By Yunong Zhang, Zhijun Zhang
Repetitive movement making plans and keep watch over of Redundant robotic Manipulators offers 4 usual movement making plans schemes according to optimization strategies, together with the elemental RMP scheme and its extensions. those schemes are unified as quadratic courses (QPs), that are solved via neural networks or numerical algorithms. The RMP schemes are established successfully by way of the simulation effects in accordance with a number of robot versions; the experiments utilising the basic RMP scheme to a actual robotic manipulator also are offered. because the schemes and the corresponding solvers provided within the publication have solved the non-repetitive movement difficulties latest in redundant robotic manipulators, it really is of specific use in using theoretical examine according to the quadratic software for redundant robotic manipulators in business occasions. This booklet may be a invaluable reference paintings for engineers, researchers, complicated undergraduate and graduate scholars in robotics fields.
Yunong Zhang is a professor on the university of knowledge technology and know-how, sunlight Yat-sen college, Guangzhou, China; Zhijun Zhang is a study fellow operating on the related institute.
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Additional resources for Repetitive Motion Planning and Control of Redundant Robot Manipulators
Example text
Graph (b) is That is, graph (a) of Fig. 1 is for the equality constraint J xˆ = d, ˆ for the one-sided inequality constraint Axˆ ≤ b, and graph (c) is for simple bound constraint ξ − ≤ xˆ ≤ ξ + . 7) if and only if there exists the (final) dual decision vector zˆ ∈ ˆ R m+dim(b)+n such that Qˆ xˆ − H T zˆ + qˆ = 0 and H xˆ = PΩ (H xˆ − zˆ ). 2 Dual-Neural-Network Design 41 ˆ dual decision vector zˆ ∈ R m+dim(b)+n such that Qˆ xˆ − H T zˆ + qˆ = 0 and ⎧ ⎪ ˆ i = ζi− if zˆ i > 0, ⎨[H x] if zˆ i < 0, [H x] ˆ i = ζi+ ⎪ ⎩ − + ˆ i ≤ ζi if zˆ i = 0.
4, at zˆ ∗ , we have the inequality ˆ T zˆ ∗ ≥ 0 ∀˜z ∈ Ω. , (˜z − H MH T zˆ ∗ + H M q) that PΩ H MH T zˆ − H M qˆ − zˆ − H MH T zˆ ∗ + H M qˆ zˆ ∗ ≥ 0. 1 that, for all ˆ zˆ ∈ R m+dim(b)+n , PΩ (z˜ˆ − zˆ ) − H MH T zˆ ∗ + H M qˆ z˜ˆ − zˆ − PΩ (z˜ˆ − zˆ ) ≥ 0. 15) zˆ ∗ + z˜ˆ − zˆ − PΩ (z˜ˆ − zˆ ) ≥ 0. 16) T Third, adding Eq. , g˜ = PΩ (z˜ˆ − ˜ zˆ ) − zˆ , Eq. 16) is thus reformulated as g˜ + H MH T zˆ − zˆ ∗ T zˆ − zˆ ∗ + g˜ ≤ 0 and, subsequently, as zˆ − zˆ ∗ g˜ + g˜ T H MH T zˆ − zˆ ∗ ≤ − g˜ T 2 − zˆ − zˆ ∗ H MH T zˆ − zˆ ∗ .
2 about the primal and dual QP problems. 9) ˆ −1 . Here, where, for notational simplicity, we use M ∈ R n×n to denote the inverse Q ˆ we may assume that Q (and M) is diagonal or we have the analytical form of M for faster computation. The following three examples are given for a better understanding of such an assumption. • In the minimum-velocity-norm and minimum-acceleration-norm motion planˆ is the identity matrix I , and so is M. ning [7, 10], the coefficient matrix Q • In the bi-criteria control of minimum-effort and minimum-energy motion planning [7, 17], the coefficient matrix Qˆ is a diagonal matrix of the form of diag(αI, ˜ 1 − α) ˜ with α˜ ∈ (0, 1) here being a weighting factor, and M is thus also diagonal and easily computed as diag(I /α, ˜ 1/(1 − α)).
