In one embodiment, planning data is received, for example, from a planning module, to drive an autonomous driving vehicle (ADV) from a starting location and a destination location. In response, a series of control commands are generated based on the planning data, where the control commands are to be applied at different points in time from the starting location to the destination location. A cost is calculated by applying a cost function to the control commands, a first road friction to be estimated in a current trip, and a second road friction estimated during a prior trip from the starting location to the destination location. The first road friction of the current trip is estimated using the cost function in view of a prior termination cost of the prior trip, such that the cost reaches minimum.