Asymmetric motion profile planning for nanopositioning and nanomeasuring machines
This work presents an analytic fourth-order trajectory planning algorithm, which is able to plan asymmetric motions with arbitrary initial and final velocities. Furthermore, the proposed algorithm is based on a set of quadratic derivates of jerk (djerk) functions and generates continuously differentiable trajectories in jerk, acceleration, velocity, and position under consideration of kinematic constraints in all these kinematical values. The trajectories planned by the algorithm also have time-optimal characteristics, and a synchronization between the three motion axes of the Cartesian coordinate system is ensured by the proposed method. These characteristics make it ideally suited for use as a trajectory planning algorithm in high-precision applications such as nanopositioning and nanomeasuring machines.