Adaptive trajectory control of an under-actuated snake robot

•An under-actuated snake robot is designed based on cable traction.•The motion of the under-actuated snake robot is controlled based on iterative tractrix.•Realize the whole process trajectory control for the under-actuated snake robot.•The algorithm can satisfy the online or offline control of snake robots. This article proposes an adaptive trajectory control method for under-actuated snake robots by simplifying the control and actuation systems of hyper-redundant robots. The under-actuated joints are formed by controlling the spatial rotation angles of multiple rigid joints in the joint group in order for them to synchronize. Based on the under-actuated configuration, a trajectory control algorithm is proposed and includes the following parts: (i) A control principle based on variable rod length is adopted so that the snake robot can track into a small working space; (ii) a trajectory planning of the snake robot in a fixed state at one end is realized by an iterative tractrix principle minimizing the joint displacement; and (iii) a fast return tracking control of the snake robot in any posture is realized by adopting the principles of the variable rod-length tractrix and the forced return iteration. A snake robot with an arm 2300 mm in length is designed and fabricated. The trajectory control simulation and experiments validate the correctness of the trajectory control algorithm and the rationality of the structural design.