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Robot-assisted urban search and rescue is an emerging topic in the field of robotics and it calls for new approaches of control. The focus of this work is the application of fuzzy logic in the grasping of objects with unknown characteristics such as rigidity and surface texture. In the task of disaster response, a rescue robot will encounter both living and non-living objects in the field. Then, the ability to grasp delicate and complex target objects such as a human with the appropriate grasping force is a necessary capability. The fuzzy logic controller that is presented in this paper allows a two-finger gripper equipped with piezoelectric slip sensors to grasp an unknown object without knowing the size, weight or surface texture of the object. The fuzzy inference mechanism establishes a decision-making ability similar to the grasping behavior of humans. The present work is part of an overall effort in developing a team of intelligent heterogeneous mobile rescue robots at the Industrial Automation Laboratory of the University of British Columbia. The goal is to have robots with various capabilities perform cooperative tasks that can provide assistance in extracting humans from life-threatening situations. Such tasks may include using multiple robots to search for humans in distress, cooperatively grasping and manipulating objects to assist humans, and constructing simple devices with multiple robots in order to transport a human to safety.