Planning of manipulator motion trajectory with higher-degree polynomials use

Boryga, Marek; Graboś, Andrzej

doi:10.1016/j.mechmachtheory.2008.11.003

Cited by 86 publications

(56 citation statements)

References 14 publications

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“…Model-free approaches are often based on geometrical approaches (Dieulot et al, 2006;Biagiotti and Melchiorri, 2008), since the trajectory is defined as a sequence of polynomial functions (Boryga and Grabos´, 2009), splines (Gasparetto and Zanotto, 2007) or Non-Uniform Rational B-Splines (NURBS) (Louembet et al, 2010). Another possible way to generate a trajectory is to use filters Melchiorri, 2010, 2013).…”

Section: Introductionmentioning

confidence: 99%

Robust model-based trajectory planning for nonlinear systems

Boscariol

Gasparetto

2016

Journal of Vibration and Control

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Model-based trajectory planning algorithms are capable of providing a high level of performance. However, they are often lacking in robustness, which severely limits their field of application. In this paper the method of parametric desensitization is applied to nonlinear models, providing a feasible solution to the problem of robust model-based trajectory planning for nonlinear plants with parametric uncertainties. By using an indirect variational solution method, the necessary optimality conditions deriving from Pontryagin's minimum principle are imposed, and lead to a differential two-point boundary value problem; numerical solution of the latter is accomplished by means of collocation techniques. The method is applied to two test cases: a nonlinear spring-mass system and a flexible link manipulator with Coulombian friction. Results show that the technique developed in this paper can significantly improve the robustness of the resulting trajectory to parametric model mismatches in comparison with the conventional method

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Section: Introductionmentioning

confidence: 99%

Robust model-based trajectory planning for nonlinear systems

Boscariol

Gasparetto

2016

Journal of Vibration and Control

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“…To overcome this shortcoming, higher-order (such as cubic and quartic) polynomials are instead employed to conduct trajectory planning. 1,3,4 In this respect, the most frequently used interpolation functions are splines which are piecewise polynomials, including the cubic splines 5,6 and the B-splines. 7,8 These polynomials-based methods are generally employed to plan the robot trajectories at the joint level, which inevitably leads to inaccurate movements of the end-effector in the Cartesian space.…”

Section: Introductionmentioning

confidence: 99%

An improved geodesic algorithm for trajectory planning of multi-joint robots

Chen

Tang

2016

International Journal of Advanced Robotic Systems

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The present work proposes an improved geodesic algorithm for the trajectory planning of multi-joint robots. First, all of the joint variables are chosen to set up a generalized local coordinate system for the product of the positional space and the orientational one. Second, by defining a new Riemannian metric that contains both the positional and rational parameters, the traditional geodesic algorithm is improved so that it becomes capable of planning robot trajectories that include both the position and the orientation. To demonstrate the effectiveness of the improvement, trajectories are planned for two typical joint robots: one being a planar 3R and the other a spatial RRPP. It is verified that the improved algorithm can generate not only smooth motions for the joints but also smooth and accurate motions for the end-effector. The improved algorithm applies to multi-joint robots with no more than six degrees of freedom.

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“…A significant amount of effort has been made in developing new trajectory generation algorithms that provide smooth motion to high-speed machining systems [3]- [4]. Gasparetto and Zanotto [3] presented a new methodology for fifth-order B-splines and used to compose the overall trajectory of robot manipulators.…”

Section: Introductionmentioning

confidence: 99%

“…Gasparetto and Zanotto [3] presented a new methodology for fifth-order B-splines and used to compose the overall trajectory of robot manipulators. Boryga [4] presented a planning mode of trajectory motion for serial-link manipulators in the higher-degree polynomials application. The linear acceleration profiles of end-effectors, for each coordinate, were planned as the high-degree polynomials.…”

Section: Introductionmentioning

confidence: 99%

Minimum-absolute-energy trajectory planning for a toggle mechanism driven by a PMSM

Hsu

Huang

Fung

2012

2012 International Conference on System Science and Engineering (ICSSE)

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In this paper, an minimum-energy point-to-point (PTP) trajectory is designed for a mechatronic system, which is a toggle mechanism driven by a permanent magnet synchronous motor (PMSM). To generate the PTP trajectory, we employ the real-coded genetic algorithm (RGA) to search for the minimum-absolute-energy trajectory for the mechatronic system. In this paper, a high-degree polynomial is used and the initial and final conditions (position, velocity, acceleration and jerk) are considered as the constraints for the trajectory. In the RGA method, the coefficients of the polynomial are determined by satisfying the desired fitness function of input absolute electric energy. The numerical simulations are compared between several degrees polynomials during motion operation time for the toggle mechanism.

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Planning of manipulator motion trajectory with higher-degree polynomials use

Cited by 86 publications

References 14 publications

Robust model-based trajectory planning for nonlinear systems

Robust model-based trajectory planning for nonlinear systems

An improved geodesic algorithm for trajectory planning of multi-joint robots

Minimum-absolute-energy trajectory planning for a toggle mechanism driven by a PMSM

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