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

By Leondes, Cornelius T

Meant for engineers, electric engineers and keep an eye on engineers, this ebook presents assurance of the newest advances in robot structures, from the applying of neural networks to robotics

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Figure 29 shows the simulation result for path planning of a point object with two obstacles. T h e initial path is arbitrarily chosen as a straight line from the initial position to the goal position as shown in Figure 29a). T h e shape of the collision penalty function associated with the obstacles is shown in Figure 2 9 b ) . Notice that, the 56 SUKHAN LEE A N D GEORGE A. BEKEY G o a l position obstacle Initial position Figure 29: Path planning of a point object with two obstacles: a) Initial path b ) 3D view of the collision penalty function c) Trajectories of the via points d) Final path.

Meanwhile, Khatib [18] incorporates the path planning into low level control based on the potential field representation of obstacles to achieve real-time performance. This section presents a massively parallel connectionist network for real-time collision-free path planning [32]. T h e network is based on representing a path as a series of via points or beads connected b y elastic strings which are subject to displacement due to a potential field or a collision penalty function generated b y obstacles.

Thus, with reference to the general dynamics equation ( 3 2 ) , the torque can b e decomposed into terms which represent the Cartesian acceleration, the Coriolis and centripetal torques, the gravitational effects and the torques due to damping. If the gravitational and damping terms are omitted for 38 SUKHAN LEE A N D GEORGE A. BEKEY simplicity, the reduced dynamics equation becomes r ( M , x ) = Μ{θ)3-\θ)[χ - [Η{θ)θ]θ] + τν{θ,θ) (36) which can be decomposed into three terms as follows: τχ(θ,χ0) = τν(θ,θ) Μ(θ)3-\θ)χ0 = τυ(θ,θ) (37) X e ( M ) = -[Η(0)0]β The implementation of these relationships by means of the generalized learning architecture requires some additional computation.