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1
Content available 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.
2
Content available 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
Content available 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
Content available On the application of elastic band method to repeatable inverse kinematics in robot manipulators
Duleba I., Opalka M.
Journal of Automation Mobile Robotics and Intelligent Systems
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2013
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Vol. 7, No. 4
5--12
EN
In this paper an idea of the elastic band method was exploited to design a repeatable inverse kinematics algorithm for robot manipulators. The method incorporates an optimization process at many stages of its performance and admits some extensions. Performance of the algorithm was illustrated on models of the three DOF planar pendulum and the PUMA robot. A comparison with a standard pseudo-inverse Jacobian algorithm, which does not preserve repeatability of inverse kinematics, is also provided.
5
Content available Impact of control representations on efficiency of local nonholonomic motion planning
Duleba I.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2011
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Vol. 59, nr 2
213-218
EN
In this paper various control representations selected from a family of harmonic controls were examined for the task of locally optimal motion planning of nonholonomic systems. To avoid dependence of results either on a particular system or a current point in a state space, considerations were carried out in a sub-space of a formal Lie algebra associated with a family of controlled systems. Analytical and simulation results are presented for two inputs and three dimensional state space and some hints for higher dimensional state spaces were given. Results of the paper are important for designers of motion planning algorithms not only to preserve controllability of the systems but also to optimize their motion.
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