arXiv subjects

Manfredi Maggiore

Publications and source records attributed to Manfredi Maggiore.

11 recordsLinked to original sources

arXiv2024

From gymnastics to virtual nonholonomic constraints: energy injection, dissipation, and regulation for the acrobot

In this article we study virtual nonholonomic constraints, which are relations between the generalized coordinates and momenta of a mechanical system that can be enforced via feedback control. We design a constraint which emulates gymnastics giant motion in an acrobot, and prove that this constraint can inject or dissipate energy based on the sign of a design parameter. The proposed constraint is tested both in simulation and experimentally on a real-world acrobot, demonstrating highly effective energy regulation properties and robustness to a variety of disturbances.

cs.RO↗

arXiv2019

Reduction Principles and the Stabilization of Closed Sets for Passive Systems

In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space.

math.OC↗

arXiv2018

A coordinate-free theory of virtual holonomic constraints

This paper presents a coordinate-free formulation of virtual holonomic constraints for underactuated Lagrangian control systems on Riemannian manifolds. It is shown that when a virtual constraint enjoys a regularity property, the constrained dynamics are described by an affine connection dynamical system. The affine connection of the constrained system has an elegant relationship to the Riemannian connection of the original Lagrangian control system. Necessary and sufficient conditions are given for the constrained dynamics to be Lagrangian. A key condition is that the affine connection of the constrained dynamics be metrizable. Basic results on metrizability of affine connections are first reviewed, then employed in three examples in order of increasing complexity. The last example is a double pendulum on a cart with two different actuator configurations. For this control system, a virtual constraint is employed which confines the second pendulum to within the upper half-plane.

math.OC↗

arXiv2018

Reduction Theorems for Hybrid Dynamical Systems

This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $Γ_1 \subset Γ_2 \subset \Re^n$, with $Γ_1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $Γ_1$ that holds relative to $Γ_2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $Γ_1$, then $Γ_1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal.

math.OC↗

arXiv2018

Dynamic Virtual Holonomic Constraints for Stabilization of Closed Orbits in Underactuated Mechanical Systems

This article investigates the problem of enforcing a virtual holonomic constraint (VHC) on a mechanical system with degree of underactuation one while simultaneously stabilizing a closed orbit on the constraint manifold. This problem, which to date is open, arises when designing controllers to induce complex repetitive motions in robots. In this paper, we propose a solution which relies on the parameterization of the VHC by the output of a double-integrator. While the original control inputs are used to enforce the VHC, the control input of the double-integrator is designed to asymptotically stabilize the closed orbit and make the state of the double-integrator converge to zero. The proposed design is applied to the problem of making a PVTOL aircraft follow a circle on the vertical plane with a desired speed profile, while guaranteeing that the aircraft does not roll over for suitable initial conditions.

math.DS↗

arXiv2017

On the Lagrangian Structure of Reduced Dynamics Under Virtual Holonomic Constraints

This paper investigates a class of Lagrangian control systems with $n$ degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which the reduced dynamics are those of a mechanical system with one DOF and, more generally, under which they have a Lagrangian structure. In both cases, we show that typical solutions satisfying the virtual constraints lie in a restricted class which we completely characterize.

math.DS↗

arXiv2016

Local and Distributed Rendezvous of Underactuated Rigid Bodies

This paper solves the rendezvous problem for a network of underactuated rigid bodies such as quadrotor helicopters. A control strategy is presented that makes the centres of mass of the vehicles converge to an arbitrarily small neighborhood of one another. The convergence is global, and each vehicle can compute its own control input using only an on-board camera and a three-axis rate gyroscope. No global positioning system is required, nor any information about the vehicles' attitudes.

math.OC↗

arXiv2016

A Smooth Distributed Feedback for Global Rendezvous of Unicycles

This paper presents a solution to the rendezvous control problem for a network of kinematic unicycles in the plane, each equipped with an onboard camera measuring its relative displacement with respect to its neighbors in body frame coordinates. A smooth, time-independent control law is presented that drives the unicycles to a common position from arbitrary initial conditions, under the assumption that the sensing digraph contains a reverse-directed spanning tree. The proposed feedback is very simple, and relies only on the onboard measurements. No global positioning system is required, nor any information about the unicycles' orientations.

math.OC↗

arXiv2013

Control of a Bicycle Using Virtual Holonomic Constraints

The paper studies the problem of making Getz's bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method. Specifically, a VHC is enforced making the roll angle of the bicycle become a function of the bicycle's position along the curve. It is shown that the VHC can be automatically generated as a periodic solution of a scalar periodic differential equation, which we call virtual constraint generator. Finally, it is shown that if the curve is sufficiently long as compared to the height of the bicycle's centre of mass and its wheel base, then the enforcement of a suitable VHC makes the bicycle traverse the curve with a steady-state speed profile which is periodic and independent of initial conditions. An outcome of this work is a proof that the constrained dynamics of a Lagrangian control system subject to a VHC are generally not Lagrangian.

math.OC↗

arXiv2000

Output Feedback Control for Stabilizable and Incompletely Observable Nonlinear Systems

This paper introduces a new approach for output feedback stabilization of SISO systems which, unlike most of the techniques found in the literature, does not use high-gain observers and control input saturation to achieve separation between the state feedback and observer designs. Rather, we show that by using nonlinear observers, together with a projection algorithm, the same kind of separation principle is achieved for a larger class of systems, namely stabilizable and incompletely observable plants. Furthermore, this new approach avoids using knowledge of the inverse of the observability mapping, which is needed by most techniques in the literature when controlling general stabilizable systems.

math.OC↗

arXiv2000

Output Feedback Control of Jet Engine Stall and Surge Using Pressure Measurements

The problem of controlling surge and stall in jet engine compressors is of fundamental importance in preventing damage and lengthening the life of these components. In this paper, we use the Moore-Greitzer mathematical model to develop an output feedback controller for these two instabilities (only one of the three states is measurable). This problem is particularly challenging since the system is not completely observable and, hence, none of the output feedback control techniques found in the literature can be applied to recover the performance of a full state feedback controller. However, we show how to successfully solve it by using a novel output feedback approach for the stabilization of general stabilizable and incompletely observable systems.

math.OC↗