Programmable robotic chains: Kinematics and dynamics of a scalable tendon-driven under-actuated multibody system

In previous work, we presented a programmable shape shifting-surface composed of modular robotic chains. As the control of a robotic chain presents many challenges, in this paper, kinematics and dynamics of such a robotic chain are modelled to enable model-predictive planning and control strategies. A robotic chain is a tendon-driven under-actuated multibody system that can piecewise control its curvature to approximate complicated 2D curves. As the actuation forces depend on the sequence of intermediate configurations to progressively achieve a target geometry - considering that too intense forces might compromise the stability and the integrity of the system - optimal planning strategies are expected to limit the maximum actuation forces. To this end, a model-predictive control process is required to properly actuate the system, for which a feedback-loop control is not possible due to the absence of sensors for low-cost and design reasons. Our contribution consists in the derivation of a dynamic model of the robotic chain to support model-predictive planning and control. An evaluation of the derived model proves its accuracy in comparison to an existing prototype.