Planning smooth trajectories is crucial in the most advanced robotic applications in industrial environments. In this paper two novel trajectory planning methods for robotic manipulators are introduced, named “545” and “5455”. Both methods are based on an interpolation of a sequence of via points using a combination of 4th and 5th order polynomial functions. These techniques allow to obtain a continuous-jerk trajectory for improved smoothness and minimum excitation of vibration. By using the “545” method, null jerk at initial time can be achieved, while with the “5455” method one can impose an arbitrary value of jerk at both the first and the last via-point. The outcome of both methods is the optimal time distribution of the via points, with respect to a predefined objective function. Results are provided for a 3 d.o.f. Cartesian manipulator, but the techniques may be applied to any industrial robot.

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