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A fast evaluation of initial configurations in repeatable inverse kinematics for redundant manipulators

Duleba I., Karcz-Duleba I., Mielczarek A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

483--492

EN

A repeatable inverse kinematic task in robot manipulators consists in finding a loop (cyclic trajectory) in a configuration space, which corresponds to a given loop in a task space. In the robotic literature, an entry configuration to the trajectory is fixed and given by a user. In this paper the assumption is released and a new, indirect method is introduced to find entry configurations generating short trajectories. The method avoids a computationally expensive evaluation of (infinite) many entry configurations for redundant manipulators (for each of them, repeatable inverse kinematics should be run). Some fast-to-compute functions are proposed to evaluate entry configurations and their correlations with resulting lengths of trajectories are computed. It appears that only an original function, based on characteristics of a manipulability subellipsoid, properly distinguishes entry configurations that generate short trajectories. This function can be used either to choose one from a few possible entry configurations or as an optimized function to compute the best initial configuration.

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A comparison of methods solving repeatable inverse kinematics for robot manipulators

Duleba I., Karcz-Duleba I.

Archives of Control Sciences

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2018

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Vol. 28, No. 1

5--18

EN

In this paper two recent methods of solving a repeatable inverse kinematic task are compared. The methods differ substantially although both are rooted in optimization techniques. The first one is based on a paradigm of continuation methods while the second one takes advantage of consecutive approximations. The methods are compared based on a quality of provided results and other quantitative and qualitative factors. In order to get a statistically valuable comparison, some data are collected from simulations performed on pendula robots with different paths to follow, initial configurations and a degree of redundancy.

3

Suboptimal approximations in repeatable inverse kinematics for robot manipulators

Duleba I., Karcz-Duleba I.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 2

209--217

EN

In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

4

The impatience mechanism as a diversity maintaining and saddle crossing strategy

Karcz-Duleba I.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 4

905--918

EN

The impatience mechanism diversifies the population and facilitates escaping from a local optima trap by modifying fitness values of poorly adapted individuals. In this paper, two versions of the impatience mechanism coupled with a phenotypic model of evolution are studied. A population subordinated to a basic version of the impatience mechanism polarizes itself and evolves as a dipole centered around an averaged individual. In the modified version, the impatience mechanism is supplied with extra knowledge about a currently found optimum. In this case, the behavior of a population is quite different than previously—considerable diversification is also observed, but the population is not polarized and evolves as a single cluster. The impatience mechanism allows crossing saddles relatively fast in different configurations of bimodal and multimodal fitness functions. Actions of impatience mechanisms are shown and compared with evolution without the impatience and with a fitness sharing. The efficiency of crossing saddles is experimentally examined for different fitness functions. Results presented in the paper confirm good properties of the impatience mechanism in diversity maintaining and saddle crossing.