This paper is devoted to the problem of controlling a robot manipulator for a class of constrained motions. The task under consideration is to control the manipulator, such that the end-effector follows a path on an unknown surface, with the aid of a single camera assumed to be uncalibrated with respect to the robot coordinates. To accomplish a task of this kind, we propose a new control strategy based on multisensor fusion. We assume that three different sensors-that is, encoders mounted at each joint of the robot with six degrees of freedom, a force-torque sensor mounted at the wrist of the manipulator, and a visual sensor with a single camera fixed to the ceiling of the workcell-are available. Also, we assume that the contact point between the tool grasped by the end-effector and the surface is frictionless. To describe the proposed algorithm that we have implemented, first we decouple the vector space of control variables into two sub-spaces. We use one for controlling the magnitude of the contact force on the surface and the other for controlling the constrained motion on the surface. This way, the control synthesis problem is decoupled and we are able to develop a new scheme that utilizes sensor fusion to handle uncalibrated parameters in the workcell, wherein the surface on which the task is to be performed is assumed to be visible, but has an a priori unknown position.