Final answer:
Augustus avoided posthumous power struggles by setting up his stepson Tiberius as his successor, ensuring he received powers from the Senate, and consolidating the Roman Empire through a facade of republican governance.
Step-by-step explanation:
To avoid a violent struggle for supreme power after his death, Augustus arranged for a political successor, his stepson Tiberius, to receive power from the Senate. Despite the absence of an official emperor position or a tradition of hereditary rule, Augustus worked to ensure a smooth transition. He used traditional republican structures to appoint Tiberius as an accomplished military leader and proconsul with senatorial support, thereby avoiding potential conflicts and preserving the Roman Empire's stability after his demise.