This paper presents Kinematics and Dynamics of a Shape-Shifting Surface, a robotic system able to take on the shape of arbitrary connected 3D surfaces. Such a surface, which we introduced and described in previous work, consists of piecewise controllable chains in turn composed of serially connected foldable “robotic particles”. Aiming at a high resolution rendering, where tiny particles need to be combined in a large number, a tendon-driven design is a lightweight and scalable solution.
However, improper actuation strategies might expose the system to undesired forces, which can compromise its integrity and stability. To tackle this problem, optimal actuation and planning strategies are required to anticipate unacceptable situations. To this end, a dynamic model is derived to predict the reaction of the system subject to control actions. Being the system both tendon-driven and under-actuated, we have to overcome a number of challenges in deriving this model.