  Snake robots composed of alternating single-axis pitch and yaw joints have
many internal degrees of freedom, which make them capable of versatile
three-dimensional locomotion. In motion planning process, snake robot motions
are often designed kinematically by a chronological sequence of continuous
backbone curves that capture desired macroscopic shapes of the robot. However,
as the geometric arrangement of single-axis rotary joints creates constraints
on the rotations in the robot, it is challenging for the robot to reconstruct
an arbitrary 3D curve. When the robot configuration does not accurately achieve
the desired shapes defined by these backbone curves, the robot can have
unexpected contacts with the environment, such that the robot does not achieve
the desired motion. In this work, we propose a method for snake robots to
reconstruct desired backbone curves by posing an optimization problem that
exploits the robot's geometric structure. We verified that our method enables
fast and accurate curve-configuration conversions through its applications to
commonly used 3D gaits. We also demonstrated via robot experiments that 1) our
method results in smooth locomotion on the robot; 2) our method allows the
robot to approach the numerically predicted locomotive performance of a
sequence of continuous backbone curve.
