On Orbital Stabilization for Industrial Manipulators: Case Study in Evaluating Performances of Modified PD+ and Inverse Dynamics Controllers

Pchelkin, Stepan; Shiriaev, Anton S.; Robertsson, Anders; Freidovich, Leonid B.; Kolyubin, Sergey A.; Paramonov, Leonid; Gusev, Sergei V.

doi:10.1109/tcst.2016.2554520

Cited by 23 publications

(20 citation statements)

References 15 publications

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“…Similar coordinates and approaches have previously been considered (see e.g. [12], [13]). Our approach, however, differs both in the way that we parameterize the trajectory by a MG implicitly defined, as well as by the velocity independent feedforward-like control input, allowing for a transverse linearization only dependent on the MG.…”

Section: Discussion and Future Workmentioning

confidence: 99%

See 1 more Smart Citation

Trajectory Optimization and Orbital Stabilization of Underactuated Euler-Lagrange Systems with Impacts

Sætre¹,

Shiriaev²,

Anstensrud³

2019

2019 18th European Control Conference (ECC)

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A numerical framework for finding and stabilizing periodic trajectories of underactuated mechanical systems with impacts is presented. By parameterizing a trajectory by a set of synchronization functions, whose parameters we search for, the dynamical constraints arising due to underactuation can be reduced to a single equation on integral form. This allows for the discretization of the planning problem into a parametric nonlinear programming problem by Gauss-Legendre quadratures. A convenient set of candidates for transverse coordinates are then introduced. The origin of these coordinates correspond to the target motion, along which their dynamics can be analytically linearized. This allows for the design of an orbitally stabilizing feedback controller, which is also applicable for degrees of underactuation higher than one.

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Section: Discussion and Future Workmentioning

confidence: 99%

“…subject tox(s,ṡ, p) ∈ TQ,û(s,ṡ, p) ∈ U (withû found from (8) usings from (10)), the continuous dynamics integral constraint (12), the instantaneous impact updatê…”

Section: B Restating and Discretizing The Optimal Control Problemmentioning

confidence: 99%

Trajectory Optimization and Orbital Stabilization of Underactuated Euler-Lagrange Systems with Impacts

Sætre¹,

Shiriaev²,

Anstensrud³

2019

2019 18th European Control Conference (ECC)

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“…is fulfilled for all = 0, r i , i = 1, p. Accordingly, since = −̃, the estimated vector̂is recovered by algebraic manipulation in (15). Therefore, the estimated statex is plainly recovered in (16).…”

Section: Uncertainties Identificationmentioning

confidence: 99%

“…Step 3) Usẽand̂retrieved in (29) and combine them in (15) to obtain̂. Later on, apply the inverse map (16) to recover the estimated statex…”

Section: Figurementioning

confidence: 99%

High‐order sliding‐mode observer–based input‐output linearization

Loza

Fridman

Aguilar

et al. 2019

Intl J Robust & Nonlinear

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Summary The problem of output control in multiple‐input–multiple‐output nonlinear systems is addressed. A high‐order sliding‐mode observer is used to estimate the states of the system and identify the discrepancy between the nominal model and the real plant. The exact and finite‐time estimation may be tackled as long as the system presents the algebraic strong observability property. Thus, a continuous robust input‐output linearization strategy can be obtained with respect to a prescribed output. As a consequence, the closed‐loop dynamics performs robustly to uncertainties/perturbations. To illustrate the advantages of the proposed method, we introduce a study case that demands a robust linear system behavior: the self‐oscillations induced in an underactuated mechanical system through a two‐relay controller. Experiments with an inertial wheel pendulum illustrate the feasibility of the proposed approach.

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“…Recent research also considers performance or optimality criteria, eg,  ∞ optimality, 45 time-domain bounds, 46 or orbital stabilization around the desired trajectory. 47 Most relevant for the developments in this article are the classic linear multivariable design 9 and the Lyapunov-based robust manipulator control designs 5 reviewed in more detail next.…”

Section: Nonlinear Model-basedmentioning

confidence: 99%

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

Friedrich

Buss

2019

Intl J Robust & Nonlinear

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We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid-body manipulators under approximate inverse dynamics control. Outer-loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well-known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer-loop feedback controller by means of an uncertain dual-Youla operator. Therefore, using the dual-Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid-body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double-Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six-degree-of-freedom robot scenario with varying payload. KEYWORDS approximate inverse dynamics, dual-Youla parameterization, robust robot manipulator control, robust/adaptive control, uncertainty quantification INTRODUCTIONOperating conditions of robot manipulators change over time, impairing the control performance, for example, by wear, varying load, etc. To adapt the controller to such situations, a variety of data-driven methods have been proposed in the literature, including adaptive and learning control. [1][2][3][4] In practice, however, very simple feedback controllers and model-based architectures are prevalent.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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On Orbital Stabilization for Industrial Manipulators: Case Study in Evaluating Performances of Modified PD+ and Inverse Dynamics Controllers

Cited by 23 publications

References 15 publications

Trajectory Optimization and Orbital Stabilization of Underactuated Euler-Lagrange Systems with Impacts

Trajectory Optimization and Orbital Stabilization of Underactuated Euler-Lagrange Systems with Impacts

High‐order sliding‐mode observer–based input‐output linearization

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

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