The paper presents algorithms for calculating the configuration’s parameters of a modular wheeled robot when moving along an arbitrary plane trajectory. The robot is a system of two-wheeled modules, sequentially connected using a ball joint. Two variants of the module wheelset are considered: fixed and with controlled rotation relative to the vertical axis. Mathematical models of the coupling equation are constructed on the basis of continuity in a ball joint. For the first option, an iterative algorithm of the second order of accuracy relative to the time step of the leading robot is proposed. The solution of the coupling equation is carried out analytically. For modules with a controlled wheelset, the configuration is determined using an algorithm that uses a second-order numerical scheme to solve a nonlinear parametric coupling equation. It was found that when moving a robot with a fixed wheelset, the trajectories of the driven models deviate from the trajectory of the leading one. The magnitude of the deviation increases with the growth of the trajectory curvature and accumulates from the first module to the last. The proposed algorithms allow for kinematic studies of a modular wheeled robot. To perform dynamic studies, a computer model of the robot in the ROS environment and using the Gazebo simulator is proposed. The simulation results can be used to develop a control system for robot modules when moving along an arbitrary flat trajectory.