Nonlinear oscillations for cyclic movements in variable impedance actuated robotic arms

Biologically inspired Variable Impedance Actuators (VIA) offer the capability to execute cyclic and/or explosive multi degree of freedom (DoF) motions efficiently by storing elastic energy. This paper studies the preconditions which allow to induce robust cyclic motions for strongly nonlinear, underactuated multi DoF robotic arms. By experimental observations of human motor control, a simple control law is deduced. This controller achieves intrinsic oscillatory motions by switching the motor position triggered by a joint torque threshold. Using the derived controller, the periodic behavior of the robotic arm is analyzed in simulations. It is found that a modal analysis of the linearized system at the equilibrium point allows to qualitatively predict the periodic behavior of this type of strongly nonlinear systems. The central statement of this paper is that cyclic motions can be induced easily in VIA systems, if the eigenfrequencies and modal damping values of the linearized system are well separated. Validation is given by simulation and experiments, where a human controls a simulated robotic arm, and the developed regulator controls a robotic arm in simulation and experiments.