Force Based Fractional Impedance Control

The main purpose of this article is to explore the effects of fractional derivatives on legged robot compliance control, more specifically, to investigate the effects on force-based impedance control. Substituting the derivative term of the outer loop impedance controller on force-based impedance control with the fractional derivative, we get a new fractional impedance controller. The robot used in the experiment is a hydraulically driven quadruped robot. So, the first experiment in this paper is to test the effect of a fractional impedance controller on a single hydraulic actuator. Experimental results show that hydraulic cylinder can restrain periodic disturbance under a sinusoidal input, which proved by the curve of force sensor. In the second experiment, we test the effect of a fractional impedance controller under a trot gait of hydraulic quadruped robot. The test results show that the fractional impedance controller can effectively improve the robot's compliance with external environment. Compared with integer-order force-based impedance control, fractional-order impedance control has less position error and contact force in trot gait of quadruped robot. In the experiment, we also studied the influence of the fractional order to impedance control.