A Lie-Theory-Based Dynamics Modeling Method of Snake-Arm Robot With Virtual Linkage Criterion

Abstract Cable-driven snake-arm robots with high degrees of freedom and flexible, slender bodies are very suitable for applications in unstructured, narrow situations. For the high-performance development of snake-arm robots, dynamics modeling is a very important issue but very difficult due to the hyperredundant degrees of freedom and long transmission chains. Thus, a recursive dynamics modeling method based on the Lie theory is proposed for the cable-driven snake-arm robot. First, the motion mapping relationship among the driving cables, universal joints, and end-effector is established based on the product of an exponential formula, which is helpful to reduce the complexity of modeling. To solve the kinematic spinor coupling problem of two rotating axes of a universal joint, a virtual linkage law is proposed. Based on the virtual linkage law, Newton–Euler method, and Lie theory, the dynamics equation of a snake-arm robot is derived. The computational complexity of the established dynamics model is O(n). Furthermore, a dynamic feedforward proportional–derivative (PD) control framework based on kinematics and dynamics is constructed. Finally, experiments based on the developed 21-degree-of-freedom (DOF) snake-arm robot are conducted, whose results prove the validation of the proposed method. Compared with the pure PD control strategy, the proposed dynamic feedforward control strategy improves the repeatability of the snake-arm robot in the X, Y, and Z directions by about 70.3%, 69.3%, and 61.4%, respectively. The experimental results show that the dynamic model is helpful in improving the motion accuracy of the snake-arm robot.