Optimal Control of Rigid‐Link Manipulators by Indirect Methods

Callies, R.; Rentrop, P.

doi:10.1002/gamm.200890001

Cited by 18 publications

(16 citation statements)

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“…Indirect methods change the optimization problem in to differential equations using optimality conditions and then solve them. In the direct methods are good selection when the DOF is high or different objectives are considered in optimization [19,20]. Despite the computational complexities and the probability of non-convergence in indirect methods, these methods are relatively accurate and reliable.…”

Section: Methodsmentioning

confidence: 99%

Separation of motion techniques for trajectory optimization in flexible redundant robot manipulators

Faritus¹,

Heidari²,

Shateyi³

2017

J. vibroeng.

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This paper presents a computational method for optimization of trajectory in redundant robot manipulators. For this purpose, all possible answers are acquired based on rigid conditions and redundancy of the robot. Using open loop optimal control method, the trajectory which minimizes the objective function will be obtained. The objective function is considered as an integral index that will be minimized in the entire trajectory. The objective function and constraints of optimization problem will be selected based on conditions of motion. Dynamic equations of the system are constraints of optimization problem in point-to-point motion. For motion conditions in the specified path, kinematic equations will be added. Also, unequal constraints are applied for limiting the velocity and torque. By selecting the state and control signal vectors which are obtained by assuming rigid motion of the robot, the objective function and constraints will be changed to standard form of an optimization problem. Pontryagin's maximum principle is used to solve equations. So, the equations of classical form will be changed into two-point boundary value problem. Suggested method is applied to point-to-point motion and movement in the specified path. Results demonstrate accuracy and efficiency of suggested method.

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Section: Methodsmentioning

confidence: 99%

Separation of motion techniques for trajectory optimization in flexible redundant robot manipulators

Faritus¹,

Heidari²,

Shateyi³

2017

J. vibroeng.

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“…Most talks at the meeting addressed the field of PDAEs, but among the other prominent topics were also optimization and optimal control problems with constraints described by DAEs , see, e.g., [CR08,KKBS04] and model order reduction for descriptor systems [RS07]. It moreover turned out that even those topics which had seemed to be mature and fully understood were still ready for surprises.…”

Section: The Oberwolfach Workhop In 2006mentioning

confidence: 99%

On the History of Differential-Algebraic Equations

Simeon

2017

Surveys in Differential-Algebraic Equations IV

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“…Whereas, planar underactuated RR robot manipulators, in which only the second joint is actuated, will be denoted with RR. Underactuated robots are mechanical systems with second-order 277 techniques is given in [21]. For time-optimal control, the existence of the solution for two-link planar manipulators is proven in [22].…”

Section: Introductionmentioning

confidence: 99%

“…Integrating(21) by the parts for all admissible variations´.x/, another necessary condition for y D y.x/ used to give a relative minimum of the variational problem…”

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confidence: 99%

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Gregory

Olivares

Staffetti

2012

Optim Control Appl Methods

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SUMMARYIn this paper, we study the trajectory-planning problem for planar underactuated robot manipulators with two revolute joints in the presence of gravity. This problem is studied as an optimal control problem. We consider both possible models of planar underactuated robot manipulators, namely with the elbow joint not actuated, called Pendubot, and with the shoulder joint not actuated, called Acrobot. Our method consists of a numerical resolution of a reformulation of the optimal control problem, as an unconstrained calculus of variations problem, in which the dynamic equations of the mechanical system are regarded as constraints and treated by means of special derivative multipliers. We solve the resulting calculus of variations problem by using a numerical approach based on the Euler-Lagrange necessary condition in integral form. In which, time is discretized, and admissible variations for each variable are approximated using a linear combination of the piecewise continuous basis functions of time. In this way, a general method for the solution of optimal control problems with constraints is obtained, which, in particular, can deal with nonintegrable differential constraints arising from the dynamic models of underactuated planar robot manipulators with two revolute joints in the presence of gravity.

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Optimal Control of Rigid‐Link Manipulators by Indirect Methods

Cited by 18 publications

References 100 publications

Separation of motion techniques for trajectory optimization in flexible redundant robot manipulators

Separation of motion techniques for trajectory optimization in flexible redundant robot manipulators

On the History of Differential-Algebraic Equations

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

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