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).
