This paper presents a theoretical approach to improving the controllability and stability of unmanned ground platforms (UGPs) and convoys through the application of a model of multicomponent complex motion within a potential vector field of accelerations. The model allows for the decomposition of the total motion of an object into translational and relative components of linear and angular accelerations. It is used to describe the dynamic interaction between a leader vehicle and follower platforms in a group, as well as to evaluate stability conditions based on Lyapunov’s theory. Equations are derived to characterize both the translational and relative accelerations of unmanned platforms, and their relationship to motion resistance and driving forces. The proposed control model introduces the concept of an acceleration potential function, enabling a conservative field of accelerations in which the motion of each vehicle depends only on initial and final states. Analytical expressions are obtained for stabilization time and trajectory deviation, demonstrating how the delay in system response increases proportionally to the square of the distance from the operator. The paper further proposes a hierarchical (leader–follower) control structure, where each subsequent vehicle in the convoy acts as both follower and temporary leader for the next platform. This structure significantly reduces stabilization time and improves formation integrity. The results confirm that partial delegation of control to the leader vehicle enhances coordination efficiency and motion stability across the entire unmanned convoy.