National Natural Science Foundation of China 
Because of hydrodynamic model error of the present dynamic model, there is a challenge in controller design for the underwater snake-like robot. To tackle this challenge, this paper proposes an adaptive control schemes based on dynamic model for a planar, underwater snake-like robot with model error and time-varying noise. The adaptive control schemes aim to achieve the adaptive control of joint angles tracking and the direction of locomotion control. First, through approximation and reducibility using Taylor expansion method, a simplified dynamics model of a planar amphibious snake-like robot is derived. Then, the L1 adaptive controller based on piecewise constant adaptive law is applied on the simplified planar, underwater snake-like robot, which can deal with both matched and unmatched nonlinear uncertainties. Finally, to control the direction of locomotion, an auxiliary bias signal is used as the control input to regulate the locomotion direction. Simulation results show that this L1 adaptive controller is valid to deal with different uncertainties and achieve the joint angles tracking and fast adaptive at the same time. The modified L1 adaptive controller, in which the auxiliary bias item is added, has the ability to change the direction of locomotion, that is, the orientation angle is periodic with arbitrarily given constant on average.