Maximum load of flexible joint manipulators using nonlinear controllers

Robotica ◽  
2015 ◽  
Vol 35 (1) ◽  
pp. 119-142 ◽  
Author(s):  
A. H. Korayem ◽  
M. Irani Rahagi ◽  
H. Babaee ◽  
M. H. Korayem
Keyword(s):  
Optimal Control ◽  
Sliding Mode ◽  
Nonlinear Partial Differential Equation ◽  
Standard Form ◽  
Angular Position ◽  
Nonlinear Optimal Control ◽  
Dynamic Equations ◽  
Flexible Joint ◽  
Control Approach ◽  
Optimal Control Approach

SUMMARYThe main innovation of this paper is determining the dynamic load carrying capacity (DLCC) of a flexible joint manipulator (FJM) using a closed form nonlinear optimal control approach. The proposed method is compared with two closed loop nonlinear methods that are usually applied to robotic systems. As a new idea, DLCC of the manipulator is considered as a criterion to compare how well controllers perform point to point mission for the FJMs. The proposed method is compared with feedback linearization (FL) and robust sliding mode control (SMC) methods to show better performance of proposed nonlinear optimal control approach. An optimal controller is designed by solving a nonlinear partial differential equation named the Hamilton–Jacobi–Bellman (HJB) equation. This equation is complicated to solve exactly for complex dynamics so it is solved numerically using an iterative approximation combined with the Galerkin method. In the FL method, angular position, velocity, acceleration and jerk of links are considered as new states to linearize the dynamic equations. In the case of SMC, the dynamic equations of manipulator are changed to the standard form then the Slotine method is used to design the sliding mode controller. Two simulations are performed for a planar and a spatial Puma manipulator and performances of controllers are compared. Finally an experimental test is done on 6R manipulator and the Stereo vision method is used to determine the position and orientation of the end-effector.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

A nonlinear optimal control approach for chaotic finance dynamics

2017 ◽  
Author(s):  
G. Rigatos ◽  
P. Siano ◽  
V. Loia ◽  
A. Tommasetti ◽  
O. Troisi
Keyword(s):  
Optimal Control ◽  
Nonlinear Optimal Control ◽  
Control Approach ◽  
Optimal Control Approach

scholarly journals A Nonlinear Optimal Control Approach for a Lower-Limb Robotic Exoskeleton

2020 ◽  
Vol 17 (05) ◽  
pp. 2050018
Author(s):  
G. Rigatos ◽  
M. Abbaszadeh ◽  
J. Pomares ◽  
P. Wira
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Lower Limb ◽  
Nonlinear Optimal Control ◽  
Algebraic Riccati Equation ◽  
Time Step ◽  
H Infinity ◽  
Control Approach ◽  
Robotic Exoskeleton ◽  
Optimal Control Approach

The use of robotic limb exoskeletons is growing fast either for rehabilitation purposes or in an aim to enhance human ability for lifting heavy objects or for walking for long distances without fatigue. The paper proposes a nonlinear optimal control approach for a lower-limb robotic exoskeleton. The method has been successfully tested so far on the control problem of several types of robotic manipulators and this paper shows that it can also provide an optimal solution to the control problem of limb robotic exoskeletons. To implement this control scheme, the state-space model of the lower-limb robotic exoskeleton undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator.

scholarly journals A Novel Nonlinear Optimal Control Approach for the Dynamic Process of a Hybrid Electric Vehicle Equipped with Electromechanical Transmission

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Changle Xiang ◽  
Donghao Zhang ◽  
Hailiang Zheng ◽  
Lijin Han ◽  
Kun Huang
Keyword(s):  
Optimal Control ◽  
Electric Vehicle ◽  
Dynamic Process ◽  
Hybrid Electric Vehicle ◽  
Nonlinear Optimal Control ◽  
Feasible Region ◽  
Control Variables ◽  
Control Approach ◽  
Hybrid Electric ◽  
Optimal Control Approach

Coordinatively controlling the engine and several motor/generators (MGs) during a dynamic process is a challenging problem because they are coupled together by the electromechanical transmission (EMT) system and all of them have strong nonlinear characteristics. We develop a novel nonlinear optimal control approach based on the multiobjective dynamic optimization model of the hybrid electric vehicle (HEV), which is equipped with an EMT system. In this approach, the current states of the components are obtained by using the state observation algorithm based on Kalman filtering; the future states of the components and the feasible region of the control variables are estimated by using the dynamic prediction algorithm based on the nonlinear model of the EMT system. Then, the control variables are achieved by using the optimal decision algorithm based on the hierarchical optimization and nonlinear programming, and the influence of the model error and the external disturbance are modified by using the feedback compensation algorithm. The simulation results illustrate the efficiency of the proposed control approach, and the test results verify its real-time performance.

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