Advances in Robot Control: From Everyday Physics to by Suguru Arimoto (auth.), Professor Sadao Kawamura, Mikhail

By Suguru Arimoto (auth.), Professor Sadao Kawamura, Mikhail Svinin Doctor (eds.)

This quantity presents a distinct selection of papers written in honor of the seventieth birthday of Suguru Arimoto who has lengthy been well-known as a pioneer within the box of robotic keep watch over. quite a few his learn is mirrored during this ebook, inclusive of contributions from best specialists within the box, who've additionally been heavily linked to Suguru Arimoto at a variety of levels in his uncommon profession. The ebook is construct round issues: the physics-based robotic regulate for dealing with the so-called daily physics difficulties on one hand, and the problem of reproducing appealing, human-like hobbies nonetheless. those topics outlined a lot of Arimoto’s learn within the box of robotic keep an eye on and are the cornerstones of his belief of human robotics. subject matters coated within the ebook handle usual movement and adaptive keep watch over of robotic manipulators, visible servoing, passivity-based and iterative studying keep watch over, synthetic potentials for nonholonomic structures, strength keep an eye on of haptic units and muscle-activated platforms, modeling and research of human-like pursuits in achieving and greedy initiatives. every one bankruptcy is self-contained and treats the topic cohesively and intensive. This quantity will offer a major reference for graduate scholars and researchers, in addition to for engineers and scientists operating within the box of robotics.

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First, we refer to the underdetermined linear system (7). t. time, we obtain: J (¯ q )¨ ¯q + J˙ (¯ q )¯q˙ = 0. (16) This equation admits the following solution: + ¨ ¯ q ) − J (¯ ¯q = β n(¯ q )J˙ (¯ q )¯q˙ (17) where β denotes an arbitrary small value, and (◦)+ stands for the pseudoinverse. The representation decomposes the joint acceleration into two orthogonal components. This is evident from the fact that the pseudoinverse component is known to be orthogonal to the null space component. The last equation can be split into two parts, to obtain second differentials of joint motion and path motion, respectively: and ¨ = βn(¯ q q ) − J T (q)J −1 q )J˙ (¯ q )¯q˙ ∗ (¯ (18) q¨∗ = β det J (q) + tT∗ (q∗ )J −1 q )J˙ (¯ q )¯q˙ , ∗ (¯ (19) where J ∗ (¯ q ) ≡ J (q)J (q) + t∗ (q∗ )tT∗ (q∗ ).

Robot application tasks quite often also require the solution of the so-called inverse problem, in terms of inverse kinematics or inverse dynamics in task coordinates [1]. The formal solution to the problem is not as straightforward as might be expected. For nonredundant structures, the inverse problem has been most often tackled by employing the inverse of the Jacobian matrix. Though, as recognized at an early stage [2], the ill-conditioning of the inverse problem at and around kinematic singularities can destabilize the controls.

Stability is Dragomir N. 5 2 x [m] Fig. 9. Approaching a stationary point singularity, with constant twist magnitude, joint friction and kinematic closed-loop control. not guaranteed, though, at a stationary point singularity. We performed a simulation of constant twist magnitude motion through a stationary point, similar to that in Fig. 4. The results are shown in Fig. 9. It is apparent that when the end-tip passes close by the singularity, an abrupt, inadmissible jump in the velocity occurs. 2 Singularity-Consistent Dynamic Controller Dynamic controller design is based on the singularity consistent parameterization of the equation of motion (23).

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