<p>The realization of automatic dredging of underground drainage pipes is of great significance for ensuring personnel safety and improving economic benefits, and the dredging robot is the preferred solution, but the complex working environment of the drainage pipes poses a severe test to the dredging robot, which requires the robot to fulfil excellent work stability and high motion accuracy at the same time, and relevant problems need to be solved urgently. In order to solve these two difficulties, a new-type dredging robot is designed and the precise trajectory planning is realized in this paper. First, the structure of the robot is designed and the physical prototype is built. Second, based on the screw theory and quaternion, an innovative forward kinematic and inverse kinematic modeling algorithm for robots is proposed. The algorithm is computationally convenient and eliminates singularities, avoids the risk of robot downtime at the singularity, solves the difficulty of work stability, and can be used to realize the stable motion of the robot over a wide angle range. Third, on the basis of kinematic analysis, a trajectory planning method based on quaternion is proposed, which has extremely high accuracy and can be used to realize the precise position control of the end effector, which solves the problem of motion accuracy. Finally, the correctness and accuracy of the kinematic modeling and trajectory planning methods in this paper are verified by trajectory planning experiments.</p>