Abstract Predominately, robotic construction is applied as prefabrication in structured indoor environments with standard building materials. Our work, on the other hand, focuses on utilizing irregular materials found on-site, such as rubble and rocks, for autonomous construction. We present a pipeline to detect arbitrarily placed objects in a scene and form a structure out of the detected objects. The next best stacking pose is selected using a searching method employing gradient descent with random initial orientations, exploiting a physics engine. This approach is validated in an experimental setup using a robotic manipulator by constructing balancing vertical stacks without mortars and adhesives. We show the results of eleven consecutive trials to form such towers autonomously using four arbitrarily in front of the robot placed rocks.