By Leondes, Cornelius T

ISBN-10: 0120127393

ISBN-13: 9780120127399

Meant for engineers, electric engineers and regulate engineers, this e-book presents insurance of the newest advances in robot platforms, from the appliance of neural networks to robotics

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Meant for engineers, electric engineers and regulate engineers, this booklet presents insurance of the most recent advances in robot platforms, from the applying of neural networks to robotics

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**Additional info for Advances in robotic systems. Part 1 of 2**

**Example text**

For the proof of theorem, see A p p e n d i x B . The update of χ based on χ determined by (17) guarantees the convergence as long as χ exists. Note however that the Liapunov function V denned by (12) is a nonlinear function of χ and may have local minima where the following equation holds: dV (•^)' = -(^ί + *') = 0 (18) 23 APPLICATIONS OF NEURAL NETWORK TO ROBOTICS If y φ 0, (17) results in a large norm of x . This explosion of χ near a local minimum is referred to as a jumping phenomenon. T h e jumping is a useful phenomenon for escaping from a local minimum but it should be controlled to curtail jumping which goes beyond the domain of the input space and to avoid jumping which wanders around the same local minimum.

In order to reduce the error to desirable bounds, r Bassi and Bekey [4] propose to use feedback. Specifically, the} propose to use, recurrently, an optimal estimate of the Cartesian trajectory in order to keep the end effector position within predetermined b o u n d s . T h e technique basically consists of the following steps. (1) A n optim u m trajectory function is obtained. Optimality is used to select among the infinity of possible trajectories which connect any two given points along the trajectory, and may be based on such criteria as minimum time, minimum acceleration or minimum jerk, while satisfying constraints.

Given the desired joint configuration, it is now necessary to compute the torques to b e applied at the joints to drive the arms, legs or robot manipulators to the desired orientation. Gener- ally, the desired motions will be subject to constraints or performance criteria, such minimum overshoot, minimum energy or minimum time. T h e computation of the necessary torques requires consideration of such parameters as inertia and damping. In view of the fact that the arm segments are coupled, the inertia matrix is not diagonal and the dynamical equations are highly nonlinear.

### Advances in robotic systems. Part 1 of 2 by Leondes, Cornelius T

by William

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