Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators

Redundant manipulators have some advantages when compared with classical arms because they allow the trajectory optimization, both on the free space and on the presence of obstacles, and the resolution of singularities. For this type of arms the proposed kinematic control algorithms adopt generalized inverse matrices but, in general, the corresponding trajectory planning schemes show important limitations. Motivated by these problems this paper studies the chaos revealed by the pseudoinverse-based trajectory planning algorithms, using the theory of fractional calculus.