The paper proposes a new real-time motion planning technique for an autonomous mobile robot that is able to find a collision-free path and a corresponding time-optimal trajectory while taking into account limits on the actuator capacities and constraints from the wheel-ground adhesion. The proposed technique includes two sub-modules. The first one, an optimal path planner, is based on the discretization of the robot workspace and dynamic programming principle. It allows finding the shortest path in the robot environment to avoid obstacles and reach the robot target. The second one, an optimal trajectory generator, operates with the discretized robot state-space and also employs dynamic programming techniques. It produces a time-optimal motion along the obtained path, which may include numerous regular and singular trajectory sections caused by the simultaneous application of actuator and wheel-ground adhesion constraints. To adapt this technique to real-time implementation, a moving window strategy is presented that allows regularly updating the robot motion profile in a dynamic environment. The advantages of the developed technique and its suitability for real-time control are illustrated by experimental studies implemented on a car-like mobile robot.