Control of an underactuated manipulator using similarities to the double integrator

Knoll, Carsten; Röbenack, Klaus

doi:10.3182/20110828-6-it-1002.02812

Cited by 8 publications

(5 citation statements)

References 13 publications

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“…where η is the friction factor, and ẋ is the velocity of the cart. According to ( 1) and ( 4) to (6), it is easy to obtain that…”

Section: Dynamical Equationmentioning

confidence: 99%

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Gain-Scheduled Model Predictive Control for Cart–Inverted-Pendulum with Friction and Disturbances

He,

Li,

Wei

et al. 2023

Applied Sciences

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The cart–inverted pendulum system (CIPS) is a typical example of underactuated mechanical systems. For the CIPS with friction and disturbances, a gain-scheduled model predictive control method is proposed to achieve the upright stabilization objective of the single inverted pendulum (SIP) while controlling the cart to reach a desired new position. To this end, first, a dynamic equation of the CIPS with friction and disturbances is formulated based on the Newton–Euler equation. On the basis of the dynamic equation of the CIPS, its motion characteristics and control process are analyzed. Next, the given dynamic equation of the CIPS is linearized to obtain a series of linearized models at seven different pendulum angles. Then, seven model predictive controllers (MPCs) are designed based on the above-linearized models, respectively. Introducing the idea of the gain-schedule, a gain-scheduled MPC (GSMPC) is designed to switch one of these seven MPCs to realize the control objective of the CIPS, according to the actual pendulum angle of the SIP during the control process. Finally, multi-group simulations that consider the friction and disturbances of the CIPS are implemented to demonstrate the effectiveness of the proposed gain-scheduled model predictive control method.

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“…where η is the friction factor, and ẋ is the velocity of the cart. According to ( 1) and ( 4) to (6), it is easy to obtain that…”

Section: Dynamical Equationmentioning

confidence: 99%

“…Such systems are not completely controllable [2][3][4][5]. To promote social progress, various underactuated mechanical systems are widely applied, such as underactuated manipulators [6][7][8], cranes [9][10][11], helicopters [12][13][14], quadrotors [15][16][17], unmanned ships [18,19], and soft robots [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Gain-Scheduled Model Predictive Control for Cart–Inverted-Pendulum with Friction and Disturbances

He,

Li,

Wei

et al. 2023

Applied Sciences

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“…The other one is the planar 2R underactuated manipulator [50]. The intelligent optimization method [51] and double integrator method [52] have been developed to achieve its stable control.…”

Section: Introductionmentioning

confidence: 99%

A General Stable Control Method for R-Type Underactuated Robot with Three Different Initial Situations

et al. 2023

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In this paper, we propose a general control method via the intelligent algorithm for a planar R-type underactuated robot. This control method solves the unified control problem of R-type underactuated manipulator. Meanwhile, the proposed method is also applicable to cases of nonzero initial velocity and interference rejection. Our total control program includes two stages. In the first stage, we design the trajectory based on the states of the actuated link, and then the controller is designed to track the planned trajectory to realize the objective of the actuated link. In the second stage, the trajectory with adjustable parameters is planned for the actuated link. Then, the adjustable parameters are calculated by the intelligent algorithm based on the underactuated constraints. Subsequently, the controller is designed to track the second trajectory to realize the objective of the actuated manipulator and the underactuated manipulator. Finally, the performance of the proposed method is verified through simulations.

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“…For a planar pendubot (two link manipulator with passive second joint), nilpotent approximation is used to transform the dynamic equations, and the control method is devised based the iterative steering paradigm (see De Luca et al, 2000). Through mathematical conversion, the dynamic equations of the planar pendubot are in Byrnes-Isidori normal form, and an approach of sliding mode control is proposed (see Knoll & Röbenack, 2011). Unfortunately, both approaches only control the system to swing around the target location, but cannot stabilize the manipulator at the target position.…”

Section: Introductionmentioning

confidence: 99%

Position and posture control for a class of second-order nonholonomic underactuated mechanical system

Xiong

Lai²,

Wu³

2016

IMA J Math Control Info

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This paper presents a position and posture control strategy for a n-link planar underactuated manipulator with passive second joint in horizontal plane. The n-link planar underactuated mechanical manipulator is a second-order nonholonomic system, the control objective is to move the end-effector to a given position with a desired posture. The whole control process is divided into n−2 stages. In each stage, the first link is maintained at its initial states unchanged, there exists an angle constraint between the passive link and one of the active links. Based on the angle constraints, the target angles of the control objective are calculated by using genetic algorithm. The controllers of each stages are designed, respectively, to achieve the control objective of one of the active links. Finally, taking a 5-link planar underactuated mechanical manipulator, for example, the simulation results demonstrate the validity of the proposed control method.

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Control of an underactuated manipulator using similarities to the double integrator

Cited by 8 publications

References 13 publications

Gain-Scheduled Model Predictive Control for Cart–Inverted-Pendulum with Friction and Disturbances

Gain-Scheduled Model Predictive Control for Cart–Inverted-Pendulum with Friction and Disturbances

A General Stable Control Method for R-Type Underactuated Robot with Three Different Initial Situations

Position and posture control for a class of second-order nonholonomic underactuated mechanical system

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