Foot-end trajectory planning for a hexapod robot using quintic polynomial interpolation through waypoints

To improve the walking stability of a hexapod robot, a foot-end trajectory planning method using quintic polynomial interpolation through waypoints is presented. The main objective is to achieve smooth joint motion at waypoint transitions and to reduce vertical body oscillation during walking. First, an integrated model of the hexapod robot and a three-joint leg is established, and the kinematic relationship between joint angles and foot-end position is derived. Then, waypoint, stride, and continuity constraints are imposed on joint position, velocity, and acceleration to construct a general trajectory planning function based on quintic polynomial interpolation. Finally, an Adams–Simulink cosimulation model is developed, and the proposed method is verified under a triangular gait. The results indicate that the planned trajectory remains smooth when passing through waypoints, with no discontinuities in joint angular velocity or angular acceleration at transition points. Moreover, the robot achieves stable triangular-gait locomotion, while the vertical oscillation of the body is maintained within 1 mm.