A method to guide local physical adaptations in a robot based on phase portraits

In this paper, we propose a method that shows how phase portraits rendered by a controller can inform the development of a physical adaptation at a single degree of freedom (DoF) for a given control task. This approach has the advantage of having physical adaptations sharing the responsibility of control to accomplish a task. We use an inverted pendulum which is reminiscent of the trunk of a biped walker to conduct numerical simulations and hardware experiments to show how our method can innovate a physical adaptation at the pivot joint to reduce the control effort. Our method discovered that a torsional spring at the pivot joint would lead to a lower input effort by the regulator type feedback controller. The method can tune the spring to minimize the total cost of control up to about 32.81%. This physical adaptation framework allows multiple degrees of freedom robotic system to suggest local physical adaptations to accomplish a given control objective.