Gamma Motor Neuron-Inspired Adaptive Impedance Control for Gripping Force Regulation in a Pipe-Climbing Robot

This research proposes a multi-modal pipe-climbing robot design and a position-based force-tracking adaptive impedance controller for pipe surface inspections and maintenance in unstructured industrial environments. The driving foot combines underactuated linkages with four Mecanum wheels for secure gripping and omnidirectional mobility. A two-level compliance strategy addresses the challenge of maintaining a stable gripping force on pipes of different diameters. Passive compliance provides preliminary mechanical adaptation. Inspired by the regulation of muscle spindle sensitivity by γ motor neurons (γ-MN), a three-parameter adaptive impedance controller was designed at the control level. By continuously estimating the contact environment parameters online and dynamically updating the impedance reference trajectory, the controller achieved zero steady-state gripping force error under the stated steady-state conditions. Lyapunov analysis established uniform stability of the ideal estimator for constant parameters and convergence of the force prediction error under the stated assumptions, and global uniform asymptotic stability (GUAS) of the parameter error under persistent excitation. Simulations verified the force-tracking performance of the controller under the specified contact parameter variations and measurement noise conditions. Experiments separately evaluated the locomotion performance of the prototype driving foot and its fixed-base force-tracking performance on pipes of three diameters. At target forces of 120 N and 200 N, the across-trial averages of the relative deviations of the steady-state means for the different pipe diameters ranged from 0.125% to 0.336%, and the across-trial standard deviations of the steady-state means ranged from 0.19 to 0.96 N, confirming small mean force deviations and good repeatability for the tested pipe diameters.