Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

The paper proposes a new method for synchronization of coupled circadian cells and for nonlinear control of the associated protein synthesis process using differential flatness theory and the derivative-free nonlinear Kalman filter. By proving that the dynamic model of the FRQ protein synthesis is a differentially flat one, its transformation to the linear canonical (Brunovsky) form becomes possible. For the transformed model, one can find a state feedback control input that makes the oscillatory characteristics in the concentration of the FRQ protein vary according to desirable setpoints. To estimate nonmeasurable elements of the state vector, the derivative-free nonlinear Kalman filter is used. The derivative-free nonlinear Kalman filter consists of the standard Kalman filter recursion on the linearized equivalent model of the coupled circadian cells and on computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. Moreover, to cope with parametric uncertainties in the model of the FRQ protein synthesis and with stochastic disturbances in measurements, the derivative-free nonlinear Kalman filter is redesigned in the form of a disturbance observer. The efficiency of the proposed Kalman filter-based control scheme is tested through simulation experiments.

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Input–Output Linearizing Control of the Underactuated Hovercraft Using the Derivative-Free Nonlinear Kalman Filter

Unmanned Systems ◽

10.1142/s2301385015500089 ◽

2015 ◽

Vol 03 (02) ◽

pp. 127-142 ◽

Cited By ~ 9

Author(s):

Gerasimos G. Rigatos ◽

Guilherme V. Raffo

Keyword(s):

Kalman Filter ◽

Nonlinear Control ◽

Nonlinear Model ◽

State Vector ◽

Feedback Linearization ◽

Differential Flatness ◽

State Variables ◽

Input Output ◽

Derivative Free ◽

Nonlinear Kalman Filter

The paper proposes a nonlinear control approach for the underactuated hovercraft model based on differential flatness theory and uses a new nonlinear state vector and disturbances estimation method under the name of derivative-free nonlinear Kalman filter. It is proven that the nonlinear model of the hovercraft is a differentially flat one. It is shown that this model cannot be subjected to static feedback linearization, however it admits dynamic feedback linearization which means that the system's state vector is extended by including as additional state variables the control inputs and their derivatives. Next, using the differential flatness properties it is also proven that this model can be subjected to input–output linearization and can be transformed to an equivalent canonical (Brunovsky) form. Based on this latter description the design of a state feedback controller is carried out enabling accurate maneuvering and trajectory tracking. Additional problems that are solved in the design of this feedback control scheme are the estimation of the nonmeasurable state variables in the hovercraft's model and the compensation of modeling uncertainties and external perturbations affecting the vessel. To this end, the application of the derivative-free nonlinear Kalman filter is proposed. This nonlinear filter consists of the Kalman Filter's recursion on the linearized equivalent model of the vessel and of an inverse nonlinear transformation based on the differential flatness features of the system which enables to compute estimates for the state variables of the initial nonlinear model. The redesign of the filter as a disturbance observer makes possible the estimation and compensation of additive perturbation terms affecting the hovercraft's model. The efficiency of the proposed nonlinear control and state estimation scheme is confirmed through simulation experiments.

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Control and disturbances compensation in underactuated robotic systems using the derivative-free nonlinear Kalman filter

Robotica ◽

10.1017/s0263574715000776 ◽

2015 ◽

Vol 35 (3) ◽

pp. 687-711 ◽

Cited By ~ 3

Author(s):

Gerasimos G. Rigatos

Keyword(s):

Kalman Filter ◽

External Disturbance ◽

Parametric Uncertainty ◽

Robotic Manipulator ◽

Robotic Systems ◽

Differential Flatness Theory ◽

Closed Chain ◽

Control Scheme ◽

Derivative Free ◽

Nonlinear Kalman Filter

SUMMARYThe Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. The control problem for underactuated robots is non-trivial and becomes further complicated if the robot is subjected to model uncertainties and external disturbances. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system cannot be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is shown that one can estimate simultaneously external disturbance terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed Kalman Filter-based control scheme is tested in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.

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