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Introduction
As a type of bionic robots, the snake robot is drawing attention in recent years. The snake robot can do a number of works such as environment detection, resource prospecting, and pipeline maintenance, which is difficult or dangerous for human beings to process. In the above application fields, the snake is usually controlled to fulfill a desired motion.
Because of the nonlinear, nonholonomic, and under-actuated characteristics of the passive-wheel snake system, the modeling and control is always difficult to handle. On one hand, the modeling quality of the snake system has significant influence on the control performance of the snake. As a many-degree-of-freedom mechanical system, the dynamic modeling of the passive-wheel snake robot is complicated and difficult to process using classical dynamic theory such as Newton equation and Lagrangian equation which are mostly used in the snake's modeling. Moreover, approximation and linearization are always used when using common methods to model the snake which detects the modeling accuracy. Besides, it is always not easy to model the passive wheels' nonholonomic constraints. Currently, there are mainly two ways to handle these constraints. First, the passive wheels' constraints are modeled by a "geometry equality method," that is, the nonholonomic constraint imposed on the snake body. Second, one can also use the "force equality method" to model these constraints, in which the passive wheel is simulated by an infinite lateral force and a zero-longitudinal force. However, most of the current dynamic theories show difficulty when dealing with such constraints.
On the other hand, as an under-actuated mechanical system, the trajectory tracking control of the snake robot is always difficult and complicated to handle. Commonly, common methods always make assumptions of the model which detects the control accuracy. Moreover, extra procedure variables, such as Lagrangian multiplier, make the controller design difficult and complex. Besides, the modified controller structure such as added visual sensors which is processed in the controller design procedure when using common control methods also makes the controller design a heavy task.
Many researchers have done much work on the dynamic modeling and controller design of the snake robot. Krishnaprasad and Tsakiris[1] and Kelly and Murray[2] modeled the passive-wheel snake robot using differential geometry method and discussed the controllability of the proposed model. Ostrowski