Physical adaptations informed by feedback control action in multi degrees of freedom robotic systems

Abstract

One challenge in developing methods to share the control responsibility between physical mechanisms and feedback controllers is the di culty to model multiple degrees of freedom (DoF) systems with complex dynamics. This research uses geometrical frameworks to develop methodical approaches for identifying possible physical adaptations with the aim of reducing the control e ort and real time allocation of tasks to the adaptable joint in response to disturbances. First a novel method is formulated for identifying possible physical adaptations with no prior knowledge of the system dynamics and for an arbitrary choice of controller design by considering the projection of the dynamics on the phase portrait of a single DoF. Another challenge in apportioning the numerical control task to physical system is quantifying how much of control task should be allocated to the physical structure. Using the proposed method, an optimal range for magnitude of the physical adaptation emerges naturally using a cost function to minimize control cost. A second method is developed to guide local physical adaptations assisting the controller in stabilizing the motion of an under-actuated system upon disturbances where the control action is not su cient to maintain stability. Here, local physical adaptations act as an internal controller/mechanical feedback to bring the system back to the controllable region and relax once the controller can stabilize the system without assistance. We view the system as an interconnection of the controller, the physical body, and the environment via power conserving elements where, the body of the system itself is viewed as the interconnection of the physically adaptable joint with the rest of the body. Once again a geometric representation is used by modulating the system using a port Hamiltonian network. To summarize, the proposed methods focus on adapting one degree of freedom at a time with the goal of reducing the controller’s e ort and are capable of identifying possible physical components, finding an optimal range for the size of Physical component, and real time allo- cation of tasks to the adaptable joint as a Response to disturbances. An inverted pendulum, representing the trunk of a biped walker, was used to conduct numerical simulations and hardware experiments.