Figure 4.

Trajectory Specific Dimensionality Analysis (TSDA) for comparing the Fourier and Legendre polynomial basis temporal synergies actuating the tethered mass system, tracing the benchmark trajectories [T₁, … T₄]. The synergy training is carried out using least-squares and full-dimensional inverse dynamics—The obtained weight matrices for the four trajectories are represented as Hinton diagrams (ellipse size is the magnitude, a dark region denotes positive weight and white region denotes a negative weight) for the (A) Fourier basis of size 2 × 9, and (B) Legendre polynomials of size 2 × 5. The corresponding cumulative normalized HSV magnitudes for (C) Fourier, and (D) Legendre polynomial basis synergies with the threshold t_r = 0.975 represented in both cases by the solid black line. The DR was computed as _fourier = [1, 3, 2, 3], and _legendre = [1, 3, 3, 3]. The straight line trajectory has the minimum dimensionality for both of these synergy bases.