| The topic considered is the modeling and control of a snake-like serial-link structure. The system is assumed to have torque controls about the joints, is considered to lie in an isotropic plane, and is assumed to interact with this plane in a manner which adheres to some suitable friction laws. Such a structure is hyper-redundant; making the robotic realization thereof potentially robust with regards to mechanical failure and highly suited for obstacle avoidance tasks and terrain adaptability. It is for these reasons that the structure is studied. Lagrangian mechanics is used to develop a mathematical model for the system. The resulting dynamics possess symmetries which allow them to be placed in a reduced form. Using this form in conjunction with a technique known as feedback linearization, one finds that the dynamics are driven by a three state system describing the evolution of generalized momenta with respect to the device's internal shape progression. The problem is to determine whether or not there is a shape trajectory that can elicit bulk structure movement. In order to determine the appropriate shape for this task a two-pronged approach is taken. One approach is to make a shape selection based on the principle mechanism of undulatory locomotion. The other approach is to set up a variational problem to determine an optimal locomotive shape. |
