Control of the double-linked trident snake robot based on the analysis of its oscillatory dynamics

In this paper, we propose a new approach to the locomotion control of the trident snake robot, focusing on its ¿double-linked¿ case where the robot is composed of a triangular body and three branches of double-linked snakelike legs. Originally, this robot was proposed by the authors as a novel example of nonholonomic mobile robot. This robot is quite interesting from a theoretical point of view; the well-known LARC (Lie Algebra Rank Condition) for its nonlinear controllability has a unique structure that it contains two `generator´ vector-fields and higher order Lie brackets, which makes its control problem extremely challenging. In this paper, for this difficult control problem, we first propose a design algorithm which partially achieves the desired locomotion. Then we discover that the resulting motion may or may not be a stable limit cycle, depending on the eigenvalues of the corresponding discrete-time dynamics on its Poincare¿ map. Finally, we propose a full controller design by combining the stable limit cycles. The validity of the proposed idea is examined by numerical simulations.