In this article we design a physically-inspired model-based assist-as-needed semi-autonomous control (ASC) algorithm to address the problem of safely driving a vehicle (a power wheelchair) in an environment with static obstacles. Once implemented online, the proposed algorithm requires limited computing power and relies on pre-computed (offline) maps (look-up tables). These are readily available by implementing policy iteration that minimizes the expected time to termination (safely stopping near an obstacle), by taking into account: (i) the vehicle dynamics; (ii) the drivers' intention modeled as three separate stochastic processes. We call them the expert driver, the naughty child and the blind driver models.A study with healthy participants confirmed that ASC outperforms a baseline rule-based control (a statistically significant result).