A simulation study is performed on a quadcopter which uses a LIDAR sensor to allow a quadcopter to navigate along and maintain a set distance from an unknown vertical surface. The dynamic equations of a quadcopter are linearized about the hovering equilibrium. For the purpose of design, all surfaces are assumed to be flat and any variations in shape are considered to be disturbances. The design process begins with the development of a potential field control design to allow the quadcopter to autonomously follow a flat surface, while maintaining a desired distance from the surface. To allow the quadcopter to follow a curved surface, the potential field technique is modified to maintain the xb axis parallel to the surface. Finally a wall following technique that directly uses the minimum range measurement to maintain the distance from the surface is developed. To simulate the control designs, a non-linear quadcopter model is used along with a model of a 2D scanning LIDAR sensor. The potential field control technique tracks flat surfaces with no steadystate error, though when curved surface following is added, a tracking error problem occurs due to measurement noise. The wall following design proves to be the superior surface following technique with greater robustness to steady-state error and results in relatively small tracking errors when navigating sinusoidal surfaces and corners.