This paper introduces a novel method for Cartesian trajectory and performance optimization control of kinematically-redundant truss-based manipulators (TBMs), The Virtual Serial Manipulator Approach. The approach is to model complex in-parallel-actuated TBMs as simpler kinematically-equivalent virtual serial manipulators. Standard control methods for kinematically-redundant serial manipulators can then be adapted to the real-time control of TBMs. The forward kinematics transformation can be calculated more efficiently using the equivalent virtual parameters, compared to the computationally intensive in-parallel-actuated forward kinematics transformation. The method is applicable to any TBM whose modules can be modeled as a virtual serial chain. It also handles TBMs constructed of dissimilar modules, and compound manipulators with serial and in-parallel-actuated joints. The method is applicable for any level of kinematic redundancy.