Understand Animal Locomotion Using Template Models

Jerboa Gait Transition Study

Egyptian jerboas are non-cursorial rodents that live in Arabia, Africa, and Asia. In the previous research, we found that the evolution of bipedalism of Egyptian jerboas enhanced their predator evasion ability, and they were able to frequently switch between gait rather than other desert rodents. To investigate the underlying mechanisms of jerboas’ frequent gait transitions, we first made the assumptions that jerboas would not shift their center of mass (COM) during locomotion and the COM located at the midpoint of their eyes and tail bases since their legs were almost massless. Then we extracted the trajectories of the torso of jerboas as well as the leg angles using a markless-position-tracking neural network called DeepLabCut (DLC). Based on the assumptions we made, we applied an extended SLIP model to reproduce the motion of jerboas.

In the above figures: (A) shows how the proposed model relates to a jerboa. The COM location is approximated as the midpoint between the eye and the tail-base. The leg angles are estimated by the orientation of the line segments connecting the COM to the feet. (B) illustrates the proposed SLIP model with passive swing leg motion. There are four continuous states (shown in blue) including the position of the torso (x , y) as well as the leg angles (α_l, α_r). Model parameters are highlighted in red, including total body mass, m, uncompressed leg length, l_o, gravity, g, and leg stiffness, k. Adding a torsional spring to a SLIP model enables motion of passive swing leg. The rotational speeds of both swing legs are determiution of bipedalism of Egyptian jerboas enhanced their predator evasion ability, and thened by ω and the neutral leg angle are φ_l and φ_r respectfully. Note that the neutral leg swing angle for the right leg, φ_r, is different from that of the left leg, demonstrating an uncoupled model. A simplified version of the model showing the range of the swing leg motion is also shown in the top-right corner.

The the apex transitions, touchdowns, and liftoffs for one stride of four different gait patterns are demonstrated by jerboas on the left, with inset gait diagrams showing footfall patterns, the corresponding simulated gait patterns using our model are shown on the right. The right leg of jerboa is shown in white and the left leg is in the same color as the corresponding gait branches shown in the inset gait diagram. The left leg of the model is shown in grey and the right leg is in white. (A) shows hopping in which both feet strike and lift off simultaneously; (B) shows skipping with overlapping but non-simultaneous foot strikes; (C) shows asymmetrical running with two different aerial phases; (D) shows symmetrical running which contains two aerial phases with approximately the same duration. Blue curved arrows indicate leg touchdown (t_td) and the gray curved arrows denote liftoff events (t_lo).

Horse Gait Study

Instrumented Horse Treadmill at Equine Sports Medicine Zurich

This work presents a simplistic passive dynamic model that is able to create realistic quadrupedal walking, tölting, and trotting motions. The model is inspired by the bipedal spring loaded inverted pendulum (SLIP) model and consists of a distributed mass on four massless legs. Each of the legs is either in ground contact, retracted for swing, or is ready for touch down with a predefined angle of attack. Different gaits, that is, periodic motions differing in interlimb coordination patterns, are generated by choosing different initial model states. Contact patterns and ground reaction forces (GRFs) evolve solely from these initial conditions. By identifying appropriate system parameters in an optimization framework, the model is able to closely match experimentally recorded vertical GRFs of walking and trotting of Warmblood horses, and of tölting of Icelandic horses. In a detailed study, we investigated the sensitivity of the obtained solutions with respect to all states and parameters and quantified the improvement in fitting GRF by including an additional head and neck segment. Our work suggests that quadrupedal gaits are merely different dynamic modes of the same structural system and that we can interpret different gaits as different nonlinear elastic oscillations that propel an animal forward.

Experimentally recorded vertical GRFs (dotted lines 61 std.) are compared to forces predicted by the headless model (solid lines, shown on the left) and to those predicted by the model with an articulated head and neck (solid lines, shown on the right). Shown are the results for walking (top), tolting (center), and trotting (bottom). Both models correctly predict the foot-fall pattern, timing, and the general shape of the force curves for all gaits. Quantitatively, a better fit is produced by the headed model, especially for the hind limbs at walk. RH, RF, LH, and LF stand for right hind, right fore, left hind, and left fore, respectively.

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