Asymmetric motion profile planning for nanopositioning and nanomeasuring machines

Abstract

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.

Algorithm for a high precision contactless measurement system

“…Both components are fixed on a base panel. The homodyne interferometer uses a stabilized He-Ne laser as beam source and realizes a position resolution on sub nanometer scale [9] [10]. Beside the Michelson interferometer a four quadrant diode (4QD) unit is integrated.…”

“…Figure 8a shows the sinusoidal motion of the tracked kinematics and Figure 8b shows the resulting tracking error of the laser beam. The dynamical set-points of the kinematics were generated by an analytic fourth order path planning algorithm, which is able to plan motions with arbitrary initial and final velocities [10]. The kinematics carried out a sinusoidal motion with amplitude of 100 mm and a frequency of 0.4 Hz.…”

Control of nanopositioning and nanomeasuring machines with a modular FPGA based data processing system

“…Thereby, it is ensured that the demanded target positions can be realized by the NPMM. A detailed description of the used algorithm can be found in [12].…”

A time-optimal isotropic Cartesian trajectory generator with limited acceleration magnitude

“…Many of them focus on time-optimal trajectories for one-dimensional problems or they decompose a multi-dimensional problem into unsynchronized or synchronized axis-specific problems [1]- [4]. Another approach is to split the task and generate a multi-dimensional path through the workspace (or the path is already known) and a one-dimensional velocity profile along this path [5]- [9]. Much effort is also put on obstacle avoidance [10], [11].…”