The problem addressed is feedback from noncontact sensing for guiding robots during docking and gripping. The sensor used is a "range camera" onboard a mobile robot (MRb). To specify the docking task completely both the posture (position/orientation) and the required tolerances must be given. These tolerances are then used in the feedback control loop during docking. The algorithms are divided into three parts: the extraction of posture parameters from the "range camera," dynamic filtering for finding association gates and protecting the system against spuriousness in the measurements, and finally a feedback controller. The feedback controller is separated into geometric control and tolerance control. The geometric control uses a range varying LQG-designed feedback control law to generate the trajectories toward the object. The tolerance control adjusts the approach velocity so that the robot is given a sufficient number of observations and control cycles to meet the required tolerances. Thus, during the approach there is a conditional re-planning of the trajectory. For simplicity, only three kinematic state variables (x, y, θ) are used for the MRb. Gripping using an industrial robot (IRb) is an equivalent problem. Successful experiments were made with range resolution varying more than a factor of 50. Thus, the resolution volume in the (x, y, θ)-space varied by several orders of magnitude during the tests. The final errors in range and orientation are essentially limited by the resolution in the "range camera." A persistent conclusion from the experiments is the importance of correct association between the range measurements and the corresponding parts of the object.