Paolo Forni

Torque and variable stiffness control for antagonistically driven pneumatic muscle actuators via a stable force feedback controller

This paper describes a novel controller that is capable of simultaneously controlling torque and variable stiffness in real-time, for actuators with antagonistically driven pneumatic artificial muscles (PAMs). To this end, two contributions are presented: i) A stable force feedback controller that can cope with inherent PAM nonlinearities is synthesized using the dissipativity theory, for each PAM unit. ii) On top of this force feedback controller, a mathematical formulation is developed to compute reference force inputs that correspond to desired joint torque and joint stiffness inputs, concerning both agonist and antagonist PAMs. This strategy enables us to introduce real-time sensory feedback; torque and stiffness control is addressed by means of PAM force feedback control with guaranteed stability. To validate the proposed control scheme, a series of experiments were conducted on an experimental setup. As the result, the controller exhibited favorable torque and stiffness tracking in real-time, demonstrating that it could meet the performance criteria to power exoskeleton systems.

Input-to-state stability for cascade systems with multiple invariant sets

Abstract In a recent paper Angeli and Efimov (2015), the notion of Input-to-State Stability (ISS) has been generalized for systems with decomposable invariant sets and evolving on Riemannian manifolds. In this work, we analyze the cascade interconnection of such ISS systems and we characterize the finest possible decomposition of its invariant set for three different scenarios: 1. the driving system exhibits multistability (convergence to fixed points only); 2. the driving system exhibits multi-almost periodicity (convergence to fixed points as well as periodic and almost-periodic orbits) and the driven system is assumed to be incremental ISS; 3. the driving system exhibits multiperiodicity (convergence to fixed points and periodic orbits) whereas the driven system is ISS in the sense of Angeli and Efimov (2015). Furthermore, we provide marginal results on the backward/forward asymptotic behavior of incremental ISS systems and on the response of a contractive system under asymptotically almost-periodic forcing. Three examples illustrate the potentiality of the proposed framework.

Input-to-State Stability for cascade systems with decomposable invariant sets

In a recent paper, the notion of Input-to-State Stability (ISS) has been generalized for systems with decomposable invariant sets and evolving on Riemannian manifolds. In this work, we analyze the cascade interconnection of such ISS systems, we characterize the finest possible decomposition of its invariant set, and we provide the admissible gain for its ISS stability. Specifically, the following two scenarios are considered: 1. the driving system exhibits multistable behavior (fixed points only); 2. the driving system oscillates or rests (periodic orbits and fixed points) while assuming the incremental ISS of the driven system. Furthermore, marginal results on the backward/forward asymptotic behavior of incremental ISS systems are presented. A simple example illustrates the potentiality of the proposed framework.

Output-to-State Stability for systems on manifolds with multiple invariant sets

Output-to-State Stability (OSS) is a notion of detectability for nonlinear systems that is formulated in the ISS framework. We generalize the notion of OSS for systems evolving on manifolds and having multiple invariant sets. Building upon a recent extension of the Input-to-State Stability (ISS) theory for this very class of systems [1], the paper provides equivalent characterizations of the OSS property in terms of asymptotic estimates of the state trajectories and, in particular, in terms of existence of Lyapunov-like functions.

Cascades of iISS and Strong iISS systems with multiple invariant sets

In recent papers, the notions of Input-to-State Stability (ISS) and Integral ISS (iISS) have been generalized for systems evolving on manifolds and having multiple invariant sets, i.e. multistable systems. The well-known property of conservation of ISS under cascade interconnection has also been proven true for multistable systems in different scenarios. Unfortunately, multistability hampers a straightforward extension of analogous conservation properties for integral ISS systems. By means of counterexamples, this work highlights the necessity of the additional assumptions which yield the conservation of the iISS and Strong iISS properties in cascades of multistable systems. In particular, a characterization of the invariant set of the cascade is provided in terms of its finest possible decomposition.

The ISS approach to the stability and robustness properties of nonautonomous systems with decomposable invariant sets: An overview

Abstract This paper is an overview of recent developments in the Input-to-State Stability framework, dealing in particular with the extension of the classical concept to systems with multiple invariant sets and possibly evolving on Riemannian manifolds. Lyapunov-based characterizations of the properties are discussed as well as applications to the study of cascaded nonlinear systems.

Integral ISS for systems with multiple invariant sets

We generalize the classical integral Input-to-State Stability (iISS) theory for systems evolving on manifolds and admitting multiple disjoint invariant sets, so as to embed a much broader variety of dynamical behaviors of interest. Building upon a recent extension of the Input-to-State (ISS) theory for this kind of systems, we provide here equivalent characterizations of the iISS concept in terms of dissipation inequalities as well as connections with the Strong iISS notion. Finally, we discuss some examples within the domain of mechanical systems.

Adaptive trajectory tracking and rejection of sinusoidal disturbances with unknown frequencies for uncertain mechanical systems

The problem of adaptively tracking a pre-planned trajectory and rejecting multi-sinusoidal input disturbances with unknown amplitudes, phases and frequencies is addressed and solved for fully-actuated uncertain mechanical systems. We consider the case of disturbances occurring in joint space (adding up with the control torques) as well as the case of cartesian disturbances acting from the external environment. Largely inspired by the work of Chen and Huang [1] on the attitude dynamics of the rigid body, the proposed controller consists of an adaptive internal model unit which estimates in a joint fashion the mismatches in the disturbance frequencies and in the physical parameters. This work is very relevant, e.g., for mechanical systems with flexible appendages where vibrations arising from the flexibility are suppressed by being modeled as exogenous unknown sinusoidal disturbances.