Efficient bending and lifting patterns in snake locomotion

We optimize three-dimensional snake kinematics for locomotor efficiency. assume a general space-curve representation of the backbone with small-to-moderate lifting off ground and negligible body inertia. The cost locomotion includes work against friction internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds same types optima as previous Newton-based method. With lifting, few optimal motions prevail. have an s-shaped alternating middle ends at transverse friction. large friction, curling sliding are typical small dissipation, replaced by large-amplitude bending we find local that resemble sidewinding across coefficient space. They always suboptimal motions, average input power 10–100% higher.