Application of the state‐dependent Riccati equation for flexible‐joint arms: Controller and estimator design

Korayem, M. H.; Lademakhi, Naeim Yousefi; Nekoo, Saeed Rafee

doi:10.1002/oca.2377

Cited by 21 publications

(26 citation statements)

References 27 publications

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“…where the observer gain Λ ( x ^ ( t ) ) ∈ ℜ n × p for the uncertain system with disturbances, has the following form (Cimen, 2010; Korayem et al, 2018):…”

Section: Obr Controller Designmentioning

confidence: 99%

“…Clearly, superposition principle is not allowable to be applied to prove the stability of the entire system (controller and observer together); therefore the role of observer in the estimation of unavailable states as a separate unit, is emphasized. Proper and exact estimation in allowable bounds leads to the stability of the entire system to be limited to the stability of the controller (Korayem et al, 2018) via the proposed Lyapunov function.…”

Section: Obr Controller Designmentioning

confidence: 99%

“…(36). Considering dynamics and SDC parameterization of FJRs (Korayem and Nekoo, 2015a, b), optimal controller and estimator design (Korayem et al, 2018), the uncertain form of FJR dynamics and its SDC parameterization can be presented as Eqs. (36) and (39), respectively.…”

Section: Obr Controller Design For Fjr and Efjrmentioning

confidence: 99%

“…Optimal control problem using the differential form of SDRE has been studied to track for robot manipulators possessing rigid or flexible joints (Korayem and Nekoo, 2015b). Korayem et al (2018) proposed a composition of SDRE-based controller and estimator to reduce the state error of the systems subject to disturbances and noise. The estimator has been applied to FJRs because the measurement of changes behind the connection of the motor and link was not easy in practice (Korayem et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…Korayem et al (2018) proposed a composition of SDRE-based controller and estimator to reduce the state error of the systems subject to disturbances and noise. The estimator has been applied to FJRs because the measurement of changes behind the connection of the motor and link was not easy in practice (Korayem et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

Nasiri

Fakharian

Menhaj

2020

Transactions of the Institute of Measurement and Control

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In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying disturbances. The proposed observer-based robust (OBR) controller is applied to two highly nonlinear, coupled and large robotic systems: namely a manipulator presenting joint flexibility due to deformation of the power transmission elements between the actuator and the robot known as flexible-joint robot (FJR) and also an FJR incorporating geared permanent magnet DC motor dynamics in its dynamic model called electrical flexible-joint robot (EFJR). A novel state-dependent coefficient (SDC) form is introduced for uncertain EFJRs. Rather than coping with the OBR control problem for such complex uncertain robotic systems, the main idea is to solve an equivalent nonlinear optimal control problem where the uncertainty and disturbance bounds are incorporated in the performance index. The stability proof is presented. Solving the complicated robust control problem for FJRs and EFJRs subject to uncertainty and disturbances via a simple and flexible nonlinear optimal approach and no need of state measurement are the main advantages of the proposed control method. Finally, simulation results are included to verify the efficiency and superiority of the control scheme.

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“…where the observer gain Λ ( x ^ ( t ) ) ∈ ℜ n × p for the uncertain system with disturbances, has the following form (Cimen, 2010; Korayem et al, 2018):…”

Section: Obr Controller Designmentioning

confidence: 99%

Section: Obr Controller Designmentioning

confidence: 99%

Section: Obr Controller Design For Fjr and Efjrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

Nasiri

Fakharian

Menhaj

2020

Transactions of the Institute of Measurement and Control

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Trajectory tracking control of a wheeled mobile robot in the presence of matched uncertainties via a composite control approach

Shafei

Bahrami

2020

Asian Journal of Control

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In the present work, a novel method is devised for controlling an uncertain wheeled mobile robot (WMR) in a desired path. To achieve this objective, an optimal and robust control system with adaptive gains is combined to benefit from the advantages of both methods. In fact, applying this controller not only controls a nonlinear system robustly against uncertainties and external disturbances, but also optimizes a quadratic cost function. Also, since the upper bound of uncertainty is determined by an adaptive law, it does not need to be adjusted manually. To ensure the designed controller's finite time stability, Lyapunov theory is used. Finally, to illustrate the effectiveness of the proposed control method, a case study involving a WMR is presented. By comparing the results of this approach with those of an adaptive sliding mode control (ASMC), it is shown that the proposed controller uses less control effort, relative to the ASMC controller, to stabilize the uncertain WMR in the presence of external disturbances.

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Designing an optimal control strategy for a mobile manipulator and its application by considering the effect of uncertainties and wheel slipping

Korayem

Ghobadi

Dehkordi

2021

Optim Control Appl Methods

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This article seeks to develop the dynamic model of a mobile robot for controlling purposes while the effects of uncertainties and longitudinal and lateral slip are assumed. The rise in the number of state variables and considering the effects of nonlinear parameters due to slip modeling can complicate the control procedure of wheeled mobile manipulators. In addition, the existence of uncertainties as well as holonomic and nonholonomic constraints would increase this complexity even more. On the one side, as wheels are considered to slip, unwanted movements due to slippage affect the movement of the manipulator and the manipulator may not be able to track the desired path. On the other side, the movement of weighted links of the manipulator constantly changes the normal forces of the wheels. As traction forces are dependent on these normal forces, the path tracked by the platform would be affected. Given these conditions, employing a robust control methodology and developing an optimal algorithm to reduce the effects of uncertainties and wheels slip seems mandatory. To this aim, a sliding mode control (SMC) strategy is formulated in this study. Furthermore, the suggested algorithm is optimized using a state-dependent Riccati equation to reduce the consumed torque and increase the accuracy of the system. Simulations are conducted, and the presented algorithm is also checked with the experimental setup of a Scout robot. Simulation results show that the optimal sliding mode control (OSMC) successfully decreases sudden jumps due to slippage in the system. In addition, the consumed power of wheels and arm for SMC decreases from 9.15 and 1.02 N⋅m to, respectively, 1.46 and 0.54 N⋅m for OSMC.

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Application of the state‐dependent Riccati equation for flexible‐joint arms: Controller and estimator design

Cited by 21 publications

References 27 publications

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

Trajectory tracking control of a wheeled mobile robot in the presence of matched uncertainties via a composite control approach

Designing an optimal control strategy for a mobile manipulator and its application by considering the effect of uncertainties and wheel slipping

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