This paper presents a novel proximal planning and control (PPC) formulation for an unmanned ground vehicle (UGV) which is affected by skidding and slip disturbances. The control approach also considers the presence of moving and static obstacles in the context of operation. The PPC technique is divided into three parts; first, a nonlinear model predictive control (NMPC) based path-planner is designed to periodically generate an updated feasible trajectory for reaching the goal pose, under the constraint of avoiding collisions with dynamic and static objects which are present in the context. In particular, a proximal averaged Newton-type method for optimal control (PANOC) is used to implement NMPC. Second, the velocity commands are produced via evolutionary programming (EP) based on kinematic control (KC). Third, a dynamic control process with an extended state observer (ESO) is introduced to estimate disturbances whose magnitudes are unknown but bounded. Finally, to verify the performance of the proposed scheme, simulations are performed for the platform operating in the presence of static obstacles (SO) and moving obstacles (MO), whose trajectories may be nonlinear and difficult to be accurately predicted. Additionally, we have investigated and confirmed that the proposed PPC is able to operate in real time under limited CPU processing resources.