Minimum time on-line joint trajectory generator based on low order spline method for industrial manipulators

In this paper, we propose the use of a low order polynomial method named 3-Cubic method to generate minimum time on-line joint trajectory for an industrial manipulator. A 3-Cubic Spline between two end points consists of a set of three cubic splines, which not only give an analytical solution to minimize travel time with velocity, acceleration and jerk constraints but also provides the continuity till second derivative of position (i.e. acceleration). This results in a position trajectory being dynamically balanced. This leads to the generation of a new type of trajectory named 3-Cubic Linear Segment with Trapezoidal Transition (3CLSTT) trajectory. In this trajectory generation, duration of constant acceleration/deceleration and constant velocity phases are calculated according to the requirements of maximum limiting values of velocity and acceleration thus traversing the trajectory in minimum possible time. Wandering (undershoot/overshoot) is completely eliminated in the resulting trajectories with limited computational effort. (C) 1999 Elsevier Science B.V. All rights reserved.