Kinematics correction algorithm for the LHDS of a legged robot with semi-cylindrical foot end based on V-DOF

The semi-cylindrical foot end of a legged robot is suitable for the robot movements in complex environments and is the most commonly used foot end type. However, its actual contact point will deviate from the ideal contact point when it touches the ground to support the robot or when it slips due to its specific structure, resulting in trajectory deviation. To solve this deviation problem between the actual and desired contact positions of the robot foot end, this study proposes a novel kinematics correction strategy for a legged robot with a semi-cylindrical foot end based on a virtual degree of freedom (V-DOF). Two sampling systems are studied as follows. First, the forward and inverse kinematic solutions are derived when the foot end is regarded as a point; then, the root joint trajectory deviation of the robot’s leg is analyzed, and the deviation value of the foot end in motion is obtained when the robot body is at different angles with the contact surface. Further, considering the tangential relationship between the semi-cylindrical foot end and the contact surface, the foot end is considered as a rod that is always perpendicular to the contact surface. Thus, a semi-cylindrical foot end correction strategy based on V-DOF is established. In addition, the deviation curves when the foot end slips are derived, and it is theoretically proven that the correction algorithm also applies to the slipping of the foot end. Finally, a co-simulation model and an experimental platform of the leg hydraulic drive system (LHDS) are used for simulation and experimental verification. The results indicate that the proposed strategy can effectively reduce the root joint trajectory deviation when the legged robot body is at different angles with the contact surface or when the foot end is slipping. The above research results can provide important reference and experimental basis for the legged-motion control with any DOF equipped with such a type of foot end.