXiv subjects

Francesco Romano

Publications and source records attributed to Francesco Romano.

30 records · Page 2Linked to original sources

arXiv2018

Analysis and Predictability for Tipping Points with Leading-Order Nonlinear Terms

Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic differential equations. A key assumption in many arguments for the existence of variance and auto-correlation growth before a tipping point is to use a linearization argument, i.e., the leading-order term governing the deterministic (or drift) part of stochastic differential equation is linear. This assumption guarantees a local approximation via an Ornstein-Uhlenbeck process in the normally hyperbolic regime before, but sufficiently bounded away from, a bifurcation. In this paper, we generalize the situation to leading-order nonlinear terms for the setting of one fast variable. We work in the quasi-steady regime and prove that the fast variable has a well-defined stationary distribution and we calculate the scaling law for the variance as a bifurcation-induced tipping point is approached. We cross-validate the scaling law numerically. Furthermore, we provide a computational study for the predictability using early-warning signs for leading-order nonlinear terms based upon receiver-operator characteristic curves.

nlin.PS↗

arXiv2018

Modeling and Control of Humanoid Robots in Dynamic Environments: iCub Balancing on a Seesaw

Forthcoming applications concerning humanoid robots may involve physical interaction between the robot and a dynamic environment. In such scenario, classical balancing and walking controllers that neglect the environment dynamics may not be sufficient for achieving a stable robot behavior. This paper presents a modeling and control framework for balancing humanoid robots in contact with a dynamic environment. We first model the robot and environment dynamics, together with the contact constraints. Then, a control strategy for stabilizing the full system is proposed. Theoretical results are verified in simulation with robot iCub balancing on a seesaw.

cs.RO↗

arXiv2018

Scaling Laws and Warning Signs for Bifurcations of SPDEs

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated to systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations (SODEs), there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting also for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.

math.DS↗

arXiv2017

A Predictive Momentum-Based Whole-Body Torque Controller: Theory and Simulations for the iCub Stepping

When balancing, a humanoid robot can be easily subjected to unexpected disturbances like external pushes. In these circumstances, reactive movements as steps become a necessary requirement in order to avoid potentially harmful falling states. In this paper we conceive a Model Predictive Controller which determines a desired set of contact wrenches by predicting the future evolution of the robot, while taking into account constraints switching in case of steps. The control inputs computed by this strategy, namely the desired contact wrenches, are directly obtained on the robot through a modification of the momentum-based whole-body torque controller currently implemented on iCub. The proposed approach is validated through simulations in a stepping scenario, revealing high robustness and reliability when executing a recovery strategy.

cs.RO↗

arXiv2017

Stability Analysis and Design of Momentum-based Controllers for Humanoid Robots

Envisioned applications for humanoid robots call for the design of balancing and walking controllers. While promising results have been recently achieved, robust and reliable controllers are still a challenge for the control community dealing with humanoid robotics. Momentum-based strategies have proven their effectiveness for controlling humanoids balancing, but the stability analysis of these controllers is still missing. The contribution of this paper is twofold. First, we numerically show that the application of state-of-the-art momentum-based control strategies may lead to unstable zero dynamics. Secondly, we propose simple modifications to the control architecture that avoid instabilities at the zero-dynamics level. Asymptotic stability of the closed loop system is shown by means of a Lyapunov analysis on the linearized system's joint space. The theoretical results are validated with both simulations and experiments on the iCub humanoid robot.

math.OC↗

arXiv2017

A Receding Horizon Push Recovery Strategy for Balancing the iCub Humanoid Robot

Balancing and reacting to strong and unexpected pushes is a critical requirement for humanoid robots. We recently designed a capture point based approach which interfaces with a momentum-based torque controller and we implemented and validated it on the iCub humanoid robot. In this work we implement a Receding Horizon control, also known as Model Predictive Control, to add the possibility to predict the future evolution of the robot, especially the constraints switching given by the hybrid nature of the system. We prove that the proposed MPC extension makes the step-recovery controller more robust and reliable when executing the recovery strategy. Experiments in simulation show the results of the proposed approach.

cs.RO↗

arXiv2017

Torque-Controlled Stepping-Strategy Push Recovery: Design and Implementation on the iCub Humanoid Robot

One of the challenges for the robotics community is to deploy robots which can reliably operate in real world scenarios together with humans. A crucial requirement for legged robots is the capability to properly balance on their feet, rejecting external disturbances. iCub is a state-of-the-art humanoid robot which has only recently started to balance on its feet. While the current balancing controller has proved successful in various scenarios, it still misses the capability to properly react to strong pushes by taking steps. This paper goes in this direction. It proposes and implements a control strategy based on the Capture Point concept [1]. Instead of relying on position control, like most of Capture Point related approaches, the proposed strategy generates references for the momentum-based torque controller already implemented on the iCub, thus extending its capabilities to react to external disturbances, while retaining the advantages of torque control when interacting with the environment. Experiments in the Gazebo simulator and on the iCub humanoid robot validate the proposed strategy.

cs.RO↗

arXiv2017

The Static Center of Pressure Sensitivity: a further Criterion to assess Contact Stability and Balancing Controllers

Legged locomotion has received increasing attention from the robotics community. In this respect, contact stability plays a critical role in ensuring that robots maintain balance, and it is a key element for balancing and walking controllers. The Center of Pressure is a contact stability criterion that defines a point that must be kept strictly inside the support polygon in order to ensure postural stability. In this paper, we introduce the concept of the sensitivity of the static center of pressure: roughly speaking, the rate of change of the center of pressure with respect to the system equilibrium configurations. This new concept can be used as an additional criterion to assess the robustness of the contact stability. We show how the sensitivity of the center of pressure can also be used as a metric to assess balancing controllers by considering two state-of-the-art control strategies. The analytical analysis is performed on a simplified model, and validated during balancing tasks on the iCub humanoid robot.

cs.RO↗

arXiv2017

A Whole-Body Software Abstraction layer for Control Design of free-floating Mechanical Systems

In this paper, we propose a software abstraction layer to simplify the design and synthesis of whole-body controllers without making any preliminary assumptions on the control law to be implemented. The main advantage of the proposed library is the decoupling of the control software from implementation details, which are related to the robotic platform. Furthermore, the resulting code is more clean and concise than ad-hoc code, as it focuses only on the implementation of the control law. In addition, we present a reference implementation of the abstraction layer together with a Simulink interface to provide support to Model-Driven based development. We also show the implementation of a simple proportional-derivative plus gravity compensation control together with a more complex momentum-based bipedal balance controller.

cs.RO↗

arXiv2016

Tracking Particles in Flows near Invariant Manifolds via Balance Functions

Particles moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an invariant manifold, when it leaves again. Here we approach this problem mathematically by introducing balance functions, which relate the entry and exit points of a particle by an integral variational formula. We define, study, and compare different natural choices for balance functions and conclude that an efficient compromise is to employ normal infinitesimal Lyapunov exponents. We apply our results to two different model flows: a regularized solid-body rotational flow and the asymmetric Kuhlmann--Muldoon model developed in the context of liquid bridges. Furthermore, we employ full numerical simulations of the Navier-Stokes equations of a two-way coupled particle in a shear--stress-driven cavity to test balance functions for a particle moving near an invariant wall. In conclusion, our theoretically-developed framework seems to be applicable to models as well as data to understand particle motion near invariant manifolds.

math.DS↗

arXiv2014

Prioritized Optimal Control

This paper presents a new technique to control highly redundant mechanical systems, such as humanoid robots. We take inspiration from two approaches. Prioritized control is a widespread multi-task technique in robotics and animation: tasks have strict priorities and they are satisfied only as long as they do not conflict with any higher-priority task. Optimal control instead formulates an optimization problem whose solution is either a feedback control policy or a feedforward trajectory of control inputs. We introduce strict priorities in multi-task optimal control problems, as an alternative to weighting task errors proportionally to their importance. This ensures the respect of the specified priorities, while avoiding numerical conditioning issues. We compared our approach with both prioritized control and optimal control with tests on a simulated robot with 11 degrees of freedom.

cs.RO↗

arXiv2014

Collocated Adaptive Control of Underactuated Mechanical Systems

Collocated adaptive control of underactuated systems is still a main concern for the control community, all the more so because the collocated dynamics is no longer linear with respect to the constant base parameters. This work extends and encompasses the well known adaptive control result for fully actuated mechanical systems to the underactuated case. The key point is the introduction of a fictitious control input that allows us to consider the complete system dynamics, which is assumed to be linear with respect to the base parameters. Local stability and convergence of time varying reference trajectories for the collocated dynamics are demonstrated by using Lyapunov and Barbalat arguments. Simulation and experimental results on a two-link manipulator verify the soundness of the proposed approach.

eess.SY↗