Maneuvering Control of Planar Snake Robots Using Virtual Holonomic Constraints

Mohammadi, Alireza; Rezapour, Ehsan; Maggiore, Manfredi; Pettersen, Kristin Y.

doi:10.1109/tcst.2015.2467208

Cited by 92 publications

(74 citation statements)

References 34 publications

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“…Here, the reduction problem stems from the decomposition of the control design into two steps: meeting the high-priority specification first, i.e., stabilize Γ 2 ; then, assuming that the high-priority specification has been achieved, meet the low-priority specification, i.e., stabilize Γ 1 relative to Γ 2 . This point of view is developed in [7], and has been applied to the almost-global stabilization of VTOL vehicles [24], distributed control [6], [32], virtual holonomic constraints [17], robotics [20], [21], and static or dynamic allocation of nonlinear redundant actuators [22]. Similar ideas have also been adopted in [19], where the concept of local stability near a set, introduced in Definition II.6, is key to ruling out situations where the feedback stabilizer may generate solutions that blow up to infinity.…”

Section: The Reduction Problemmentioning

confidence: 99%

Reduction Theorems for Hybrid Dynamical Systems

Maggiore

Sassano

Zaccarian

2019

IEEE Trans. Automat. Contr.

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This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets Γ1 ⊂ Γ2 ⊂ R n , with Γ1 compact, the theorems presented in this paper give conditions under which a qualitative property of Γ1 that holds relative to Γ2 (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set Γ1, then Γ1 is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal.

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Section: The Reduction Problemmentioning

confidence: 99%

Reduction Theorems for Hybrid Dynamical Systems

Maggiore

Sassano

Zaccarian

2019

IEEE Trans. Automat. Contr.

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“…In addition to biped and powered prostheses control, they have also been used for controlling biologically-inspired snake robots [16], [17], [18]. Δ…”

Section: Biped Robot Hybrid Dynamicsmentioning

confidence: 99%

Removing phase variables from biped robot parametric gaits

Mohammadi

Horn

Gregg

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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Hybrid zero dynamics-based control is a promising framework for controlling underactuated biped robots and powered prosthetic legs. In this control paradigm, stable walking gaits are implicitly encoded in polynomial output functions of the robot configuration variables, which are to be zeroed via feedback. The biped output functions are parameterized by a suitable mechanical phasing variable whose evolution determines the biped gait progression during each step. Determining a proper phase variable, however, might not always be a trivial task. In this paper, we present a method for generating output functions from given parametric walking gaits without any explicit knowledge of the phase variables. Our elimination method is based on computing the resultant of polynomials, an algebraic tool widely used in computer algebra.

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“…They have been successfully employed in several robotic locomotion control applications such as controlling underactuated biped robots [10], [11], powered prosthetic legs [12], [13], and biologically inspired snake robots [14]–[16]. In the context of powered prosthetic leg control, virtual constraints were used to unify the gait cycle control of the stance phase for the first time in [12].…”

Section: Introductionmentioning

confidence: 99%

Automatic tuning of virtual constraint-based control algorithms for powered knee-ankle prostheses

Kumar

Mohammadi

Gans

et al. 2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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State-of-art powered prosthetic legs are often controlled using a collection of joint impedance controllers designed for different phases of a walking cycle. Consequently, finite state machines are used to control transitions between different phases. This approach requires a large number of impedance parameters and switching rules to be tuned. Since one set of control parameters cannot be used across different amputees, clinicians spend enormous time tuning these gains for each patient. This paper proposes a virtual constraint-based control scheme with a smaller set of control parameters, which are automatically tuned in real-time using an extremum seeking controller (ESC). ESC, being a model-free control method, assumes no prior knowledge of either the prosthesis or human. Using a singular perturbation analysis, we prove that the virtual constraint tracking errors are small and the PD gains remain bounded. Simulations demonstrate that our ESC-based method is capable of adapting the virtual-constraint based control parameters for amputees with different masses.

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Maneuvering Control of Planar Snake Robots Using Virtual Holonomic Constraints

Cited by 92 publications

References 34 publications

Reduction Theorems for Hybrid Dynamical Systems

Reduction Theorems for Hybrid Dynamical Systems

Removing phase variables from biped robot parametric gaits

Automatic tuning of virtual constraint-based control algorithms for powered knee-ankle prostheses

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