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.

Several kinematic control algorithms for redundant manipulators adopt generalized inverse matrices. In this line of thought, the generalized inverse control scheme is tested through experiments that reveal the difficulties that often arise. Motivated by these problems this paper studies kinematics and dynamics of the trajectory planning scheme. The experiment confirm the nonlinear and chaotic performance of the algorithm and gives a deeper insight towards the future development of superior trajectory control systems.