Time-Energy Optimal Trajectory Planning of Cable-Suspended Manipulators

Bamdad, Mahdi

doi:10.1007/978-3-642-31988-4_3

Cited by 13 publications

(6 citation statements)

References 14 publications

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“…The most common way to solve such problem is to use the calculus of variations, such as the Pontryagin's Minimum Principle (PMP) [22]. To improve the optimization problem in (10) with robustness specifications, it can be augmented with some sensitivity functions, as suggested in the previous work of one of the Authors [19].…”

Section: Variational Formulation Of Robust Trajectory Planningmentioning

confidence: 99%

“…Indirect methods are instead based on calculus of variations, which is used to set-up and solve the motion design problem as a Two-Point Boundary Value Problem (TPBVP). Successful applications of this methods are found, among others, for flexible link robots [6], flexible joint robots [7], mobile robots [8], lumped spring-mass systems with nonlinear springs [9], and for cable-driven robots [10], [11], [12] . Indirect control methods are generally chosen for their accuracy [4], however their field of application is often limited to small scale problems by the difficulty of finding a numerical solution of the problem under investigation.…”

Section: Introductionmentioning

confidence: 99%

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Desensitized motion planning for underactuated multibody systems

Boscariol¹,

Richiedei²

2021

Proceedings of the 10th ECCOMAS Thematic Conference on MULTIBODY DYNAMICS

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Model-plant mismatches can severely limit the effectiveness of conventional model-based motion design methods. To solve this issue, a method for robust trajectory planning that can reduce the effects of parametric uncertainties is presented in this work. The method is based on an indirect variational formulation, which is translated into a Two-Point Boundary Value Problem (TPBVP) and then solved numerically. Robustness is obtained by incorporating into the problem the sensitivity functions of the plant, and imposing some additional constraints on the initial and final points of the trajectory. A formulation aimed at reducing both the residual and the transient oscillations, as well as keeping small the control effort, is also proposed. The work presents a numerical verification of the effectiveness of the method for an underactuated system, such as a double-pendulum crane, by showing its effectiveness and robustness when performing fast rest-to-rest motions.

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Section: Variational Formulation Of Robust Trajectory Planningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Desensitized motion planning for underactuated multibody systems

Boscariol¹,

Richiedei²

2021

Proceedings of the 10th ECCOMAS Thematic Conference on MULTIBODY DYNAMICS

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“…However, this method can only reduce consumption qualitatively and cannot calculate the motion trajectory with the minimum energy consumption. Bamdad 9 introduced a time-energy optimal control with a trajectory planning approach, in which the optimal control law was solved by using the two-point boundary value problem. Gosselin et al [10][11][12][13][14] proposed a trajectory planning approach based on the natural frequency of the pendulum-like free motion.…”

Section: Introductionmentioning

confidence: 99%

Stiffness-based trajectory planning of a 6-DOF cable-driven parallel manipulator

Zhang

Shang

Zhang

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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The stiffness of the cable-driven parallel manipulator is usually poor because of the cable flexibility, and the existing methods on trajectory planning mainly take the minimum time and the optimal energy into account, not the stiffness. To solve it, the effects of different trajectories on stiffness are studied for a six degree-of-freedom cable-driven parallel manipulator, according to the kinematic model and the dynamic model. The condition number and the minimum eigenvalue of the dimensionally homogeneous stiffness matrix are selected as performance indices to analyze the stiffness changes during the motion. The simulation experiments are implemented on a six degree-of-freedom cable-driven parallel manipulator, to study the stiffness of three different trajectory planning approaches such as S-type velocity profile, quintic polynomial, and trigonometric function. The accelerations of different methods are analyzed, and the stiffness performances for the methods are compared after planning the point-to-point straight and the curved trajectories. The simulation results indicate that the quintic polynomial and S-type velocity profile have the optimal performance to keep the stiffness stable during the motion control and the travel time of the quintic polynomial can be optimized sufficiently while keeping stable.

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“…One important issue on cable-driven parallel robot is the orientation planning of end effector, as investigated in quite a few literatures [6,7]. For the FAST case, all planned trajectories for star observations can be held in the focal surface, as shown in Figure 2.…”

Section: Introductionmentioning

confidence: 99%

Optimal Orientation Planning and Control Deviation Estimation on FAST Cable-Driven Parallel Robot

Yao

2014

Advances in Mechanical Engineering

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The paper is devoted theoretically to the optimal orientation planning and control deviation estimation of FAST cable-driven parallel robot. Regarding the robot characteristics, the solutions are obtained from two constrained optimizations, both of which are based on the equilibrium of the cabin and the attention on force allocation among 6 cable tensions. A kind of control algorithm is proposed based on the position and force feedbacks. The analysis proves that the orientation control depends on force feedback and the optimal tension solution corresponding to the planned orientation. Finally, the estimation of orientation deviation is given under the limit range of tension errors.

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Time-Energy Optimal Trajectory Planning of Cable-Suspended Manipulators

Cited by 13 publications

References 14 publications

Desensitized motion planning for underactuated multibody systems

Desensitized motion planning for underactuated multibody systems

Stiffness-based trajectory planning of a 6-DOF cable-driven parallel manipulator

Optimal Orientation Planning and Control Deviation Estimation on FAST Cable-Driven Parallel Robot

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