Chapter 1 Modeling and identity of Serial Robots (pages 1–79): Wisama Khalil and Etienne Dombre
Chapter 2 Modeling of Parallel Robots (pages 81–139): Jean?Pierre Merlet and Francois Pierrot
Chapter three functionality research of Robots (pages 141–183): Philippe Wenger
Chapter four Trajectory iteration (pages 189–239): Moussa Haddad, Taha Chettibi, Wisama Khalil and Halim Lehtihet
Chapter five place and strength regulate of a robotic in a loose or restricted house (pages 241–278): Pierre Dauchez and Philippe Fraisse
Chapter 6 visible Servoing (pages 279–336): Francois Chaumette
Chapter 7 Modeling and keep an eye on of versatile Robots (pages 337–394): Frederic Boyer, Wisama Khalil, Mouhacine Benosman and Georges Le Vey
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Additional info for Modeling, Performance Analysis and Control of Robot Manipulators
3. Solution at the proximity of singular positions We have seen that when the robot is not redundant, the singularities of order one are the solution of det(J) = 0. In the redundant case, they are given by det(JJT) = 0. The higher order singularities are determined based on singular configurations of order one. The passage in the proximity of a singular position is however determined in a more precise way by considering the singular values: the decrease of one or several singular values is generally more significant than the decrease of the determinant.
107b] which is linear in Mj and in the elements of jMSj. The kinetic and potential energy being linear with respect to the inertial parameters, the dynamic model is linear as well in these parameters. 3. 94], the matrix d A–2C(q, q )] is antisymmetric [KOD 84], [ARI 84], which is an interesting dt property for the control; [ e) the dynamic model is linear with respect to the elements of the inertial parameters Mj, jMSj and jJj, called standard inertial parameters. This property will be used in order to identify the inertial parameters and reduce the number of operations of the dynamic model.
General form of the kinematic model Let X = [XpT XrT]T be any representation with respect to R0 of the location of frame Rn, the elements Xp and Xr designating, respectively, the operational position and orientation vectors. 32] the matrices Ωp and Ωr depending on the representation having been chosen for position and for orientation respectively [KHA 02]. 2. 37] Thus, the solution of this problem lies on the inversion of two matrices of smaller dimension. 36], A and C having the dimension (3 × 3) [GOR 84].