Figure 10.

Running gait that minimizes the work cost for the springless telescoping biped at V = 0.39 and D = 1.38, (a–c) in the presence of bounds on the leg force rates (−3 ≤ Ḟ ≤ 3) and (d–f) in the presence of bounds on the second derivative of forces (−100 ≤ F¨ ≤ 100). Both optimizations assumed a leg force bound as well (F ≤ 3). It is found that the leg force as a function of the leg compression, while nonlinear, is not far from linear on average, suggesting that the so-called linear spring-like leg behaviour at optimality requires no springs.