Trajectory planning is one of the important contents in robot control systems, which plays a key role in improving the robot performance. In order to solve the problem that the robot has larger error when fitting straight line and arc into free curve in Cartesian space, a trajectory planning algorithm with optimal robot impact is proposed. With the maximum bow height error and the maximum acceleration speed as the constraint conditions, the robot trajectory is interpolated by the polynomial velocity control curve and the Adams differential equation. At the same time, the four-element number is used to describe the robot posture, and the spherical linear interpolation method is used to interpolate the posture. Finally, taking IRB2600 industrial robot as the simulation ontology, the algorithm is simulated in Matlab. The results show that the running trajectory of the industrial robot in the error allowable range can be obtained, which proves the validity of this algorithm theoretically.