Hyperbolic trajectories for pick-and-place operations to elude obstacles

Müller-Karger, Carmen; Mirena, A. Leonell Granados; Lopez, J.T. Scarpati

doi:10.1109/70.850647

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…( ) is a interpolation function. Researchers have adopted NURBS (Nonuniform Rational B-Splines) curves, timeminimum piecewise quintic polynomials, periodic cubic spline function, hyperbolic trajectories, and other algorithms for automatic planning of smooth trajectories, respectively [19][20][21][22][23][24]. In this paper, to meet six constraints equations (8), a quintic polynomial ( ) = 0…”

Section: Collision-avoidance Trajectory Planning Of the Adbmmentioning

confidence: 99%

Motion Constraints and Trajectory Planning of a Planar Active Dynamic Balancing Mechanism

Wang

Peng

et al. 2015

Mathematical Problems in Engineering

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We propose a new solution to the active balancing issue under mechanical structural constraint. A dynamic model of the 3-DOF active balancer is established considering the limitations of the mechanical construction due to the lengths of the sliding rails. A methodology for the collision-avoidance trajectory planning is presented in addition to the normal trajectory planning to design the collision-free active balancing strategy. Numerical examples are presented to illustrate the effect of the parameter constrains as well as verify the effectiveness and necessity of trajectory planning.

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Section: Collision-avoidance Trajectory Planning Of the Adbmmentioning

confidence: 99%

Motion Constraints and Trajectory Planning of a Planar Active Dynamic Balancing Mechanism

Wang

Peng

et al. 2015

Mathematical Problems in Engineering

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“…Gradient search method is used to find the optimized control parameters for trajectory preshaping. Karger et al [16] have proposed a hyperbolic trajectory for any degrees of freedom robot. The advantage of this trajectory is that it can be planned both in Joint space and Cartesian space with the requirement of inverse kinematics only at the initial and final positions.…”

Section: Introductionmentioning

confidence: 99%

Coupled Error Dynamic Formulation for Modal Control of a Two Link Manipulator having Two Revolute Joints

Mishra¹

2022

GJRE

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In the present work, reformulation of the dynamics of a planar two-link manipulator has been presented in the form of joint errors and their derivatives. The linear second-order differential equations with time-varying coefficients represent the Coupled Error Dynamics of the system. In these equations, the non-linear centrifugal and Coriolis terms are expressed as linear functions of joint error rates and the non-linear gravity terms as a linear function of joint errors with time-varying coefficients. After inclusion of linearized version of these terms, the concept of modal analysis is used in the design of a control system for the robot. The developed control approach is compared with the commonly used computed-torque control approach, as applied for a high-speed direct-drive two-link manipulator with revolute joints. Thus in the proposed approach for controller design, the system non-linearities are taken as part of the system representation itself instead of disturbances as assumed in existing approaches.

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“…The Double-Gyre is time-periodic, which allows for thinking of the dynamical system either in continuous time, or in discrete time (in relation to a Poincaré map). However, it is possible to use the curvature in nonautonomous systems with any time-dependence, by thinking of the stable and unstable manifolds as being attached to hyperbolic trajectories 49,78,80 rather than fixed points. Moreover, using curvature in this way can also be done for specialized curves arising from using any diagnostic procedure in finite-time flows.…”

Section: Introductionmentioning

confidence: 99%

Quantifying the Role of Folding in Nonautonomous Flows: The Unsteady Double-Gyre

Priyankara

Balasuriya

Bollt

2017

Int. J. Bifurcation Chaos

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We analyze chaos in the well-known nonautonomous Double-Gyre system. A key focus is on folding, which is possibly the less-studied aspect of the “stretching+folding=chaos” mantra of chaotic dynamics. Despite the Double-Gyre not having the classical homoclinic structure for the usage of the Smale–Birkhoff theorem to establish chaos, we use the concept of folding to prove the existence of an embedded horseshoe map. We also show how curvature of manifolds can be used to identify fold points in the Double-Gyre. This method is applicable to general nonautonomous flows in two dimensions, defined for either finite or infinite times.

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Hyperbolic trajectories for pick-and-place operations to elude obstacles

Cited by 9 publications

References 15 publications

Motion Constraints and Trajectory Planning of a Planar Active Dynamic Balancing Mechanism

Motion Constraints and Trajectory Planning of a Planar Active Dynamic Balancing Mechanism

Coupled Error Dynamic Formulation for Modal Control of a Two Link Manipulator having Two Revolute Joints

Quantifying the Role of Folding in Nonautonomous Flows: The Unsteady Double-Gyre

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