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1 International Journal of Applied Mathematics and Computer Science

1 2018

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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

2018

Vol. 28, no. 3

483--492

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.