In this article, a unified motion modeling approach for the 3-D snake robot is proposed, which enables motion prediction of all kinds of gaits generated by the backbone curve method on the ground. More specifically, the motion of the snake robot is novelly decomposed into two components, namely, the curve component and the shift component, which are explicitly related to the backbone curve's parameters and control's input. Considering the actual behavior of snake robots, a nonslip assumption is made to facilitate the modeling approach. Based on that, the ground-contacting points of the robot's links during shift control are conveniently analyzed, which helps to determine the moving direction of the curve components. Finally, with ground contacting points and backbone curve parameters determined, the characteristics of the two components, as well as the motion model, are successfully obtained. Utilizing this modeling approach, the widely used gaits, such as sidewinding, crawler, and S-pedal, are successfully modeled and then carefully analyzed to predict the movement of the snake robot with arbitrary given control input. Three groups of experiments are conducted, with the collected results showing the satisfactory accuracy of the obtained models. Compared with existing methods, the proposed modeling approach achieves a much more precise prediction, both in the direction and magnitude of snake robot motions.

To meet real-world production demands, two or more cranes are used to cooperatively complete transportation tasks. Dual boom cranes (DBCs) are widely used in large construction sites owing to their strong load capacity. However, for typical nonlinear underactuated multi-crane systems, most of the existing control methods focus on the overhead crane systems with simpler dynamic characteristics and not enough attentions are paid to DBCs with stronger coupling and more complex dynamics. Based on the existing model, geometric constraints are analyzed to obtain the relationship between the higher-order derivatives of state variables, which can simplify the dynamic model of DBCs reasonably. The dynamic relationship between the boom pitch angles and the payload attitude is analyzed accurately. Moreover, the oscillation period of DBCs is obtained, and an extra insensitive input shaper is designed by rigorous mathematical derivation. Finally, simulation results verify that the input shaping control method has a satisfactory anti-swing ability and can realize accurate positioning.