Abstract: Combining the advantages of spherical and quadruped robots, an innovative ball-legged compound mobile robot is proposed, which can adapt to various working environments. In the rolling mode, the linear rolling and roll steering are analyzed to verify the feasibility of robot steering. In the quadruped mode, the coordinates of foot tips are obtained by the complex vector method, and the foot trajectory curve drawn with Matlab is compared with the Adams simulation curve, which verifies the correctness of the theory. Taking the elevation of leg as the objective function, the optimal trajectory of the foot tip is obtained by the non-linear programming algorithm. The centroid projection method is used to analyze the stability of the robot in quadruped walking. A simulation model is established to test the quadruped straight movement, quadruped steering, quadruped climbing and sphere rolling modes. A prototype is manufactured and a series of experiments are conducted to verify the feasibility of the design and various motion modes.