On optimal control of multi-link vertical planar robot arms systems moving under the effect of gravity

Lee, Heung Wing Joseph; Teo, Kok Lay; Jennings, Leslie

doi:10.1017/s0334270000008808

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…If y.x/ is piecewise smooth and satisfies the boundary conditions y.a/ D A, y.b/ D B, then y.x/ is said to be an admissible arc. In other words, this problem consists of finding, among all arcs connecting end points .a, A/ and .b, B/, the one minimizing the integral (17).…”

Section: Calculus Of Variations Approachmentioning

confidence: 99%

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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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Section: Calculus Of Variations Approachmentioning

confidence: 99%

“…An example of a method based on the complete discretization of the optimal control problem using B‐splines is . A method based on the control parameterization technique is described in . In which, only the control is discretized, and piecewise constant functions are used for the approximation of the control function.…”

Section: Introductionmentioning

confidence: 99%

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Gregory

Olivares

Staffetti

2012

Optim Control Appl Methods

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“…Inverse analysis is usually used to obtain the initial torque estimates as shown in [5]. A particular study has also been conducted in [9] where an intuitive "Blind Man" algorithm was proposed for searching for a workable initial guess of control to avoid numerical integration failures, which usually occur due to extreme unrealistic velocities of lighter segments.…”

Section: Models To Maintain Angle Constraints Between Segmentsmentioning

confidence: 99%

Computational models satisfying relative angle constraints for 2-dimensional segmented bodies

Munzir

Jennings

Koh³

2006

ANZIAM J.

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Planar hinged segmented bodies have been used to represent models of biomechanical systems. One characteristic of a segmented body moving under gravitational acceleration and torques between segments is the possibility that the body's segments spin through more than a revolution or past a natural limit, and a computational mechanism to stop such behaviour should be provided. This could be done by introducing angle constraints between segments, and computational models utilising optimal control are studied here. Three models to maintain angle constraints between segments are proposed and compared. These models are: all-time angle constraints, a restoring torque in the state equations and an exponential penalty model. The models are applied to a 2-D three-segment body to test the behaviour of each model when optimising torques to minimise an objective. The optimisation is run to find torques so that the end effector of the body follows the trajectory of a half-circle. The result shows the behaviour of each model in maintaining the angle constraints. The all-time constraints case exhibits a behaviour of not allowing torques (at a solution) which makes segments move past the constraints, while the other two show a flexibility in handling the angle constraints which is more similar to what occurs in a real biomechanical system. 2000 Mathematics subject classification: primary 92C10; secondary 49N15.

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“…Introduction. Many real-world problems in areas, such as aquaculture [8], cancer chemotherapy [49,51], industrial engineering [26,45], artificial intelligence [9,41] and management science [20,47,48,57], can be naturally formulated as their respective optimal control problems. These real-world practical problems are highly complex, and hence they cannot be solved analytically.…”

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confidence: 99%

Control parameterization approach to time-delay optimal control problems: A survey

Wu¹,

Chen²,

Yu³

et al. 2023

JIMO

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<p style='text-indent:20px;'>Control parameterization technique is an effective method to solve optimal control problems. It works by approximating the control function by piece-wise constant (or linear) function. In this way, the optimal control problems are approximated by optimal parameter selection problems, which can be regarded as finite-dimensional optimization problems, where the control heights and switching times of the piece-wise constant function are taken as the decision variables. They can be solved by using gradient-based optimization methods. For this, it requires the gradient formulas of the objective and constraint functions with respect to the decision variables. There are two methods for deriving the required gradient formulas. The aim of this paper is to survey various numerical methods developed based on control parameterization for solving optimal control problems governed by time-delay systems. Particular focus is on those numerical methods for optimizing switching time points. This is because the process of optimizing the switching time points is much more complicated for optimal control problems with time delays. In addition, we shall also review the computational methods developed based on control parameterization technique for solving two optimal control problems involving more complicated time delays.</p>

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On optimal control of multi-link vertical planar robot arms systems moving under the effect of gravity

Cited by 4 publications

References 9 publications

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Computational models satisfying relative angle constraints for 2-dimensional segmented bodies

Control parameterization approach to time-delay optimal control problems: A survey

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