The problem of planning motions for a mobile robot in the presence of objects moving on unknown trajectories and with unknown velocities is addressed. The robot must follow a predefined path with a given tolerance and reach its destination by a given time without colliding with any obstacle. Objects are represented by nonintersecting discs in the plane, and the robot by a point. The proposed method relies on the use of sensors to detect obstacles, and interleaves path planning with execution. Experimental results obtained both in simulation and with a real robot are shown.