This paper presents a topology optimization methodology to synthesize cable-actuated, shape-changing, tensegrity systems specified through path generation requirements. Estabished tensegrity topology optimization procedures exist for static structures. For active tensegrity systems, motion characteristics are typically explored after the structural topology is determined. The work presented in this paper extends the established procedure to introduce prescribed motion into the topology optimization. A ground structure approach is used in conjunction with the design space. The topology optimization problem is formulated into a mixed integer linear programming problem. Desired motion is prescribed by identifying trace points in the design space and corresponding paths. The result of this methodology is the creation of a tensegrity system that can achieve shape-change as specified with prescribed paths.