Existing approaches to sensor-based motion planning tend to deal solely with kinematic and geometric issues, and ignore the system dynamics. This work attempts to incorporate body dynamics into the paradigm of sensor-based motion planning. We consider the case of a point-mass mobile robot operating in a planar environment with unknown stationary obstacles of arbitrary shapes. Given the constraints on the robot’s dynamics, sensing and control means, conditions are formulated for generating collision-free trajectories with guaranteed convergence. The approach calls for continuous computation, and is fast enough for real-time implementation. Based on its velocity and sensing data, the robot continuously plans its motion based on canonical solutions, each of which presents a time-optimal path within the robot’s sensing range. For a special case of a sudden potential collision, an option of a safe emergency stopping path is always maintained. Simulated examples demonstrate the algorithm’s performance.