Morphing quadrotors are capable of adapting to constrained environments through geometric reconfiguration. However, existing systems are limited by mechanical complexity and rigid links, which affect both safety and performance in such environments. In this paper, we propose a strut-actuated tensegrity aerial vehicle that integrates shape adaptation with collision resilience. By incorporating deformable struts and a cable network, our vehicle enables real-time morphological adjustments during flight while maintaining stability. We present a hierarchical planning framework that ensures the entire vehicle remains confined within an icosahedral space, thereby guaranteeing full-body safety. An on-manifold Model Predictive Controller (MPC) is employed to track these optimized trajectories and compensate for inertia shifts during shape deformation. Simulation results validate the effectiveness of the proposed framework, demonstrating its capability to navigate in restricted scenarios.