Model Predictive Control for an Inverted-pendulum Robot with Time-varying Constraints

Ohhira, Takashi; Shimada, Akira

doi:10.1016/j.ifacol.2017.08.252

Cited by 9 publications

(6 citation statements)

References 2 publications

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“…Based on Reference [30], we designed an MPC for a single-leg robot with restricted motion. Considering the similarity between the first and second joints, we rewrite decoupled linear systems (Equation ( 14)) into the state equation form for a single joint as follows:…”

Section: Control-law Designmentioning

confidence: 99%

Enhanced Tracking in Legged Robots through Model Reduction and Hybrid Control Techniques: Addressing Disturbances, Delays, and Saturation

Zhao,

Wang,

Cao

et al. 2024

Applied Sciences

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This study introduces a reduced-order leg dynamic model to simplify the controller design and enhance robustness. The proposed multi-loop control scheme tackles tracking control issues in legged robots, including joint angle and contact-force regulation, disturbance suppression, measurement delay, and motor saturation avoidance. Firstly, model predictive control (MPC) and sliding mode control (SMC) schemes are developed using a simplified model, and their stability is analyzed using the Lyapunov method. Numerical simulations under two disturbances validate the superior tracking performance of the SMC scheme. Secondly, an Nth-order linear active disturbance rejection control (LADRC) is designed based on a simplified model and optimization problems. The second-order LADRC-SMC scheme reduces the contact-force control error in the SMC scheme by ten times. Finally, a fourth-order LADRC-SMC with a Smith Predictor (LADRC-SMC-SP) scheme is formulated, employing each loop controller independently. This scheme simplifies the design and enhances performance. Compared to numerical simulations of the above and existing schemes, the LADRC-SMC-SP scheme eliminates delay oscillations, shortens convergence time, and demonstrates fast force-position tracking responses, minimal overshoot, and strong disturbance rejection. The peak contact-force error in the LADRC-SMC-SP scheme was ten times smaller than that in the LADRC-SMC scheme. The integral square error (ISE) values for the tracking errors of joint angles θ1 and θ2, and contact force f, are 1.6636×10−28 rad2⋅s, 1.7983×10−28 rad2⋅s, and 1.8062×10−30 N2⋅s, respectively. These significant improvements in control performance address the challenges in single-leg dynamic systems, effectively handling disturbances, delays, and motor saturation.

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Section: Control-law Designmentioning

confidence: 99%

Enhanced Tracking in Legged Robots through Model Reduction and Hybrid Control Techniques: Addressing Disturbances, Delays, and Saturation

Zhao,

Wang,

Cao

et al. 2024

Applied Sciences

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“…Besides, with two Degrees Of Freedom (DOF); and only the horizontal force, the inverted pendulum is the simplest Underactuated Mechanical System (UMS). Therefore, the inverted pendulum seems to be the platform for the implementation of different nonlinear and linear approaches; augmented PID controller (Siradjuddin et al, 2018), fuzzy logic control (El-Bardini and El-Nagar, 2014), sliding mode (Park and Chwa, 2009), predictive control (Ohhira and Shimada, 2017), and optimal control (Prasad et al, 2014).…”

Section: Context and Motivationsmentioning

confidence: 99%

Robust LFT-LPV H∞ Control of an Underactuated Inverted Pendulum on a Cart with Optimal Weighting Functions Selection by GA and ES

Hasseni

Abdou

2020

Acta Mechanica Et Automatica

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This article investigates the robust stabilization and control of the inverted pendulum on a cart against disturbances, measurement noises, and parametric uncertainties by the LFT-based LPV technique (Linear-Fractional-Transformation based Linear-Parameter-Varying). To make the applying of the LPV technique possible, the LPV representation of the inverted pendulum on a cart model is developed. Besides, the underactuated constraint of this vehicle is overcome by considering both degrees of freedom (the rotational one and the translational one) in the structure. Moreover, the selection of the weighting functions that represent the desired performance is solved by two approaches of evolutionary algorithms; Genetic Algorithms (GA) and Evolutionary Strategies (ES) to find the weighting functions’ optimal parameters. To validate the proposed approach, simulations are performed and they show the effectiveness of the proposed approach to obtain robust controllers against external signals, as well as the parametric uncertainties.

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“…As some examples, one may point at missiles, Segways (Kim and Park, 2016) as well as biped (Bae and Oh, 2018), humanoid, and self-balancing robots (Huang and Yeh, 2019). Balancing inverted pendulum systems have always been a challenge for researchers, and novel control algorithms are regularly presented (Choi and Oh, 2008; Huang et al, 2013; Irfan et al, 2018; Johnson et al, 2020; Minatohara and Furukawa, 2011; Ohhira and Shimada, 2017; Su et al, 2016; Susanto et al, 2020) by many scientists for balancing the pendulum and controlling the cart position. In fact, balancing inverted pendulums are known as a suitable benchmark problem for investigating the applicability and robustness of different linear (Choi and Oh, 2008; Siradjuddin et al, 2017; Susanto et al, 2020) or nonlinear (Becerikli and Celik, 2007; Irfan et al, 2018; Minatohara and Furukawa, 2011; Su et al, 2016) control algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…An inverted pendulum system is consisted of a cart which moves in a line and a pendulum which is supposed to be stabilized at upright position. In the simulations provided by most researchers (Aliakbari et al, 2016; Irfan et al, 2018; Kim et al, 2019; Ohhira and Shimada, 2017), the pendulum has been assumed to be rigid. Even though the inverted pendulum system with rigid pendulum has received lots of attention in prior arts, in many applications, the rigidity assumption of the pendulum bar may not be sufficiently accurate.…”

Section: Introductionmentioning

confidence: 99%

Development of a fuzzy-state feedback regulator for stabilizing a flexible inverted pendulum system

Pourgholam

Moeenfard

2021

Journal of Vibration and Control

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Accurate modeling and efficient control of inverted pendulums have always been a challenge for researchers. So, the current research aims to achieve the following objectives: (I) proposing a comprehensive dynamic model for the inverted pendulums which accounts for the flexibility of the pendulum bar and (II) suggesting an appropriate supervisory fuzzy-pole placement control strategy for stabilizing the pendulum system. Using a Lagrangian formulation, the equations of motion are derived and linearized. Then, a state feedback controller with a reduced-order observer is designed to stabilize the system. Closed-loop simulations reveal that at least six modes shall be considered in the dynamic equations. To improve the quality of the transient response, a novel fuzzy system is developed for real-time assignment of the controller poles. Simulation results demonstrate that the control quality is significantly improved by adding a supervisory fuzzy system to the control loop. The developed approach for dynamic modeling of the system, and the idea of multi-level fuzzy-pole placement control architecture developed in this paper, may be successfully applied to improve the response specifications in other dynamic systems.

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Model Predictive Control for an Inverted-pendulum Robot with Time-varying Constraints

Cited by 9 publications

References 2 publications

Enhanced Tracking in Legged Robots through Model Reduction and Hybrid Control Techniques: Addressing Disturbances, Delays, and Saturation

Enhanced Tracking in Legged Robots through Model Reduction and Hybrid Control Techniques: Addressing Disturbances, Delays, and Saturation

Robust LFT-LPV H∞ Control of an Underactuated Inverted Pendulum on a Cart with Optimal Weighting Functions Selection by GA and ES

Development of a fuzzy-state feedback regulator for stabilizing a flexible inverted pendulum system

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