AbstractThis article proposes a method for the global optimization of redundancy over the whole task period in a kinematically redundant manipulator. The necessary conditions based on the calculus of variations for integral‐type criteria result in a second‐order differential equation. For a cyclic task, the boundary conditions for conservative joint motions are discussed. Then, we reformulate a two‐point boundary value problem to an initial value adjustment problem and suggest a numerical search method based on the iterative optimization for providing a globally optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of redundancy, we only search parameter values in the parameterized space using the configuration error between the initial and final time. We show through numerical examples that multiple nonhomotopic extremal solutions satisfying periodic boundary conditions exist according to initial joint velocities for the same initial configuration. Finally, we discuss an algorithm for topological liftings of the paths and demonstrate the generality of the proposed method by considering the dynamics of a manipulator.