Motion Planning of Uncertain Ordinary Differential Equation Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

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Reliable and Failure-Free Workspaces for Motion Planning Algorithms for Parallel Manipulators Under Geometrical Uncertainties

Vieira

Fontes

Beck

et al. 2019

Journal of Computational and Nonlinear Dynamics

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Manufacturing tolerances and other uncertainties may play an important role in the performance of parallel manipulators since they can affect the distance to a singular configuration. Motion planning strategies for parallel manipulators under uncertainty require decision making approaches for classifying reliable regions within the workspace. In this paper, we address fail free and reliable motion planning for parallel manipulators. Failure is related to parallel kinematic singularities in the motion equations or to ill-conditioning of the Jacobian matrices. Monte Carlo algorithm is employed to compute failure probabilities for a dense grid of manipulator workspace configurations. The inverse condition number of the Jacobian matrix is used to compute the distance between each configuration and a singularity. For supporting motion planning strategies, not only failure maps are constructed but also reliable and failure-free workspaces are obtained. On the one hand, the reliable workspace is obtained by minimizing the failure probabilities subject to a minimal workspace area. Differently, a failure-free workspace is found by maximizing the workspace area subject to a probability of failure equal to zero. A 3RRR manipulator is used as a case study. For this case study, the usage of the reliable strategy can be useful for robustifying motion planning algorithm without a significant reduction of the reliable regions within the workspace.

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Motion Planning of Uncertain Ordinary Differential Equation Systems

Cited by 3 publications

References 64 publications

Theoretical modeling and numerical solution methods for flexible multibody system dynamics

Theoretical modeling and numerical solution methods for flexible multibody system dynamics

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

Reliable and Failure-Free Workspaces for Motion Planning Algorithms for Parallel Manipulators Under Geometrical Uncertainties

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