Ioannis Sarras

Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems

The problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper. Our interest is centered on systems that can be rendered linear in the velocities via a (partial) change of coordinates. It is shown that the class is fully characterized by the solvability of a set of partial differential equations (PDEs) and strictly contains the class studied in the existing literature on linearization for speed observation or control. A reduced order globally exponentially stable observer, constructed using the immersion and invariance methodology, is proposed. The design requires the solution of another set of PDEs, which are shown to be solvable in several practical examples. It is also proven that the full order observer with dynamic scaling recently proposed by Karagiannis and Astolfi obviates the need to solve the latter PDEs. Finally, it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state--feedback interconnection and damping assignment passivity--based controller preserving asymptotic stability.

Brief paper: A constructive solution for stabilization via immersion and invariance: The cart and pendulum system

Immersion and Invariance (II (ii) the construction of an invariant manifold such that the restriction of the system dynamics to this manifold coincides with the target dynamics; (iii) the design of a control law that renders the manifold attractive and ensures that all signals are bounded. The second step requires the solution of a partial differential equation (PDE) that may be difficult to obtain. In this short note we use the classical cart and pendulum system to show that by interlacing the first and second steps, and invoking physical considerations, it is possible to obviate the solution of the PDE. To underscore the generality of the proposed variation of I&I, we show that it is also applicable to a class of n-dimensional systems that contain, as a particular case, the cart and pendulum system.

Constructive immersion and invariance stabilization for a class of underactuated mechanical systems

A constructive approach to stabilize a desired equilibrium for a class of underactuated mechanical systems, which obviates the solution of partial differential equations, is proposed. The Immersion & Invariance methodology is adopted, with the main result formulated in the Port-Hamiltonian framework, for both model and target dynamics. The procedure is applicable to mechanical systems with under-actuation degree larger than one, extending the results recently reported by some of the authors. The approach is successfully applied to two benchmark examples and some basic connections with the interconnection and damping assignment passivity-based control are revealed. An additional contribution of this work is the identification of a class of mechanical systems whose mechanical structure remains invariant under partial feedback linearization.

A Globally Exponentially Stable Tracking Controller for Mechanical Systems Using Position Feedback

A solution to the problem of global exponential tracking of mechanical systems without velocity measurements is given in the paper. The proposed controller is obtained combining a recently reported exponentially stable immersion and invariance observer and a suitably designed state-feedback passivity-based controller, which assigns to the closed-loop a port-Hamiltonian structure with a desired energy function. The result is applicable to a large class of mechanical systems and, in particular, no assumptions are made on the presence-and exact knowledge-of friction forces.

An adaptive controller for nonlinear teleoperators with variable time-delays

Abstract In most real-life bilateral teleoperators the available physical parameters are uncertain and the communications exhibit variable time-delays. In order to confront these situations and only assuming that a bound of the time-delays is known, the present work reports an adaptive controller which ensures asymptotic convergence of both position errors and velocities to zero, provided that a sufficient condition on the control gains is met. Compared to previous related works that only treated constant time-delays, the stability analysis does not rely on the cascade interconnection structure of the local and remote nonlinear dynamics and the linear interconnection map. Instead, the paper employs a different Lyapunov candidate function that incorporates a strictly positive term, the local and remote position error. Some simulations, in free space and interacting with a rigid wall, and experiments, using two nonlinear manipulators, illustrate the performance of the proposed control scheme in the presence of uncertain parameters and variable time-delays.

Total energy-shaping IDA-PBC control of the 2D-SpiderCrane

The objective of this paper is to further extend the application of the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique to the 2D-SpiderCrane mechanism with both kinetic and potential energy being shaped. An earlier effort had focused exclusively on potential energy alone. By shaping the total energy and by adding appropriate damping we achieve almost global asymptotic stability of the desired equilibrium.

Stabilization of the Experimental Cart-Pendulum System with Proven Domain of Attraction

The Immersion and Invariance methodology has proven to be a very effective theoretical tool for the stabilization of nonlinear systems. However, its applicability depends on the solvability of a set of partial differential equations (PDEs). In order to tackle this problem it was recently proposed to consider these PDEs as parameterized algebraic equations. This approach was illustrated for the cart–pendulum system with satisfactory results. However, no estimate of the domain of attraction of the equilibrium was given. In this paper, we complement the aforementioned work first, by proving that the domain of attraction contains the open upper-half plane and secondly, by showing the validation of the proposed controller when applied to an experimental set-up of the cart–pendulum system. Moreover, it is shown that the controller designed herein is simpler than others considered so far in the literature. Finally, it is pointed out that taking into consideration the presence of friction in the experimental set-up is crucial to attain the required performance and make the stabilization robust.

Output-feedback control of nonlinear bilateral teleoperators

The output-feedback design problem for a bilateral teleoperator scheme is considered. The recently proposed Immersion and Invariance (I&I) observer is used to obtain an exponentially convergent estimate of the unmeasured velocities. Moreover, it is proven that when this observer is interconnected to the nonlinear teleoperator together with a Proportional plus damping (P+d) controller, the overall system is globally stable. Finally, in the case when the human operator and the environment do not exert forces on the local and remote manipulator, respectively, global asymptotic convergence to zero of the velocities and of the position tracking error is achieved. These results are obtained by introducing two important design modifications ensuring the explicit derivation of the observer dynamics and that the interconnected system inherits the same stability properties as in the full-measurement case. The theoretical results are illustrated with simulations using local and remote two degree-of-freedom nonlinear manipulators.

Control of teleoperators with joint flexibility, uncertain parameters and time-delays

The problem of controlling a rigid bilateral teleoperator has been the subject of study since the late 1980s and several control approaches have been reported to deal with time-delays, position tracking and transparency. However, the general flexible case is still an open problem. The present paper reports an adaptive and damping injection controller and a proportional plus damping injection ( P + d ) controller which are capable of globally stabilizing a nonlinear bilateral teleoperator with joint flexibility and time-delays. More precisely, the adaptive scheme is able to cope with uncertainty in the parameters and constant time-delays, while the P + d scheme is shown to treat variable time-delays. In both cases, the teleoperator is composed of a rigid local manipulator and a flexible joint remote manipulator. The extension to the case where the local and remote manipulators exhibit joint flexibility is also reported using the P + d scheme. Under the common assumption that the human operator and the environment are passive it is proven, for the P + d schemes, that the joint and actuator velocities as well as the local and remote position errors are bounded. Moreover, if the human operator and remote environment forces are zero then, for both controllers, position tracking is established and local and remote velocities asymptotically converge to zero. Simulations and experiments are presented to depict the performance of the proposed schemes.

Consensus in networks of nonidentical Euler-Lagrange systems with variable time-delays

The present work reports a sufficient condition for the consensus of a network of nonidentical Euler-Lagrange (EL) systems with variable time-delays in the communications. The EL-systems are controlled by simple Proportional plus damping (P+d) schemes and the interconnection network is modeled as an undirected weighted graph. Additionally, for the case without delays, the paper reports a new Strict Lyapunov Function (SLF) for the closed-loop system. Experimental evidence, using three 3-Degrees-of-Freedom manipulators interconnected through the Internet, support the theoretical results of this paper.