Adaptive Control based Friction Estimation for Tracking Control of Robot Manipulators

Abstract

Adaptive control is often used for friction compensation in trajectory tracking tasks because it does not require torque sensors. However, it has some drawbacks: first, the most common certainty-equivalence adaptive control design is based on linearized parameterization of the friction model, therefore nonlinear effects, including the stiction and Stribeck effect, are usually omitted. Second, the adaptive control-based estimation can be biased due to non-zero steady-state error. Third, neglecting unknown model mismatch could result in non-robust estimation. This paper proposes a novel linear parameterized friction model capturing the nonlinear static friction phenomenon. Subsequently, an adaptive control-based friction estimator is proposed to reduce the bias during estimation based on backstepping. Finally, we propose an algorithm to generate excitation for robust estimation. Using a KUKA iiwa 14, we conducted trajectory tracking experiments to evaluate the estimated friction model, including random Fourier and drawing trajectories, showing the effectiveness of our methodology in different control schemes.

Figures (9)

• Figure 1: The setup of the robot drawing platform.
• Figure 2: The effect of excitation generation and backstepping design. (Left) the effect of std to the condition number of initial (blue) and optimized (orange) trajectories. (Middle) the position tracking error for estimation with initial and optimized excitations. (Right) the position tracking error for estimation compare with the backstepping and non-backstepping design.
• Figure 3: Parameter convergence in estimation. The parameters are from joint 1, 4, 7. From top to bottom, the coulomb friction $f_c$, viscous friction $f_v$, and the difference between breakaway force and coulomb force $f_{brk}-f_c$ are shown.
• Figure 4: Evaluation results with Fourier trajectories. The first row compares the absolute joint position tracking error for nominal controllers. The second row shows the same comparison, but under low-speed conditions $|\dot{q}_d|<0.01$. In each sub-figure, from left to right shows the result from joint 1 to 7. In each box plot, the orange line represents the median value, the box represents the interquartile range, and the whiskers represent the range of the data.
• Figure 5: The disturbance estimation from ADRC with and without the estimated friction model.