Swing up and Balancing Control of Pendubot via Model Orbit Stabilization: Algorithm Synthesis and Experimental Verification

Orlov, Yury; Aguilar, Luis T.; Acho, Leonardo; Ortiz, Adan

doi:10.1109/cdc.2006.377589

Cited by 14 publications

(11 citation statements)

References 11 publications

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“…The acrobot is identical except the input torque acts about the second joint. The nonlinear dynamics and pendubot model parameters match those from simulations in [35] and experiments in [36]. The acrobot model parameters and dynamics are from simulations in [39] and in seminal work [38].…”

Section: B Pendubot and Acrobotmentioning

confidence: 93%

“…While the pendubot simulations in [35] require control torques up to a magnitude of 15 N m for inversion, the experimental results in [36] perform inversion with motor torques restricted to ±7 N m. Hence, the pendubot inputs are constrained to τ ∈ [−7, 7] N m. The acrobot torques are constrained with τ ∈ [− 15,15] N m to invert the system using less than the 20 N m required in [39].…”

Section: B Pendubot and Acrobotmentioning

confidence: 99%

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Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

2016

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This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimize finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions on-line, in receding horizon fashion, the proposed controller provides a min-max constrained response to state that avoids the overhead typically required to impose control constraints. Benchmark examples show the approach can avoid local minima and outperform nonlinear optimal controllers and recent, case-specific methods in terms of tracking performance, and at speeds orders of magnitude faster than traditionally achievable.3 are nonlinear in state x : R → R n . Though these methods apply more broadly, we derive controls for the case where (1) is linear with respect to the control, u : R → R m , satisfying control-affine form, f (t, x(t), u(t)) = g(t, x(t)) + h(t, x(t)) u(t) .(2)The time dependence in (1) and (2) will be dropped for brevity. The prediction phase simulates motion resulting from some choice of nominal control, u = u 1 . Thus, the nominal predicted motion corresponds to, u 1 (t)).Although the nominal control may be chosen arbitrarily, all examples here use a null nominal control, u 1 = 0. Hence, in the SLIP example, SAC seeks actions that improve performance relative to doing nothing, i.e., letting the SLIP fall.With l 1 : R n → R and m : R n → R, the cost functional,

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Section: B Pendubot and Acrobotmentioning

confidence: 93%

Section: B Pendubot and Acrobotmentioning

confidence: 99%

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

2016

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“…The dynamics of the pendubot ( [15], [16]) are also given by (12)-(18), with B = (1 0) T , i.e. the torque input is applied at the shoulder joint.…”

Section: Pendubotmentioning

confidence: 99%

Controllers as filters: Noise-driven swing-up control based on Maxwell's demon

Tzorakoleftherakis

Murphey

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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In this paper we show in simulation that if the controller and the filter are combined into a single computational unit operating like a "Maxwell's demon", controllerfiltered noise can successfully control a system of interest. Using this method, we perform Monte Carlo tests for the swing-up control of the cart pendulum, acrobot and pendubot systems. Results show that filtered noise can indeed act as a swingup controller, leading these systems to configurations where a locally stabilizing controller can complete the stabilization process. Potential applications of this work include the development of reliable, never-failing human-machine interfaces for rehabilitation, training and skill evaluation.

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“…Asymptotic tracking of a very particular periodic trajectory for this example can be found in Mazenc and Bowong (2003). A more classical problem for the cart-pendulum system is solved in Olfati-Saber (1999), while sliding-mode-based design is suggested in Santiesteban, Riachy, Floquet, Orlov, and Richard (2007); see also Orlov et al 2006.…”

Section: Introductionmentioning

confidence: 97%

“…The first one is based on motion planning via projecting dynamics onto a set of virtual holonomic constraints (Shiriaev, Perram, and Canudas-de-Wit 2005;Shiriaev, Freidovich, and Manchester 2008), and the other one relies on selfexcited oscillations under sliding-mode feedback (Aguilar, Boiko, Fridman, and Iriarte 2006;Orlov, Aguilar, Acho, and Ortiz 2006). It is not clear how to use these techniques to match the target dynamics of the passive link.…”

Section: Introductionmentioning

confidence: 99%

Modification via averaging of partial-energy-shaping control for creating oscillations: cart-pendulum example

Freidovich

Shiriaev

Gómez-Estern

et al. 2009

International Journal of Control

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We consider the challenging problem of creating oscillations in underactuated mechanical systems. Target oscillatory motions of the indirectly actuated degree of freedom of a mechanical system can often be achieved via a straightforward to design feedback transformation. Moreover, the corresponding part of the dynamics can be forced to match a desired second-order system possessing the target periodic solution (Aracil, ). Sometimes, it is possible to establish the presence of periodic or bounded motions for the remaining degrees of freedom in the transformed system. However, typically this motion planning procedure leads to an open-loop unstable orbit and by necessity should be followed by a feedback control design. We propose a new approach for synthesis of a (practically) stabilising feedback controller, which ensures convergence of the solutions of the closed-loop system into a narrow tube around the preplanned orbit. The method is illustrated in detail by shaping oscillations in the inverted pendulum on a cart around its upright equilibrium. The complete analysis is based on application of a non-standard higher-order averaging technique assuming sufficiently high frequency of oscillations and is presented for this particular example.

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Swing up and Balancing Control of Pendubot via Model Orbit Stabilization: Algorithm Synthesis and Experimental Verification

Cited by 14 publications

References 11 publications

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

Controllers as filters: Noise-driven swing-up control based on Maxwell's demon

Modification via averaging of partial-energy-shaping control for creating oscillations: cart-pendulum example

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