A Unified Approach to Input-output Linearization and Concurrent Control of Underactuated Open-chain Multi-body Systems with Holonomic and Nonholonomic Constraints

Chhabra, Robin; Emami, M. Reza

doi:10.1007/s10883-014-9266-z

Cited by 19 publications

(16 citation statements)

References 30 publications

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“…In [54], a modeling approach was proposed that makes use of local exponential coordinates on the covering Lie subgroup defining the relative joint motions. A more holistic approach was taken by Chhabra [42,43] who introduced a generalized exponential formula.…”

Section: Open Issuesmentioning

confidence: 99%

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Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

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Section: Open Issuesmentioning

confidence: 99%

“…Recently, it was attempted in [42,43] and [54] to generalize this approach to non-holonomic systems. Along this line, an approach to model kinematic couplings that do not generate a motion subgroup was presented in [158].…”

Section: Open Issuesmentioning

confidence: 99%

Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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“…In past years, much consideration has been paid for tracking control and stabilization of the underactuated structures. Numerous control methods, for instance, Lyapunov redesign [29], passivity-based control [30], optimal control [31], input-output linearization [32], backstepping control [33], nonlinear state-feedback control [34], anti-swing control [35], artificial neural network [36], fuzzy control [37], feedforward control [38], H ∞ control [39], coupling-based control [40], adaptive predictive control [41] and sliding mode control (SMC) [42] have been proposed to design proper trackers and stabilizers of underactuated dynamical systems. SMC is a well-known control technique for design of the robust stabilizers and trackers of various dynamical systems with uncertainty and external perturbation [43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Fast Terminal Sliding Control of Underactuated Robotic Systems Based on Disturbance Observer with Experimental Validation

et al. 2021

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In this study, a novel fast terminal sliding mode control technique based on the disturbance observer is recommended for the stabilization of underactuated robotic systems. The finite time disturbance observer is employed to estimate the exterior disturbances of the system and develop the finite time control law. The proposed controller can regulate the state trajectories of the underactuated systems to the origin within a finite time in the existence of external disturbances. The stability analysis of the proposed control scheme is verified via the Lyapunov stabilization theory. The designed control law is enough to drive a switching surface achieving the fast terminal sliding mode against severe model nonlinearities with large parametric uncertainties and external disturbances. Illustrative simulation results and experimental validations on a cart-inverted pendulum system are provided to display the success and efficacy of the offered method.

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“…In recent years, much consideration has been given to the stabilization and tracking control of underactuated systems (Do et al., 2002, 2004; Liu et al., 2014a; Zhang et al., 2015). Several control approaches such as input–output linearization (Chhabra and Emami, 2016), H ∞ control (Rascón et al., 2016), backstepping control (Azimi and Koofigar, 2015), Lyapunov redesign (Ravichandran and Mahindrakar, 2011), and sliding mode control (SMC) (Khan and Akmeliawati, 2016; Miranda-Colorado et al., 2017) have been presented to design suitable stabilizers and trackers for these systems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive global sliding mode control of underactuated systems using a super-twisting scheme: an experimental study

Mobayen

2019

Journal of Vibration and Control

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The control problem of underactuated systems with external perturbations is investigating in this paper. Using the super-twisting-based global sliding mode control (GSMC) method, an original control law is proposed to guarantee removal of the reaching mode and obtain the robustness and exponential stability of the underactuated systems. Via the offered scheme, a robust control law is designed so that the state trajectories of the underactuated systems are convergent to the global sliding surface in an exponential manner. Moreover, this article develops an adaptive super-twisting algorithm for these systems. The adaptive-tuning controller eliminates the need of the knowledge about upper bound of the exterior disturbance. The discontinuous sign function appears in the controller derivative; as a result, the actual control signal reached after integration is continuous and free of chattering. Demonstrative simulations on a cart–inverted pendulum system as well as an experimental study are presented to show the effectiveness and applicability of the proposed technique.

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A Unified Approach to Input-output Linearization and Concurrent Control of Underactuated Open-chain Multi-body Systems with Holonomic and Nonholonomic Constraints

Cited by 19 publications

References 30 publications

Geometric methods and formulations in computational multibody system dynamics

Geometric methods and formulations in computational multibody system dynamics

Fast Terminal Sliding Control of Underactuated Robotic Systems Based on Disturbance Observer with Experimental Validation

Adaptive global sliding mode control of underactuated systems using a super-twisting scheme: an experimental study

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