Curve tracking is a challenging and central problem in robotics. In this note, we study adaptive control and parameter estimation for two dimensional robotic curve tracking with unknown control gains. We build adaptive controllers that stabilize equilibria corresponding to a fixed constant distance to the curve and zero bearing. The significance of our work is in (a) our ability to identify the unknown control gain, (b) our proof of input-to-state stability with respect to actuator errors, and (c) the optimality of our disturbance bounds for maintaining robust forward invariance of a nested class of hexagons that fill the state space, under actuator disturbances and the unknown control gain. We demonstrate our work in simulations. (c) 2013 Elsevier Ltd. All rights reserved.