Uncertainty and disturbance are common in a planar snake robot model due to its structural complexity and variation in system parameters. To achieve efficient head angle and velocity tracking with least computational complexity and unknown uncertainty bounds, a time-delayed control (TDC) scheme has been presented in this paper. A Serpenoid gait function is being tracked by the joint angles utilizing virtual holonomic constraints (VHCs) method. The first layer of TDC has been proposed for stabilizing the VHC dynamics to the origin. Once the VHCs are satisfied, the system is said to be on the constraint manifold. The second layer of TDC has been applied to an output system defined over the reduced order dynamics on the constrained manifold. To establish the robustness of the control approach through simulation, uncertainty in the friction coefficients is considered to be time-varying emulating change in the ground conditions. Simulation results and Lyapunov stability analysis affirm the uniformly ultimately bounded stability of the robot employing the proposed approach.

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