Compliant robotic systems on graphs

In this paper, a modular method of modeling compliant robotic systems using graph theory is treated. Graph theoretic analyses ensure a structured way of describing a system and allow a straightforward extension to more complex systems. The graph models of a series elastic actuator, a variable stiffness actuator and a multi degrees of freedom compliant system are derived. These systems are controlled using an optimal control law that is able to find the optimal stiffness setting and distribution to accomplish a certain task. A case study shows a multi degrees of freedom compliant system which is required to resonate at the output and to accomplish a back-and-forth motion. It is shown that a constant optimal stiffness is found in the resonance simulation, and a varying optimal stiffness in case of the back-and-forth task. This indicates that this methodology can assist in finding an optimal stiffness distribution of complex robotic systems for a given task.