To ensure that each joint of redundant robot manipulators can return to its initial state when completes a closed-path tracking task, a repetitive motion planning (RMP) scheme is presented. On the basis of a quadratic programming (QP) framework, this RMP can be equivalently converted into a linear-variational-inequality (LVI) problem, and then into a piecewise linear projection equation (PLPE). In this paper, three novel numerical methods (i.e., M3, M5 and M6) and three traditional numerical methods (i.e., 94LVI, E47 and M4) are exploited, analyzed, and compared to solve PLPE, as well as RMP. The convergence of M5 method is theoretically proved, and that of M3 and M6 methods is analyzed by simulations. Moreover, comparative simulations of two complex path tracking tasks performed on a PUMA560 robot manipulator further verify the feasibility and effectiveness of the proposed numerical methods.