This paper describes a novel method for non-holonomic robots of convex shape to avoid imminent collisions with moving obstacles. The method's purpose is to assist navigation in crowds by correcting steering from the robot's path planner or driver. We evaluate its performance using a custom simulator which replicates real crowd movements and corresponding metrics which quantify the agent's efficiency and the robot's impact on the crowd and count collisions. We implement and evaluate the method on the standing wheelchair Qolo. In our experiments, it drives in autonomous mode using on-board sensing (LiDAR, RGB-D camera and a system to track pedestrians) and avoids collisions with up to five pedestrians and passes through a door.