Stability is a prerequisite for legged robots to execute tasks and traverse rough terrains. To guarantee the stability of quadruped locomotion and improve the terrain adaptability of quadruped robots, a stability-guaranteed and high terrain adaptability static gait for quadruped robots is addressed. Firstly, three chosen stability-guaranteed static gaits: intermittent gait 1&2 and coordinated gait are investigated. In addition, then the static gait: intermittent gait 1, which is with the biggest stability margin, is chosen to do a further research about quadruped robots walking on rough terrains. Secondly, a position/force based impedance control is employed to achieve a compliant behavior of quadruped robots on rough terrains. Thirdly, an exploratory gait planning method on uneven terrains with touch sensing and an attitude-position adjustment strategy with terrain estimation are proposed to improve the terrain adaptability of quadruped robots. Finally, the proposed methods are validated by simulations.