A unified dynamic model for locomotion and manipulation of a snake-like robot based on differential geometry

A snake-like robot, whose body is a seried-wound articulated mechanism, can move in various environments. In addition, when one end is fixed on a base, the robot can manipulate objects. A method of dynamic modeling for locomotion and manipulation of the snake-like robot is developed in order to unify the dynamic equations of two states. The transformation from locomotion to manipulation is a mechanism reconfiguration, that is, the robot in locomotion has not a fixed base, but it in manipulation has one. First, a virtual structure method unifies the two states in mechanism （e.g., an embedding in the configuration space）; second, the product-of-exponentials formula describes the kinematics; third, the dynamics of locomotion and manipulation are established in a Riemannian manifold; finally, based on the analysis of the dynamic model, the dynamics of manipulation can be directly degenerated from those of locomotion, and this degeneration relation is proved through using the Gauss equations. In the differential geometry formulation, this method realizes the unification of the dynamics of locomotion and manipulation. According to a geometrical point of view, the unified dynamic model for locomotion and manipulation is considered as a submanifold problem endowed with geometric meaning. In addition, the unified model offers an insight into the dynamics of the snake-like robot beyond the dynamic model separately established for locomotion or manipulation.