An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal
Fig 1
The simple quadrupedal model used in this paper.
Two point masses sit on massless legs that can extend and contract. The point masses are connected with a rigid trunk. Five morphological parameters are inputs: the mass of the fore and hindquarters (mF and mH, respectively), the trunk length (lB), and the maximum length of the fore and hindlimbs (lFmax and lHmax, respectively). Two kinematic variables are also used as inputs: the stride length (D) and the average horizontal speed (U). From these seven constant inputs, trajectory optimization determines footfall positions (fijk, where i, j and k refer to Fore-Hind, Right-Left and {Trailing contact}-{Leading contact}, respectively) and over twenty temporal variables, including ground reaction forces and their rate of change (Fijk and ), center of mass position and velocity (x and
) and body pitch angle and angular velocity (θ and
). rF and rH are the displacement vectors from the COM to forequarters or hindquarters, respectively. Other notation conventions are described in Table 1.