Minimum Time Kinematic Motions of a Cartesian Mobile Manipulator for a Fruit Harvesting Robot

This paper describes an analytical procedure to calculate the time-optimal trajectory for a mobile Cartesian manipulator to traverse between any two fruits it picks up it. The goal is to minimize the time required from the retrieval of one fruit to that of the next while adhering to velocity, acceleration, location, and endpoint constraints. This is accomplished using a six stage procedure, based on Bellman's Principle of Optimality and nonsmooth optimization that is completely analytical and requires no numerical computations. The procedure sequentially calculates all relevant parameters, from which side of the mobile platform to place the fruit on to the velocity profile and drop-off point, that yield a minimum time trajectory. In addition, it provides a time window under which the mobile manipulator can traverse from any fruit to any other, which can be used for a globally optimal retrieving sequence algorithm.

Planning Continuous-Jerk Trajectories for Industrial Manipulators

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.