<p>Gliding mammals, such as flying squirrels, exhibit remarkable flight abilities by dynamically controlling their wing membranes (patagia), using their limbs and tail to manoeuvre between trees. They achieve agile and manoeuvrable gliding by adjusting their body and wing shape to control trajectory and stability. While research on bio-inspired drones primarily focuses on avian flight, the aerodynamic implications of whole-body morphing paired with soft membrane deformations in mammalian gliders remain unexplored. To address this, we developed the SquirrelDrone, a bioinspired drone capable of continuously modulating its shape via limb and tail actuation, coupled with passive deformations of its skin-like membrane. This design enables the investigation of how coordinated limb motion and membrane morphing affect aerodynamic forces during flying. Wind-tunnel and flight experiments show that gliding-mammal-inspired morphing significantly improves drone stability, agility, and manoeuvrability, providing a bioinspired framework for understanding how whole-body morphing contributes to flight control in future morphing aircraft.</p>