Energy-based Control of a Pneumatic Oscillator with Application to Energy Efficient Hopping Robots

ABSTRACT This paper presents an energetically derived control methodology to specify and regulate the frequency and amplitude of oscillatory motion of a pneumatic actuation system. A lossless horizontal pneumatic actuation system with an inertia is energetically shown to represent an oscillator with a stiffness, and hence frequency, related to the equilibrium pressures in the actuator. Following from an analysis of the conservative energy storage elements in the system, a control methodology is derived to sustain a specified frequency and amplitude of oscillation in the presence of energy dissipation. The control strategy takes advantage of the natural passive dynamics of the system to provide much of the required actuation forces, while the remaining forces needed to overcome the energy dissipation present in a non-ideal system with losses are provided by a nonlinear control law for the charging and discharging of the actuator. This control methodology is demonstrated experimentally to provide accurate and repeatable frequency and amplitude control of oscillation in the presence of dissipative forces. Finally, the energetic analysis of the horizontal pneumatic system is extended to the vertical case where gravity is present. This extension provides an energetically efficient hopping control methodology for pneumatically actuated robots.