By Seyed Ehsan Shafiei
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Extra info for Advanced Strategies for Robot Manipulators
These angles are measured directly or indirectly. The angle θ ( s ) is measured dircetly by the projection on the image plane ZS1 OS1 YS1 (relation 78) and q(s) is computed from the projection on the image plane ZS2 OS2 YS2 (relation 79). ,1996) was be developed (see Appendix 2). 46 Advanced Strategies for Robot Manipulators Proposition: The closed-loop hyper redundant arm system is stable if the control law is • Fθ ( s , t ) = − kθ1 ( s ) ⋅ eθ s ( s' , t ) − kθ2 ( s ) ⋅ eθs ( s' , t ) (89) ] [ Fq ( s , t ) = − kq1 ( s ) ⋅ tg −1 (cosθ s ( s' , t )) ⋅ tgqs ( s'' , t ) − q d ( s ) (90) where s'∈ [ 0 , l' ] , s''∈ [ 0 , l'' ] and kθ1 ( s ), kθ2 ( s ), k q1 ( s ) are positive coefficients of the control law for all s ∈ [ 0 , l ] .
In this approach the nonholonomic constraints do not appear in TPBVP directly, unlike • the method given in (Mohri et al. 2001; Furuno et al. 2003). This approach allows completely nonlinear states and control constraints treated • without any simplifications. The obtained results illustrate the power and efficiency of the method to overcome the • high nonlinearity nature of the optimization problem, which with other methods, it may be very difficult or impossible. In this method, boundary conditions are satisfied exactly, while the results obtained by • methods such as Iterative Linear Programming (ILP) have a considerable error in final time (Ghariblu & Korayem, 2006).
Conclusion In this chapter, modelling and control of mechanical manipulator had been studied. First, kinematic and dynamic modelling of flexible link, flexible joint and mobile manipulators have been considered. Then, optimal control of a flexible mobile manipulator in point-topoint motion had been formulated based on the open-loop optimal control approach. The first objective of the chapter is to state the dynamic optimization problem under a quite generalized form in order to be applied to a variety of situations with any guess objective functions for the optimality solution.
Advanced Strategies for Robot Manipulators by Seyed Ehsan Shafiei