Smooth Static Walking for Quadruped Robots based on the Lemniscate of Gerono

In the research of quadruped robots, stability is a very important consideration for gait design. When the robots have symmetrical structure, stability can be easily guaranteed. However, when the robots are carrying some additional devices or payloads unevenly, the position of the center of gravity (COG) may deviate from the geometrical center, which makes it a challenging task to guarantee stability. To handle this, it is of great significance to improve the stability margin during gait design. To this end, a smooth static walking gait with the maximum stability margin is developed in this paper. An algorithm of COG trajectory optimization based on the lemniscate of Gerono is proposed. The advantage of this algorithm is that the COG trajectory is smooth and continuous at any order, which avoids abrupt changes in velocity or acceleration of the robot during walking. The two parameters in the lemniscate are the main tuning parameters. According to the size of the robot, the algorithm can automatically calculate the optimal parameters (adjust the shape of the Gerono lemniscate curve) and balance the relationship between the step size and the stability margin during the robot movement. Simulation results demonstrate the effectiveness of the proposed method, and we use a mass block experiment to prove the insensitivity of the gait algorithm to the position of the COG.