Experimental verification on the robustness and stability of an interaction control: Single‐degree‐of‐freedom robot case

Abstract

The nonlinear bang-bang impact control (NBBIC) had been proposed for robots performing tasks having frequent contact with different environments because it takes advantage of the frictions in robot joints that are not helpful for constrained space control usually, does not need to change gains throughout tasks, and requires little information on robot dynamics. Despite these advantages, due to the lack of stability proof, it was not widely adopted. Recently, the stability of the NBBIC for one degree-of-freedom (DOF) robot has been proved almost two decades after its first proposal. The stability condition provided a theoretical stable region of the inertia estimate and was not dependent on environment dynamics, indicating the robustness of NBBIC to environment dynamics (e.g. stiffness). Thus, there is a strong need to verify the stability condition and the robustness of NBBIC to environment dynamics. Experiments of single DOF robots colliding with various environments showed that the stability condition predicted the stable range of the inertia estimate well, though there was a reduction in upper-bound because of sensor noise. The impact force response did not vary significantly for environments with different stiffness (silicon, aluminium, and steel wall), thereby confirming the robustness of the NBBIC to environment dynamics.

Experimental study on a robust interaction control with unknown environments

“…NBBIC was promising but has never been tested extensively. Even the stability was completely proved only very recently [17][18][19]. NBBIC has shown that performance is at least comparable to or better than other controllers.…”

“…where M denotes a constant diagonal matrix, an estimate of M. The first term of ( 5) is the known part, and the second term, H(t), is the uncertain non-linear dynamics [16,17,21]. The TDE is derived using (5) [17][18][19] as…”

“…To address the issue, non-linear bang-bang impact control (NBBIC) had been proposed with the experimental verification of its superior performance in impact conditions in settling time and oscillation in force response [16]. NBBIC may be theoretically innovative in that, instead of the dynamics of environment and robot, NBBIC uses time-delay estimation (TDE)-requiring only the most recent control torque, acceleration, and a constant inertia estimation matrix-to compensate for the robot dynamics and disturbances [16][17][18][19]. Moreover, the non-linear bang-bang action (NBBA) subsides the impact energy by utilizing the non-linear robot joint frictions through wise turning off of the control action [16][17][18][19].…”

“…NBBIC may be theoretically innovative in that, instead of the dynamics of environment and robot, NBBIC uses time-delay estimation (TDE)-requiring only the most recent control torque, acceleration, and a constant inertia estimation matrix-to compensate for the robot dynamics and disturbances [16][17][18][19]. Moreover, the non-linear bang-bang action (NBBA) subsides the impact energy by utilizing the non-linear robot joint frictions through wise turning off of the control action [16][17][18][19]. Further, NBBIC does not need any change of gains and/or structure throughout the tasks consisting of free-space motion, impact, and constrained-space motion.…”

“…Further, NBBIC does not need any change of gains and/or structure throughout the tasks consisting of free-space motion, impact, and constrained-space motion. Because of the complexity of the impact and the multi-degree-of-freedom (DOF) non-linear time-varying robot dy-namics, only recently, the complete and rigorous stability was proved [17,19], and experimentally validated [18,19]. The robustness to environmental change and disturbances, predicted by the stability condition, was tested [18].…”