A nonlinear optimal control method for the ballbot autonomous vehicle

Rigatos, Gerasimos; Abbaszadeh, Masoud; Pomares, Jorge

doi:10.23919/acc45564.2020.9147297

Cited by 19 publications

(68 citation statements)

References 11 publications

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“…Comparing to past attempts for solving the H-infinity control problem for nonlinear dynamical systems, the article's control approach is substantially different [37]. Preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics and considered that the control inputs gain matrix is not dependent on the values of the system's state vector.…”

Section: Simulation Tests 71 Results On Nonlinear Optimal Control Of ...mentioning

confidence: 99%

“…The proposed H-infinity (optimal) control method for the 4-DOF SCARA robot exhibits several advantages when compared against other linear or nonlinear control schemes [37]. For instance, (i) in contrast to global linearization-based control schemes (Lie algebra-based control and differential flatness theory-based control) it does not need complicated changes of state variables (diffeomorphisms) and does not come against singularity problems in the computation of the control inputs, (ii) in contrast to sliding-mode control or to backstepping control the proposed nonlinear optimal control scheme does not require the state-space model of the system to be in a specific form (e.g., triangular, canonical, etc.…”

Section: Simulation Tests 71 Results On Nonlinear Optimal Control Of ...mentioning

confidence: 99%

“…In the present article, a nonlinear optimal control method is proposed for the nonlinear model of a 4-degrees of freedom (DOF) SCARA robot [36,37]. The dynamic model of the 4-DOF SCARA robot undergoes first approximate linearization around a temporary operating point which is updated at each sampling instance.…”

Section: Introductionmentioning

confidence: 99%

“…The article has a meaningful contribution to the area of nonlinear control. One can point out the advantages of the nonlinear optimal control method against nonlinear model predictive control (NMPC) [37]. In NMPC, the stability properties of the control scheme remain unproven and the convergence of the iterative search for an optimum often depends on initialization and parameter values' selection.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear optimal control for a 4-DOF SCARA robotic manipulator

et al. 2023

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Selective compliance articulated robot arms (SCARA) robotic manipulators find wide use in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-degrees of freedom (DOF) SCARA robotic manipulator. The dynamic model of the SCARA robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control method is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, it is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs and (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot’s actuators. The nonlinear optimal controller for the 4-DOF SCARA robot is finally compared against a flatness-based controller implemented in successive loops.

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Section: Simulation Tests 71 Results On Nonlinear Optimal Control Of ...mentioning

confidence: 99%

Section: Simulation Tests 71 Results On Nonlinear Optimal Control Of ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear optimal control for a 4-DOF SCARA robotic manipulator

et al. 2023

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“…The global stability properties of the control scheme are proven through Lyapunov analysis. It is proven that the proposed control scheme satisfies the H-infinity tracking performance criterion, which signifies robustness to model uncertainty and external perturbations [34][35]. Moreover, under moderate conditions it is proven that the control loop is globally asymptotically stable.…”

Section: Introductionmentioning

confidence: 84%

Nonlinear optimal control of the parallel double inverted pendulum

Rigatos

Pomares

Abbaszadeh

et al. 2023

Preprint

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The article proposes a nonlinear optimal control method for the dynamic model of the parallel double inverted pendulum. Three different forms of this system are considered: (i) two poles mounted on the same cart resulting into a model with four state variables and one control input, (ii) two poles mounted on the same cart resulting into a model with six state variables and one control input, (iii) two different cart-pole systems connected through an elastic link, resulting into a model with eight state variables and two control inputs. To implement the proposed nonlinear optimal control method the dynamic model of the parallel double pendulum undergoes approximate linearization around a temporary operating point which is updated at each sampling instance. This operating point is defined within each sampling period by the present value of the state vector of the parallel double inverted pendulum and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the parallel double inverted pendulum a stabilizing H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is also being solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion holds, which signifies robustness of the control method under model uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop of the parallel double inverted pendulum is globally asymptotically stable. To implement state estimation-based control the H-infinity Kalman Filter is used as a robust observer. The nonlinear optimal control scheme for the parallel double inverted pendulum achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

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Nonlinear optimal control for the rotary double inverted pendulum

et al. 2023

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The control problem of the rotary double inverted pendulum (double Furuta pendulum) is nontrivial because of underactuation and strong nonlinearities in the associated state‐space model. The system has three degrees of freedom (one actuated and two unactuated joints) while receiving only one control input. In this article, a novel nonlinear optimal (H‐infinity) control approach is developed for the dynamic model of the rotary double inverted pendulum. First, the dynamic model of the double pendulum undergoes approximate linearization with the use of first‐order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. At a next stage a stabilizing H‐infinity feedback controller is designed. To compute the controller's feedback gains an algebraic Riccati equation has to be solved at each time‐step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. To implement state estimation‐based control without the need to measure the entire state vector of the rotary double‐pendulum the H‐infinity Kalman filter is used as a robust state observer. The nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the rotary double inverted pendulum under moderate variations of the control input.

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A nonlinear optimal control method for the ballbot autonomous vehicle

Cited by 19 publications

References 11 publications

Nonlinear optimal control for a 4-DOF SCARA robotic manipulator

Nonlinear optimal control for a 4-DOF SCARA robotic manipulator

Nonlinear optimal control of the parallel double inverted pendulum

Nonlinear optimal control for the rotary double inverted pendulum

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