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Achieving Smoothness: Trajectory Planning Through Flatness Techniques
Here are some videos showcasing the algorithms I developed during my internship at The Systems and Control Centre (in French, Centre Automatique et Systèmes, or CAS) at MINES ParisTech.
In the first video, a straightforward example of open-loop control is explored. The physical parameters of a disc rolling on a moving surface are first measured. Based on these measurements, a trajectory is designed to guide the disc smoothly from an initial resting position to a final resting position.
The other two videos demonstrate the application of the Flatness concept to create trajectories that minimize residual oscillations in mechanical systems. These examples include systems with finite vibration modes, such as a suspended crane, and those with infinite vibration modes, like a water tank.
The trajectories moving to the right side of the screen follow carefully planned paths. In contrast, those heading to the left follow an arbitrary, default rail displacement speed. You’ll see a noticeable difference in the levels of residual oscillation when comparing movement in both directions.
The whole playlist can be found here.
Optimizing Train Movement: A Study on Non-Oscillating Trajectories
In my Bachelor's thesis at the Universidade de São Paulo, I explore trajectory planning methods designed to eliminate residual oscillations in systems with a finite number of decoupled vibration modes. Simple examples, such as the n-pendulum system, are used to introduce these techniques and to establish the hypotheses and mathematical proofs that demonstrate their applicability.
The application of these techniques to the longitudinal dynamics of trains is then presented, demonstrating the potential to incorporate an additional feature: the minimization of a cost function that balances fuel consumption with the reduction of shock forces between wagons during movement.
Reports:
PRe.pdfTCC_USP_english.pdfPage updated
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