Jerk-Continuous Trajectories for Cyclic Tasks

Planning smooth trajectories is a crucial task for most advanced robotic applications. Poorly planned trajectories can be inefficient under many aspects, since they might require long execution time and induce unnecessary vibration on the end-effector of the robot as well as high solicitation on its mechanical structure and actuators. In this paper a novel trajectory planning methods for robotic manipulators is introduced, named “5455”. This method is based on an interpolation of a sequence of via points using a combination of 4^th and 5^th order polynomial functions. This technique allows to obtain a continuous-jerk trajectory for improved smoothness and minimum excitation of vibration. Such method allows also to impose an arbitrary value of jerk at the first and last via-point. This feature can be effectively used to produce a smooth trajectory for repetitive tasks, trough an innovative optimization algorithm which is introduced in this paper. Both numerical and experimental results are provided for a 3 d.o.f. Cartesian robot, but the techniques provided here can be applied to any industrial manipulator.