Gait kinematics for a serpentine robot

\follow" the lead of the three-segment kinematic system. By formulating the motion of the system in terms of a connection, we can clearly highlight the important factors which contribute to the serpentine locomotion. Using sinusoidal inputs which are phase-delayed down the length of the snake robot, we were able to simulate various possible gaits, including a serpentine gait characterized by net forward motion, and a rotate gait marked by a rotation or turning of the robot. For the serpentine gait, we show that it very closely approximates the serpenoid curve developed by Hirose as a description of the path followed by actual snakes. The next logical step for this research is to begin to ask deeper questions regarding controllability of snake-like robots. We have shown here basic motions that can be generated, but can not conclude how to generate more general gait patterns (for instance, we have yet to nd a gait pattern that generates motion transverse to the length of the snake). Having established the form of the connection, however, there are existing results that we would like to be able to apply. For instance, Kelly and Murray 9] have given controllability tests based on taking derivatives of the connection, A. These derivatives play a similar role as, and are directly related to, taking Lie brackets of the input control vector elds. Various results 13, 14, 15] suggest that there may be a direct correlation between the directions given in Lie bracket calculations and the corresponding gait patterns generating using integrally related sinusoidal inputs. Further research is still necessary to make conclusive remarks, but certainly the work of Leonard and Krishnaprasad 11] holds some promise, as they use averaging theory to show this to be true using small-amplitude periodic signals when A is constant. Finally, we remark that this model can be used to do some basic optimization of gait patterns for a snake robot. For example, given a particular set of lengths for the body segments, it would be possible to pick the input patterns which generate the largest forward displacements using the serpentine gait. In certain environments, snake-like robots can demonstrate numerous advantages over more conventional modes of locomotion. For this reason, it is important to explore the basic tools necessary to make full use of these types of robots. This paper provides initial results as to how these gaits can be selected and implemented, and presents …