Exempel på spline

• As the cubic splines for and are constructed, these functions are found in piecewise polynomial form.

• As an example of such a scheme, we consider the scheme generating the double-knot cubic splines.

• Using splines, a parameter trajectory model is defined by means of the position of the basis functions and the order of the polynomial.

• As expected, the more the splines are used, the smaller the minimum performance indices are, but at the same time, the more the computational burdens.

• The parameterisation concerns the generalised coordinates that are approximated using cubic splines.

• The biped joint coordinates are approximated by cubic splines functions connected at uniformly distributed knots along the motion time.

• However, twice differentiable property of cubic splines was not a requirement in our approach.

• They found that higher-dimensional splines offered significant improvements over standard discretization methods (although for dimensions higher than three, their algorithms are still very time-consuming).

• The viscosity function was then calculated from these splines.

• The control methods were evolved using genetic programming, once a suitable framework had been set up using splines to compute smooth trajectories.

• The two probably best-known and most often applied radial basis functions are called multiquadrics and thin-plate splines, respectively.

• An approach that was considered was to use interpolation splines to form a smoothed edge.

• The knots for the splines were determined from inspection of the hazard function for males and females combined.

• In each case, complex forms are first resolved into a minimum network of simple splines.

• Figure 5 shows the positions of the real robot controlled by the inverse dynamic strategies with a ramp and splines references.