Jose Guadalupe Romero

Robust energy shaping control of mechanical systems

The problem of robustness improvement, vis a vis external disturbances, of energy shaping controllers for mechanical systems is addressed in this paper. First, it is shown that, if the inertia matrix is constant, constant disturbances (both, matched and unmatched) can be rejected simply adding a suitable integral action—interestingly, not at the passive output. For systems with non-constant inertia matrix, additional damping and gyroscopic forces terms must be added to reject matched disturbances and, moreover, enforce the property of integral input-to-state stability with respect to matched disturbances. The stronger property of input-to-state stability, this time with respect to matched and unmatched disturbances, is ensured with further addition of nonlinear damping. Finally, it is shown that including a partial change of coordinates, the controller can be significantly simplified, preserving input-to-state stability with respect to matched disturbances.

Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances

Regulation of passive outputs of nonlinear systems can be easily achieved with an integral control (IC). In many applications, however, the signal of interest is not a passive output and ensuring its regulation remains an open problem. Also, IC of passive systems rejects constant input disturbances, but no similar property can be ensured if the disturbance is not matched. In this paper we address the aforementioned problems and propose a procedure to design robust ICs for port-Hamiltonian models, that characterize the behavior of a large class of physical systems. Necessary and sufficient conditions for the solvability of the problem, in terms of some rank and controllability properties of the linearized system, are provided. For a class of fully actuated mechanical systems, a globally asymptotically stabilizing solution is given.

Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations

Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this technical note a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples.

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.

Model-Free Visually Servoed Deformation Control of Elastic Objects by Robot Manipulators

Despite the recent progress in physically interactive and surgical robotics, the active deformation of compliant objects remains an open problem. The main obstacle to its implementation comes from the difficulty to identify or estimate the objects deformation model. In this paper, we propose a novel vision-based deformation controller for robot manipulators interacting with unknown elastic objects. We derive a new dynamic-state feedback velocity control law using the passivity-based framework. Our method exploits visual feedback to estimate the deformation Jacobian matrix in real time, avoiding any model identification steps. We prove that even in the presence of inexact estimations, the closed-loop dynamical system ensures input-to-state stability (i.e., full dissipativity) with respect to external disturbances. An experimental study with several deformation tasks is presented to validate the theory.

On the visual deformation servoing of compliant objects: Uncalibrated control methods and experiments

In this paper, we address the active deformation control of compliant objects by robot manipulators. The control of deformations is needed to automate several important tasks, for example, the manipulation of soft tissues, shaping of food materials, or needle insertion. Note that in many of these applications, the object’s deformation properties are not known. To cope with this issue, in this paper we present two new visual servoing approaches to explicitly servo-control elastic deformations. The novelty of our kinematic controllers lies in its uncalibrated behavior; our adaptive methods do not require the prior identification of the object’s deformation model and the camera’s intrinsic/extrinsic parameters. This feature provides a way to automatically control deformations in a model-free manner. The experimental results that we report validate the feasibility of our controllers.

Two globally convergent adaptive speed observers for mechanical systems

A globally exponentially stable speed observer for mechanical systems was recently reported in the literature, under the assumptions of known (or no) Coulomb friction and no disturbances. In this note we propose and adaptive version of this observer, which is robust vis-a-vis constant disturbances. Moreover, we propose a new globally convergent speed observer that, besides rejecting the disturbances, estimates some unknown friction coefficients for a class of mechanical systems that contains several practical examples.

Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces

To extend the realm of application of the well known controller design technique of interconnection and damping assignment passivity-based control (IDA-PBC) of mechanical systems two modifications to the standard method are presented in this article. First, similarly to Batlle et al. (2009) and Gomez-Estern and van der Schaft (2004), it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously. Second, motivated by Chang (2014), we propose to consider the inclusion of dissipative forces, going beyond the gyroscopic ones used in standard IDA-PBC. The contribution of our work is the proof that the addition of these two elements provides a non-trivial extension to the basic IDA-PBC methodology. It is also shown that several new controllers for mechanical systems designed invoking other (less systematic procedures) that do not satisfy the conditions of standard IDA-PBC, actually belong to this new class of SIDA-PBC.

Robustifying energy shaping control of mechanical systems

The problem of robustness improvement, vis à vis external disturbances, of energy shaping controllers for mechanical systems is addressed in this paper. First, it is shown that-if the inertia matrix is constant-constant disturbances (both, matched and unmatched) can be rejected simply adding a suitable integral action. For systems with non-constant inertia matrix, additional damping and gyroscopic forces terms must be added to reject matched disturbances and, moreover, enforce the property of integral input-to-state stability with respect to matched disturbances. Finally, the stronger property of input-to-state stability, this time with respect to matched and unmatched disturbances, is ensured with further addition of nonlinear damping.

Energy Shaping of Mechanical Systems via PID Control and Extension to Constant Speed Tracking

In a recent contribution, it was shown that a class of mechanical systems, which contains many practical examples, can be stabilized via energy shaping without solving partial differential equations. The proposed controller consists of two terms, a partial linearizing state-feedback and a linear PID loop around two new passive outputs. In this brief note we prove that the first, admittedly non-robust, step can be obviated leaving only the linear PID. A second contribution of the note is to propose a slight modification to the controller to go beyond regulation tasks-being able to follow ramp references in the actuated coordinates.