Figure 8.

Trajectory Specific Dimensionality Analysis (TSDA) computed on Legendre basis synergies (order 7) actuating the compliant kinematic chain system, the task was to reach position P_d = (0.5, 0.2) in a time span of 2.5 s, the initial condition was a nearly fully extended kinematic chain. (A) Four benchmark trajectories [T₁, … T₄] traced by the mass under synergy control—synergy weights were computed from via-points using a least-squares approach; (B) Hinton diagram of the weight matrix (ellipse size is the magnitude, a dark region denotes positive weight and white region denotes a negative weight). (C) The normalized empirical HSV magnitudes for the non-linear reformulated composite systems for each trajectory. For a threshold magnitude choice of t_r = 0.935, represented by the solid black line, the DR was computed as = [1, 2, 2, 2]. The straight line trajectory T₁ has minimum dimensionality as measured by the HSV magnitudes.