To reliably localize and control wheeled autonomous rovers, their controllers must keep the wheels away from traction loss. In this paper, we develop a fast and practical traction control system for rovers that track dynamic trajectories on rough firm terrains, leveraging their normally existing redundant control directions. Trajectory-tracking performance is guaranteed by input-output linearizing a nonholonomic model of the system and employing an appropriate stabilizing control law. We propose a novel methodology to optimally lift the control signals at the rover’s output level to determine the control actions that enhance the system’s traction without affecting the tracking performance. The methodology uses the knowledge of wheels’ friction coefficients and estimation of normal and tractive forces based on a nonholonomic rover model to optimally distribute the tractive forces among the wheels. The novelty is in redefining the optimization problem in both lateral and longitudinal directions that require minimum information about wheel-ground interactions and leads to linear optimality conditions. We define the notion of total required force/moment at system’s center of mass to (i) introduce reference directions for tractive forces in the proposed cost functions, and (ii) identify the rover wheels fighting against the motion. To prevent wheel-fighting, we find sub-optimal solutions that suppress tractive forces at the fighting wheels. The proposed traction control system is implemented on a six-wheel autonomous Lunar rover and its efficacy is investigated by a developed software-in-the-loop simulation environment using Vortex Studio. This software simulates a 3-dimensional digital twin of the system, with different terrain and tire model options. When compared to the conventional pseudo-inverse solution, the developed traction controller demonstrates improved overall traction and it saves the rover from traction loss.