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

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.