Constructibility of AdS Supergluon Amplitudes.

We prove that all tree-level n-point supergluon (scalar) amplitudes in AdS_{5} can be recursively constructed, using factorization and flat-space limit. Our method is greatly facilitated by a natural R-symmetry basis for planar color-ordered amplitudes, which reduces the latter to "partial amplitudes" with simpler pole structures and factorization properties. Given the n-point scalar amplitude, we first extract spinning amplitudes with n-2 scalars and one gluon by imposing "gauge invariance," and then use a special "no-gluon kinematics" to determine the (n+1)-point scalar amplitude completely (which in turn contains the n-point single-gluon amplitude). Explicit results of up to 8-point scalar amplitudes and up to 6-point single-gluon amplitudes are included as Supplemental Material.

On the energetics of quadrupedal running: predicting the metabolic cost of transport via a flexible-torso model.

In this paper, the effect of torso flexibility on the energetics of quadrupedal bounding is examined in a template setting. Two reductive sagittal-plane models, one with a rigid, non-deformable torso and one with a flexible, unactuated torso are proposed. Both models feature non-trivial leg mass and inertia to capture the energy associated with repositioning the legs after liftoff as well as the energy lost due to impacts. Bounding motions that minimize the cost of transport are generated for both models via a simple controller that coordinates leg recirculation. Comparisons reveal that torso compliance promotes locomotion efficiency by facilitating leg recirculation in anticipation of touchdown at speeds that are sufficiently high. Furthermore, by considering non-ideal torque generating and compliant elements with biologically reasonable efficiency values, it is shown that the flexible-torso model can predict the metabolic cost of transport for different animals, estimated using measurements of oxygen consumption. This way, the proposed model offers a means for approximating the energetic cost of transport of running quadrupeds in a simple and direct fashion.

Quadrupedal bounding with a segmented flexible torso: passive stability and feedback control.

In this paper, the implications of torso flexibility on the dynamics of quadrupedal running are examined in a template setting. In the same vein with the spring loaded inverted pendulum, a reductive sagittal-plane model with a segmented flexible torso and compliant legs is introduced to capture the dynamics of bounding in the presence of torso flexibility via a minimum number of variables and parameters. Numerical return map studies of the system in dimensionless setting reveal that a large variety of cyclic bounding motions can be realized passively, through the natural interaction of the model with its environment. Despite the simplicity of the model, the resulting motions correspond to torso bending movements that resemble those in galloping mammals without explicit reliance on the fine structural and morphological details. Furthermore, for certain combinations of the system parameters--in particular the torso and leg relative stiffness--self-stable bounding motions emerge. The implications of the existence of such self-stable bounding orbits to control design are also discussed and a hybrid control law is derived that is capable of stabilizing the system as it encounters significantly large disturbances using only a single actuator located at the torso joint.