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.
This work concerns the modelling and experimental verification of the highly nonlinear friction behavior in positioning on the nanometer scale. The main goal of this work is to adjust and identify a simple dynamic friction model which allows a model-based estimation of the friction force in combination with the system inertia against displacement. Experiments in the pre-sliding and sliding friction regimes are conducted on an experimental setup. A hybrid two-stage parameter estimation algorithm is used to fit the model parameters based on the experimental data. Finally, the identified friction model is utilized as a model-based feedforward controller combined with a classical feedback controller to compensate the nonlinear friction force and reduce tracking errors.
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