A hyper-redundant manipulator is made by mounting the serial and/or parallel mechanisms on top of each other as modules. In discrete actuation, the actuation amounts are a limited number of certain values. It is not feasible to solve the kinematic analysis problems of discretely actuated hyper-redundant manipulators (DAHMs) by using the common methods, which are used for continuous actuated manipulators. In this paper, a new method is proposed to solve the trajectory tracking problem in a static prescribed obstacle field. To date, this problem has not been considered in the literature. The removing first collision (RFC) method, which is originally proposed for solving the inverse kinematic problems in the obstacle fields was modified and used to solve the motion planning problem. For verification, the numerical results of the proposed method were compared with the results of the genetic algorithm (GA) method. Furthermore, a novel DAHM designed and implemented by the authors is introduced.