Power optimization of planar redundant manipulator moving along constrained-end trajectory using hybrid techniques

Optimum trajectory planning for a planar redundant manipulator which consumes minimum power is considered in this paper. The equations of motion for the manipulator are derived in matrix form using Lagrange Equation. Two hybrid optimization algorithms with constrained variables during the search have been presented and compared to design an optimal trajectory for planar redundant manipulator based on minimum power to be consumed. Two trajectories with the same initial angular displacement of the manipulator joints and two different angular positions at the end of the trajectories are studied. Both the hybrid technique of the Genetic Algorithm (GA) and the constrained Fmin function (GA-Fmincon) and the hybrid genetic algorithm with the pattern search (GA-PS) subjected to the same constraints give the same results for the trajectory that ends with angular displacements of (π/2, 0, 0) rad with trivial differences in the power values at any arbitrary mission period. For the second trajectory, which ends with angular positions of (1, 1, 1) rad, the GA-PS gives a penalty function of smaller value.