Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincaré Maps

Kant, Nilay; Mukherjee, Ranjan

doi:10.1016/j.sysconle.2020.104813

Cited by 20 publications

(12 citation statements)

References 26 publications

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“…2.1]. To stabilize the fixed point Ȳ * , we use the ICPM approach [8], which was developed for continuous orbits, and later extended to hybrid orbits associated with planar stick juggling [10]. The ICPM approach is explained with the help of Fig.…”

Section: B Hybrid Orbit Stabilizationmentioning

confidence: 99%

“…The dynamic model represents an underactuated system with five generalized coordinates and three control inputs; the three-dimensional juggling problem is more challenging than the planar case where the stick is described by three generalized coordinates and two control inputs. The Impulse Controlled Poincaré Map (ICPM) approach [8], [10], in which impulsive forces are intermittently applied on a Poincaré section, is used for stabilizing the hybrid orbit that describes the desired juggling motion.…”

Section: Introductionmentioning

confidence: 99%

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Nonprehensile Manipulation of a Stick Using Impulsive Forces

Khandelwal¹,

Kant²,

Mukherjee³

2022

Preprint

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Section: B Hybrid Orbit Stabilizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonprehensile Manipulation of a Stick Using Impulsive Forces

Khandelwal¹,

Kant²,

Mukherjee³

2022

Preprint

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“…The motor has a gearbox with a reduction ratio of 3.71 : 1. 6 The amplifier is a product of Advanced Motion Control. 7 The electromagnetic brake is manufactured by Anaheim Automation, model BRK-20H-480-024.…”

Section: System Descriptionmentioning

confidence: 99%

“…In many applications, such as legged locomotion [1,2], underactuated systems are required to undergo repetitive motion and orbital stabilization is the control objective. To achieve repetitive motion, geometric con-straints are imposed on the generalized coordinates using the virtual holonomic constraint (VHC) approach [3][4][5][6]. Orbital stabilization has also been used for swingup control of underactuated systems with one passive degree-of-freedom (DOF).…”

Section: Introductionmentioning

confidence: 99%

“…Prior works on impulsive control [15][16][17][18][19][20][21] have been theoretical in nature but in recent works [6,[22][23][24][25][26][27][28][29], impulsive inputs have been utilized for control of underactuated systems in both simulations and experiments. In experiments, impulsive inputs have been implemented in standard hardware using high-gain feedback [23,24], dispelling the notion that impulsive inputs require large actuators and are impractical.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

2021

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Recent investigations of underactuated systems have demonstrated the benefits of control inputs that are impulsive in nature. Here we consider the problem of stabilization of energy level sets of underactuated systems exploiting impulsive braking. We consider systems with one passive degree-of-freedom (DOF) and the energy level set is a manifold where the active coordinates are fixed and the mechanical energy equals some desired value. A control strategy comprised of continuous inputs and intermittent impulsive braking inputs is presented. The generality of the approach is shown through simulation of a three-DOF Tiptoebot; the feasibility of implementation of impulsive control using standard hardware is demonstrated using a rotary pendulum.

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Orbital synchronization of homogeneous mechanical systems with one degree of underactuation

Herrera

Rodríguez-Liñán

Meza‐Sánchez

et al. 2022

Intl J Robust & Nonlinear

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A methodology for asymptotic orbital synchronization of a set of homogeneous mechanical systems with one degree of underactuation is proposed. A reference model generating a reference orbit is first constructed under the virtual holonomic constraints approach. Then, the  ∞ synthesis is designed to, first, estimate the state vector of the homogeneous systems, provided that only position measurements are available, and second, to drive the state of the systems to that of the reference model. Due to the  ∞ synthesis properties, the homogeneous systems converge asymptotically to the reference orbit when there are no disturbances affecting the systems nor the measurements. When disturbances are present, robustness is guaranteed provided that the  2 gain of the closed-loop systems remains lower than an attenuation level 𝛾. Numerical results for a set of underactuated cart-pendulums corroborate the proposed methodology.

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Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincaré Maps

Cited by 20 publications

References 26 publications

Nonprehensile Manipulation of a Stick Using Impulsive Forces

Nonprehensile Manipulation of a Stick Using Impulsive Forces

Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

Orbital synchronization of homogeneous mechanical systems with one degree of underactuation

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