On Application of Elastic Band Method to Repeatable Inverse Kinematics in Robot Manipulators

International Journal of Applied Mathematics and Computer Science

Mielczarek

2018

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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.

Section: Introductionmentioning

confidence: 99%

A Fast Evaluation of Initial Configurations in Repeatable Inverse Kinematics for Redundant Manipulators

International Journal of Applied Mathematics and Computer Science

Mielczarek

2018

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“…A convergence of the presented procedure is guaranteed as the distance between a current X-loop and the given X-loop decreases monotonically. Details of the method have been presented in [2].…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

2018

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A comparison of methods solving repeatable inverse kinematics for robot manipulators IGNACY DULEBA and IWONA KARCZ-DULEBAIn 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.

“…Recently, an alternative approach to repeatable inverse kinematics was proposed which avoids a construction of augmented kinematics and designs an appropriate loop straightforward in a configuration space [1]. The approach extensively uses ideas of continuation methods [9].…”

mentioning

confidence: 99%

Suboptimal approximations in repeatable inverse kinematics for robot manipulators

Bulletin of the Polish Academy of Sciences Technical Sciences

2017

Abstract. 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.