Robust Trajectory Tracking Control for Snake Robots: A Backstepping and VHC-Integrated Strategy

Snake robots are plagued by a critical bottleneck in attaining high-precision regulation of both velocity magnitude and movement direction amid kinematic coupling during gait execution. To address this challenge, this paper formulates a hybrid control strategy via the synergistic integration of backstepping and Virtual Holonomic Constraint (VHC) methods. Firstly, the dynamics model of the snake robot is rigorously formulated under two scenarios: in the presence of external actuating inputs and in their absence. Concurrently, the dynamics system for the targeted input torque is analytically derived. Subsequently, by using the time-scale separation principle, the main system is framed as a perturbed system, and state equations related to both velocity direction and velocity magnitude are established. Meanwhile, a velocity controller based on VHC is synthesized to enforce kinematic constraints while accommodating dynamic uncertainties. Utilizing Lyapunov stability theory and the backstepping method, asymptotic stability of the snake robot is achieved. Finally, simulation results showed that the proposed controller reduced the tangential-speed tracking error by 73.3%. In the physical trial, the heading error remained within the 5% tolerance after approximately 40 s and within the 3% tolerance after approximately 190 s.