Safety in Admittance Control using Reference Trajectory Shaping

Abstract

This paper presents a switched model reference admittance control framework to achieve safe and compliant human-robot collaboration through reference trajectory shaping. The proposed method generates variable admittance parameters according to task compliance and task-space safety requirements. Additionally, a disturbance bound is incorporated to enhance robustness against disturbances. Safety guarantees are explicitly established by integrating invariance control, ensuring that the reference trajectory remains within the admissible region. Stability of the switched system is analyzed using a common quadratic Lyapunov function, which confirms asymptotic convergence of the tracking error. The effectiveness of the approach is demonstrated through simulations on a two link manipulator and comparisons with existing methods are also presented. Furthermore, real time implementation on a single link manipulator validates the practical feasibility of the controller, highlighting its ability to achieve both compliance and safety in physical interaction scenarios.

Figures (9)

• Figure 1: The bound of the set $\mathcal{S}$ is shown in blue solid line, the green region shows the disturbance bound $\mathcal{S}_d$ and the red dot-dashed line shows the actual state boundary, i.e., the boundary of $\mathcal{S}_r.$
• Figure 2: Tracking Response by proposed controller maintaining safety constraint where $\xi_1,\xi_2$ are the end-effector position, $\xi_{r_1}, \xi_{r_2}$ are the reference trajectories, and $\xi_{bound}$ is the bound as given in \ref{['eq.xbound']}.
• Figure 3: Variable stiffness and damping profiles under switched MRAC design
• Figure 4: Trajectory along the X-axis: comparison of the proposed controller (blue solid line), invariance controller (red dotted line), PPC (orange dot–dashed line), and ABLF (purple dashed line)
• Figure 5: Control input comparison of different controllers

Theorems & Definitions (5)

• Definition 1: Positively controlled invariant set blanchini2008set
• Remark 1
• Remark 2
• Theorem 1
• proof