Analysis of the energy‐based swing‐up control of the Acrobot

Xu, Xin; Kaneda, Masahiro

doi:10.1002/rnc.1184

Cited by 96 publications

(76 citation statements)

References 16 publications

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“…Unlike the first simulation, the energy after the impulsive brake does not satisfy the condition |E − E des | < δ, and therefore, the rest-to-rest maneuvers are used to regulate the energy to E des . The linear controller is invoked at t = 7.3 sec which is marginally better compared to 7.33 seconds required in [6]. The maximum continuous torque is 6.81 N.m which is significantly smaller than the maximum torque, 20 N.m, used in [6].…”

Section: Numerical Simulationmentioning

confidence: 99%

“…The linear controller is invoked at t = 7.3 sec which is marginally better compared to 7.33 seconds required in [6]. The maximum continuous torque is 6.81 N.m which is significantly smaller than the maximum torque, 20 N.m, used in [6].…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Invoke the linear controller, designed in the first step of the algorithm, to stabilize the desired equilibrium. In comparison to the approaches proposed by Xin and Kaneda [6] and Mahindrakar and Banavar [7], our approach does not impose any restrictions on the controller gains or initial conditions for swing-up of the acrobot.…”

Section: Stabilizationmentioning

confidence: 99%

“…We compare the efficacy of our algorithm with those proposed in [6] and [7]. The kinematic and dynamic parameters of the first simulation are taken from Mahindrakar and Banavar [7]:…”

Section: Numerical Simulationmentioning

confidence: 99%

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Swing-up control of the acrobot: An impulse-momentum approach

Jafari

Mathis

Mukherjee

2011

Proceedings of the 2011 American Control Conference

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Abstract-An impulse-momentum approach is proposed for swing-up control of the acrobot. The algorithm is based on increasing the total energy of the system using impulsive inputs. After increasing the energy of the system, rest-to-rest maneuvers are employed to regulate the system energy to the desired level that corresponds to the upright configuration of the acrobot. The proposed algorithm is implemented with two sets of acrobot parameters taken from the literature. As compared to the approaches in the literature, the simulation results show shorter swing-up time and lower maximum continuous torques. Furthermore, the proposed algorithm does not impose any restrictions on the initial conditions and controller gains for swing-up. NOMENCLATUREFor the nomenclature below, k ∈ {1, 2} and j ∈ {1, 5}.

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Section: Numerical Simulationmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

Section: Stabilizationmentioning

confidence: 99%

“…We compare the efficacy of our algorithm with those proposed in [6] and [7]. The kinematic and dynamic parameters of the first simulation are taken from Mahindrakar and Banavar [7]:…”

Section: Numerical Simulationmentioning

confidence: 99%

See 2 more Smart Citations

Swing-up control of the acrobot: An impulse-momentum approach

Jafari

Mathis

Mukherjee

2011

Proceedings of the 2011 American Control Conference

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“…The common types are the single inverted pendulum on a cart [1,2], the double inverted pendulum on a cart [3,4], the double inverted pendulum with an actuator at the first joint only (Pendubot) [5], the double inverted pendulum with an actuator at the second joint only (Acrobot) [6,7], the rotational single-arm pendulum [8][9][10][11], and the rotational two-arm pendulum [12]. The control techniques involved in inverted pendulum systems are also numerous, ranging from simple conventional controllers to advanced control techniques based on modern nonlinear control theory.…”

Section: Introductionmentioning

confidence: 99%

Swing-Up and Stability Control of Wheeled Acrobot (WAcrobot)

2014

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In this paper the Wheeled Acrobot (WAcrobot), a novel mechanical system consisting of an underactuated double inverted pendulum robot (Acrobot) equipped with actuated wheels, is described. This underactuated and highly nonlinear system has potential applications in mobile manipulators and leg-wheeled robots. It is also a testbed for researchers studying advanced methodologies in nonlinear control. The control system for swing-up of the WAcrobot based on collocated or non-collocated feedback linearisation to linearise the active or passive Degree Of Freedom (DOF) followed by Linear Quadratic Regulator (LQR) to stabilise the robot is discussed. The effectiveness of the proposed scheme is validated with numerical simulation. The numerical results are visualised by graphical simulation to demonstrate the correlation between the numerical results and the WAcrobot physical response. Njihanje i upravljanje stabilnošću koturajućeg Acrobota. Učlanku je opisan koturajući Acrobot (WAcrobot), novi mehanički sustav koji se sastoji od podupravljanog robota u obliku dvostrukog inverznog njihala (Acrobot) opremljenog s aktuiranim kotačem. Ovaj podupravljani i izrazito nelinearni sustav ima potencijalnu primjenu u mobilnim manipulatorima i robotima na kotačima. Tako er služi kao testni model za istraživače koji proučavaju napredne metode nelinearnog upravljanja. U radu je opisan sustav upravljanja za podizanje WAcrobot-a u ispravan položaj baziran na metodama kolocirane i nekolocirane eksterne linearizacije za linearizaciju aktivnog ili pasivnog stupnja slobode, i linearnom kvadratičnom regulatoru za stabilizaciju robota. Učinkovitost predvi ene metode je validirana simulacijskim rezultatima. Rezultati su prikazani u obliku animacije kako bi se demonstrirala korelacija izme u simulacijskih odziva i fizičkog odziva WAcrobota-a.Ključne riječi: dvostruko inverzno njihalo; robot na kotačima; podupravljani robot; parcijalna eksterna linearizacija; linearni kvadratični regulator; stabilizacija

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Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Gregory

Olivares

Staffetti

2012

Optim Control Appl Methods

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SUMMARYIn this paper, we study the trajectory-planning problem for planar underactuated robot manipulators with two revolute joints in the presence of gravity. This problem is studied as an optimal control problem. We consider both possible models of planar underactuated robot manipulators, namely with the elbow joint not actuated, called Pendubot, and with the shoulder joint not actuated, called Acrobot. Our method consists of a numerical resolution of a reformulation of the optimal control problem, as an unconstrained calculus of variations problem, in which the dynamic equations of the mechanical system are regarded as constraints and treated by means of special derivative multipliers. We solve the resulting calculus of variations problem by using a numerical approach based on the Euler-Lagrange necessary condition in integral form. In which, time is discretized, and admissible variations for each variable are approximated using a linear combination of the piecewise continuous basis functions of time. In this way, a general method for the solution of optimal control problems with constraints is obtained, which, in particular, can deal with nonintegrable differential constraints arising from the dynamic models of underactuated planar robot manipulators with two revolute joints in the presence of gravity.

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Analysis of the energy‐based swing‐up control of the Acrobot

Cited by 96 publications

References 16 publications

Swing-up control of the acrobot: An impulse-momentum approach

Swing-up control of the acrobot: An impulse-momentum approach

Swing-Up and Stability Control of Wheeled Acrobot (WAcrobot)

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

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