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We present an approach to robotic manipulation of unknown objects through regulation of the object's contact configuration: the location, geometry, and mode of all contacts between the object, robot, and environment. A contact configuration constrains the forces and motions that can be applied to the object; however, synthesizing these constraints generally requires knowledge of the object's pose and geometry. We develop an object-agnostic approach for estimation and control that circumvents this need. Our framework directly estimates a set of wrench and motion constraints which it uses to regulate the contact configuration. We use this to reactively manipulate unknown planar objects in the gravity plane. A video describing our work can be found on our project page: http://mcube.mit.edu/research/contactConfig.html., Authors contributed equally, names listed in alphabetical order. ICRA 2022