## Section: New Results

### Multi-axes control systems for machining

Participants : Olivier Gibaru, Marouene Oueslati.

Nowadays, the adaptation of industrial robots to carry out high-speed machining operations is strongly required by the manufacturing industry. This new technology of machining process demands the improvement of the overall performances of robots in order to achieve an accuracy level close to that realized by machine-tools. In [28] , we present a method of trajectory planning adapted for continuous machining by robot. Our methodology is based on a parametric interpolation of the geometry in the operational space. FIR filters properties are exploited to generate the tool feedrate with limited jerk. This planning method is validated experimentally on an industrial robot for machining. The geometric trajectories of the end-effector of the robot are based on quintic C^{2} -continuous splines. These splines are calculated according to a new method where we minimize the L^{1} norm of second order derivative of the quintic spline. This method prevents the Gibb's phenomenon. This optimization is a nonlinear problem. It is solved by the use of an efficient local strategy which allows us to calculate exactly all the algebraic solutions. The details of this new method are given in [27] .

All these systems have to be identified or observed. For this, we need to estimate the derivatives up to a finite order of the output of these systems. So, we currently study the optimal parameters to be used so as to define real time derivative estimators with a minimum time-delay and a minimum noisy contribution part. In [58] an analysis of the error due to a corrupting noise is conducted for a new affine derivative estimator. Some upper-bounds on this error are given. A convincing simulation example gives an estimation of the state variable of a nonlinear system when the measured output is noisy.