Optimal model‐free control for a generic MIMO nonlinear system with application to autonomous mobile robots

Safaei, Ali; Mahyuddin, Muhammad Nasiruddin

doi:10.1002/acs.2865

Cited by 24 publications

(23 citation statements)

References 41 publications

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“…Also,

{\vec{v}}_{q}

and

{\vec{w}}_{q}

are the vectors of linear and angular velocities. Two matrices R q and R qt defined in

R^{3 \times 3}

are the transformation matrices used to transform the coordinates between the body frame and the inertial frame . M q is the quadrotor mass and

J_{q} \in R^{3 \times 3}

is its inertia matrix .…”

Section: Simulation Resultsmentioning

confidence: 99%

“…

{\vec{F}}_{g} = [0; 0; g_{e a r t h}]

is the vector of gravity force and

{\vec{f}}_{q}

and

{\vec{t}}_{q}

are the vectors of unknown disturbances. The generated force and torques by the electric motors are represented by

{\vec{F}}_{q} = [0; 0; F_{T}]

and

{\vec{τ}}_{q} = [τ_{x}; τ_{y}; τ_{x}]

, where their values are completely related with the rotational speeds of the electric motors in the quadrotor . In the following simulation case studies, the values of parameters are M q =2 , J q =1.24 e −3×diag(1,1,2) , K d = K a =0.01 , g =9.81 ,

{\vec{f}}_{q} = 1 \sin (t) {\vec{v}}_{1}

, and

{\vec{t}}_{q} = 1 \sin (t) {\vec{v}}_{3}

, where

{\vec{v}}_{1} = [0; 0; 1]

and

{\vec{v}}_{3} = [1; 1; 1]

.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…is the signum function . This lemma first proposed for determining the time derivative of elements in the vector of desired set‐points for the states of general dynamic systems …”

Section: Arve Algorithmmentioning

confidence: 99%

“…At the bottom layer of the process for providing the autonomy at AMRs, there are algorithms to solve the tracking control problem and observing the internal states of the AMRs. In a tracking control problem, the objective is to track the trajectory defined in the previous layers . The feedback over the internal states of the AMR is a requirement for achieving the goal in control tracking problem.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

Safaei

2020

Adaptive Control & Signal

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Summary In this article, an adaptive algorithm is proposed for online velocity estimation of the autonomous mobile robots (AMRs) without positioning data received from a Global Positioning System (GPS) module or other means for odometry. Unlike the popular Kalman and particle filters that use the measurements on vectors of global (or local) position and acceleration of a mobile robot, the proposed adaptive relative velocity estimation (ARVE) algorithm requires the scalar value of measured distance to a beacon agent and also the measurement on acceleration vector, in order to generate an online estimation of the global velocity vector of a mobile robot. Combining the ARVE algorithm with the recently proposed adaptive relative position estimation (ARPE) algorithm provides a solution for online estimation of the translational states of a mobile robot without accessing the GPS data, which makes the package applicable in both indoor and outdoor environments. The stability of the ARVE algorithm is analyzed with LaSalle‐Yoshizawa theorem. In addition, two simulation studies are provided to show the application of the proposed estimation package (ARVE+ARPE) for aerial AMRs in two cases corresponding to the stationary and moving beacon agents. In the simulation results, it is shown that the estimation package can be used in conjunction with the recently proposed adaptive model‐free control (AMFC) algorithm to achieve desired tracking objective in autonomous movement of a quadrotor, without requiring the information on the internal dynamics of the robot.

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“…Also,

{\vec{v}}_{q}

and

{\vec{w}}_{q}

are the vectors of linear and angular velocities. Two matrices R q and R qt defined in

R^{3 \times 3}

are the transformation matrices used to transform the coordinates between the body frame and the inertial frame . M q is the quadrotor mass and

J_{q} \in R^{3 \times 3}

is its inertia matrix .…”

Section: Simulation Resultsmentioning

confidence: 99%

“…

{\vec{F}}_{g} = [0; 0; g_{e a r t h}]

is the vector of gravity force and

{\vec{f}}_{q}

and

{\vec{t}}_{q}

are the vectors of unknown disturbances. The generated force and torques by the electric motors are represented by

{\vec{F}}_{q} = [0; 0; F_{T}]

and

{\vec{τ}}_{q} = [τ_{x}; τ_{y}; τ_{x}]

{\vec{f}}_{q} = 1 \sin (t) {\vec{v}}_{1}

, and

{\vec{t}}_{q} = 1 \sin (t) {\vec{v}}_{3}

, where

{\vec{v}}_{1} = [0; 0; 1]

and

{\vec{v}}_{3} = [1; 1; 1]

.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…is the signum function . This lemma first proposed for determining the time derivative of elements in the vector of desired set‐points for the states of general dynamic systems …”

Section: Arve Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

Safaei

2020

Adaptive Control & Signal

Self Cite

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show abstract

“…Consider a mobile robot equipped with two parallel steering wheels, whose forward differential kinematic model is described in previous studies [15][16][17] (see also Figure 1). …”

Section: Kinematic Modelmentioning

confidence: 99%

Robust contour tracking of nonholonomic mobile robots via adaptive velocity field motion planning scheme

Muñoz‐Vázquez

Sánchez‐Torres

Parra-Vega

et al. 2019

Adaptive Control & Signal

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This paper aims at designing a contour tracking scheme based on an adaptive velocity field formulation, for the case of uncertain nonholonomic (differential drive) mobile robots, with its dynamic controller. First, to handle kinematic uncertainties that deviate the map of the velocity field into wheel velocities, a linear parameterization of the uncertain Jacobian operator is proposed to synthesize an adaptive kinematic controller that shapes correctly the velocity field. Then, a robust model-free dynamic controller is proposed to compensate in finite time for uncertain dynamics and disturbances, enforcing the kinematic reference. Finally, a representative simulation study is discussed to show the reliability of the proposed scheme. KEYWORDSadaptive control, fault-tolerant control, sliding mode control, velocity field control 890

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Computation of discriminating kernel and robust capture basin with regulation map by interval methods

Peng

Stancu

Dang

2019

Intl J Robust & Nonlinear

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This paper proposes a novel algorithm that characterizes the robust capture basin and the discriminating kernel for constrained nonlinear systems with uncertainties based on viability theory. For nonlinear systems with constrained inputs and bounded uncertainties, the viability kernel is the largest set of states possessing a possibility to be viable in a set, and the capture basin is the largest set of states possessing a possibility to reach a target in a finite time, and keeping viable in a set before reaching the target. However, in the viability theory, both control and uncertainty in a parameterized system are considered as parameters:the discriminating kernel and the proposed robust capture basin link viability theory with robust control, which take both control and uncertainties into account. For the constrained uncertain nonlinear systems, the discriminating kernel is the largest set of states that is robust invariant in a set with proper control, and the robust capture basin is the largest set of states reaching their target in finite time with proper control despite of uncertainties and keeping viable in a set before reaching the target. Furthermore, we map all the states to optimal regulatory control such that the systems are regulated by a regulation map. To compute the robust capture basin and the discriminating kernel, we use interval methods to provide guaranteed solutions. The proposed algorithms in this paper approximate an outer approximation of the minimum reachable target and inner approximations of the robust capture basin and the discriminating kernel in a guaranteed way.

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Optimal model‐free control for a generic MIMO nonlinear system with application to autonomous mobile robots

Cited by 24 publications

References 41 publications

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

Robust contour tracking of nonholonomic mobile robots via adaptive velocity field motion planning scheme

Computation of discriminating kernel and robust capture basin with regulation map by interval methods

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