Page 49 - Textos de Matemática Vol. 43

PATH PLANNING FOR A DOUBLE PENDULUM USING NATURAL SPLINES. . . 37
Figure 3. Spline on torus (thick line) between starting (thin solid) and ending (thin dashed) geodesics a) example 1, b) example 2
Figure 4. Comparing N-spline segments (solid line) and cubic interpolation (dashed line), a) example 1, b) example 2
4.84, respectively. From velocity profiles presented in Fig. 5 one can conclude that depending on boundary conditions either the N-spline or the cubic interpolation appears to be better.
In the third example we check whether satisfactory performance of N-splines on a single interval appears also when we consider splines passing through several intermediate points. As a comparison we use 3 types of X-splines, denoted X1, X2 and X3, which are typically used in robotics for interpolation with continuous velocity, [9]. Note that in the case of the X-splines velocities in the intermediate