Loop Shaping of Hybrid Motion Control with Contact Transition

TL;DR

The paper addresses safe contact transitions in motion control by employing a loop-shaping approach to convert a stiff controller into a hybrid, sensor-free scheme that relies solely on displacement feedback. It links environmental impedance to the disturbance sensitivity function via S(s) = 1/(Z(s)s) and designs explicit stiff (C_s) and soft (C_v, C_ve) controllers, with a threshold U to trigger reshaping without force sensing. The method is validated experimentally on a 1-DOF actuator interacting with soft, penetrable grapes, showing that hybrid controllers provide smooth contact transitions and prevent object penetration, unlike purely stiff control. This sensorless, frequency-domain-based strategy offers a practical route to safe, tactile-contact-enabled robotics, including medical applications. $S(s) = rac{x(s)}{F(s)} = rac{1}{Z(s)s}$, $Z_v(s)=\alpha$, and $Z_{ve}(s)=\alpha+\frac{\beta}{s}$ are central relationships underpinning the design.

Abstract

A standard motion control with feedback of the output displacement cannot handle unforeseen contact with environment without penetrating into the soft, i.e. viscoelastic, materials or even damaging the fragile materials. Robotics and mechatronics with tactile and haptic capabilities, and in particular medical robotics for example, place special demands on the advanced motion control systems that should enable the safe and harmless contact transitions. This paper shows how the basic principles of loop shaping can be easily used to handle sufficiently stiff motion control in such a way that it is extended by sensor-free dynamic reconfiguration upon contact with the environment. A thereupon based hybrid control scheme is proposed. A remarkable feature of the developed approach is that no measurement of the contact force is required and the input signal and the measured output displacement are the only quantities used for design and operation. Experiments on 1-DOF actuator are shown, where the moving tool comes into contact with grapes that are soft and simultaneously penetrable.

Figures (8)

• Figure 1: Schematic representation of the contact environments: (a) viscous dashpot, (b) viscoelastic (Kelvin-Voigt type) contact.
• Figure 2: Magnitude response of $G(j\omega)$, $H(j\omega)$, $S_s(j\omega)$, and $S_v(j\omega)$.
• Figure 3: Magnitude response of $U(j\omega)$ for $C_s$ and $C_v$ controllers.
• Figure 4: Experimental setup of the controlled motion in contact with a soft environment -- final steady phase after contact with a grape: (a) stiff motion control $C_s$, (b) hybrid motion control $C_s \rightarrow C_v$ with reshaped sensitivity.
• Figure 5: Experimentally measured and least-squares identified magnitude response of the system input-output transfer function $G(j\omega)$.