Solving nonlinear optimal path tracking problem using a new closed loop direct–indirect optimization method: application on mechanical manipulators

Rahaghi, Mohsen Irani; Barat, Farzane

doi:10.1017/s0263574718000851

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…where b is the vector of design parameters, which contains the unknown constant parameters of the model. Then, Hamiltonian function is defined as [36]:…”

Section: Ptcm Methodologymentioning

confidence: 99%

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Perfect Torque Compensation of Planar 5R Parallel Robot in Point-to-Point Motions, Optimal Control Approach

2020

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SUMMARY In this paper, a new approach is presented for perfect torque compensation of the robot in point-to-point motions. The proposed method is formulated as an open-loop optimal control problem. The problem is defined as optimal trajectory planning with adjustable design parameters to compensate applied torques of a planar 5R parallel robot for a given task, perfectly. To illustrate the effectiveness of the approach, the obtained optimal path is used as the reference command in the experiment. The experimental outputs show that the performance index has been reduced by over 80% compared to the typical design of the robot.

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“…where b is the vector of design parameters, which contains the unknown constant parameters of the model. Then, Hamiltonian function is defined as [36]:…”

Section: Ptcm Methodologymentioning

confidence: 99%

“…They used a new closed-loop optimal control method. 36 In these studies, the performance index was minimized or maximized rather than obtaining a global optimum response. Also, the adjustable design parameters for the system are not considered in the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Perfect Torque Compensation of Planar 5R Parallel Robot in Point-to-Point Motions, Optimal Control Approach

2020

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“…Recently, this approach has received a lot of attention in the field of robotics. Most studies are in the field of motion planning (Fang et al, 2019; Gallant and Gosselin, 2018; Manor et al, 2018; Rahaghi and Barat, 2019; Zheng et al, 2019), dynamic load-carrying capacity (Shafei and Korayem, 2017), and optimal balancing problems (Moradi et al, 2018; Nikoobin and Moradi, 2018).…”

Section: Introductionmentioning

confidence: 99%

A variational approach to determination of maximum throw-able workspace of robotic manipulators in optimal ball pitching motion

Asgari

Nikoobin

2021

Transactions of the Institute of Measurement and Control

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This study is aimed at finding the entire points that a manipulator can launch an object onto by an optimal motion. These points are called throw-able workspace, which are located outside the reachable workspace of the robot. From an optimization point of view, some throwing parameters can be found to decrease motion cost. In this paper, by using this concept, the best combination of throwing and trajectory planning is attempted. The proposed method consists of two basic ideas: first, defining the optimal throwing problem as the optimal control problem (OCP) and solving it using the indirect solution approach based on the fundamental lemma of calculus of variations. To achieve the best release angle and speed, the throwing equation of motion is applied as a moving-end boundary condition (BC). Second, based on the obtained optimal throwing, an algorithm is presented to calculate the maximum throw-able workspace. The simulation results demonstrate the effectiveness of the proposed framework for both single link and spatial two-degree-of-freedom throwing robots.

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“…In ref. [41], a treatment of the nonlinear optimal control problem is attempted for nonlinear affine-in-the-input dynamical systems by assuming once again the decomposition of the solution of the Hamilton-Jacobi-Bellman equation into Galerkin series. It remains to prove global stability and to ensure convergence to the solution of the nonlinear optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear optimal control approach for underactuated power-line inspection robots

et al. 2021

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The article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuated power-line inspection robots. To implement this control scheme, the state-space model of the power-line inspection robots 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 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. The significance of the article’s results is outlined in the following: (i) the proposed control method is suitable for treating underactuated robotic systems and in general nonlinear dynamical systems with control inputs gain matrices which are in a nonquadratic form, (ii) by achieving stabilization of the power-line inspection robots in underactuation conditions the proposed control method ensures the reliable functioning of these robotic systems in the case of actuators’ failures or enables the complete removal of certain actuators and the reduction of the weight of these robotic systems, (iii) the proposed control method offers a solution to the nonlinear optimal control problem which is of proven global stability while also remaining computationally tractable, (iv) the proposed nonlinear optimal control method retains the advantages of linear optimal control that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs, and (v) by minimizing the amount of energy that is dispersed by the actuators of the power-line inspection robots the proposed control method improves the autonomy and operational capacity of such robotic systems.

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Solving nonlinear optimal path tracking problem using a new closed loop direct–indirect optimization method: application on mechanical manipulators

Cited by 4 publications

References 16 publications

Perfect Torque Compensation of Planar 5R Parallel Robot in Point-to-Point Motions, Optimal Control Approach

Perfect Torque Compensation of Planar 5R Parallel Robot in Point-to-Point Motions, Optimal Control Approach

A variational approach to determination of maximum throw-able workspace of robotic manipulators in optimal ball pitching motion

A nonlinear optimal control approach for underactuated power-line inspection robots

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