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This paper investigates mobility strategies of mobile robots to improve the lifetime of a mobile sensor network with energy harvesting capability. The network lifetime problem is formulated as a nonlinear non-convex optimization problem, which is solved distributively by a series of convex approximations and a novel saddle-point computation algorithm. The convergence of the proposed method is guaranteed. Computer simulations showed quick convergence to the optimal solution in most cases, and verified the use of mobility for energy efficiency by showing its significant improvement to the network lifetime and relatively low cost in mobility.