Task Space Trajectory Planning for Robot Manipulators to Follow 3-D Curved Contours

The demand for robots has increased in the industrial field, where robots are utilized in tasks that require them to move through complex paths. In the motion planning of a manipulator, path planning is carried out to determine a series of the positions of robot end effectors without collision. Therefore, it is necessary to carry out trajectory planning to determine position, velocity, and acceleration over time and to control an actual industrial manipulator. Although several methods have already been introduced for point-to-point trajectory planning, a trajectory plan which moves through multiple knots is required to allow robots to adapt to more complicated tasks. In this study, a trajectory planning based on the Catmull-Rom spline is proposed to allow a robot to move via several points in a task space. A method is presented to assign intermediate velocities and time to satisfy the velocity conditions of initial and final knots. To optimize the motion of the robot, a time-scaling method is presented to minimize the margin between the physical maximum values of velocity and acceleration in real robots and the planned trajectory, respectively. A simulation is then performed to verify that the proposed method can plan the trajectory for moving multiple knots without stopping, and also to check the effects of control parameters. The results obtained show that the proposed methods are applicable to trajectory planning and require less computation compared with the cubic spline method. Furthermore, the robot follows the planned trajectory, and its motion does not exceed the maximum values of velocity and acceleration. An experiment is also executed to prove that the proposed method can be applied to real robotic tasks to dispense glue onto the sole in the shoe manufacturing process. The results from this experiment show that the robot can follow the 3-D curved contour in uniform speed using the proposed method.