The Three-Cubic Method: An Optimal Online Robot Joint Trajectory Generator under Velocity, Acceleration, and Wandering Constraints

Abstract

An original method called the three-cubic method is proposed to generate online robot joint trajectories interpolating given position points with associated velocities. The method is based on an acceleration profile composed of three cubic polynomial segments, which ensure a zero acceleration at each intermediate point. Velocity and acceleration continuity is obtained, and this three-cubics combination allows the analytical solution to the minimum time trajectory problem under maximum velocity and acceleration constraints. Possible wandering is detected and can be overcome. Furthermore, the analytical solution to the minimum time trajectory problem leads to an online trajectory computation.

Real-time 3-D path generation method for a robot arm by a 2-D dipole field

“…Since lifesupport robots must be able to accomplish a given task in dynamic environments, on-line path planning method is indispensable. So, various on-line path planning methods were proposed [3], [4].…”

A Novel Trajectory Generation Method for Robot Control

“…Most similarly there are Spline-based solutions [1,[4][5][6][7][8][9], against which our methods must "compete". The original DMP framework, on the other hand, contains several aspects which are different from our new approach (despite the fact that our approach was partly derived from DMPs).…”

“…Two fundamental methods (and many variations thereof) exist, which address these demands to different degrees. In a somewhat simplified view one can broadly state that Splines (and other lower order polynomials) are very well suited for via-point control [1,[4][5][6][7][8][9], whereas trajectories generated by a dynamical systems approach (dynamic motion primitives, DMPs [10][11][12][13]) are smooth and robust against perturbations.…”

Path planning strategy design under the experience of mobile robot navigation

“…If there are no obstacles on the way to the target spot, the straight line locomotion would be the best choice. The path from start point to the target point may be inserted some control points [12]; the control points are used for optimizing the motion control, saving energy, and reducing processing time. It is, however, that the control points are selected for saving energy or saving processing time.…”