Safe Control of Quadruped in Varying Dynamics via Safety Index Adaptation

TL;DR

The paper tackles safe control for quadruped navigation under varying payload dynamics by leveraging Safety Index Adaptation (SIA) to update safety indices in real time, preserving forward invariance and finite-time convergence. It builds on Safety Index Synthesis (SIS) within the Safety Set Algorithm framework and extends it with Determinant Gradient Ascent (DGA) to adapt to changes in dynamics without full re-synthesis. The approach is instantiated on an extended 2D unicycle model and validated with a Unitree Go2, including system identification to capture payload-dependent parameters. Results show SIA significantly reduces computation time and maintains 100% obstacle-avoidance success across payload changes, while non-adapted indices fail under heavier loads, demonstrating practical safety in real-world varying-dynamics scenarios.

Abstract

Varying dynamics pose a fundamental difficulty when deploying safe control laws in the real world. Safety Index Synthesis (SIS) deeply relies on the system dynamics and once the dynamics change, the previously synthesized safety index becomes invalid. In this work, we show the real-time efficacy of Safety Index Adaptation (SIA) in varying dynamics. SIA enables real-time adaptation to the changing dynamics so that the adapted safe control law can still guarantee 1) forward invariance within a safe region and 2) finite time convergence to that safe region. This work employs SIA on a package-carrying quadruped robot, where the payload weight changes in real-time. SIA updates the safety index when the dynamics change, e.g., a change in payload weight, so that the quadruped can avoid obstacles while achieving its performance objectives. Numerical study provides theoretical guarantees for SIA and a series of hardware experiments demonstrate the effectiveness of SIA in real-world deployment in avoiding obstacles under varying dynamics.

Figures (5)

• Figure 1: Trajectory of the quadruped carrying various packages of different weights (left column) and overall pipeline (right column). The quadruped avoids each obstacle sequentially, in the order of (1) blue, (2) green, and (3) red cubes, using safety index. Once the quadruped arrives at a goal position after avoiding an obstacle, a different package is loaded on its back. At this point, the safety index is adapted to the new dynamics.
• Figure 2: The extended unicycle system models the Go2 quadruped in 2D and allows lateral movements on top of the classical unicycle dynamics.
• Figure 3: Failure cases using a non-adapted safety index for heavy payloads. From left to right: Course 1, 2, 3. The top row shows motion trail images of the failure cases. The bottom row shows the trajectories at failures using motion capture data. In the bottom row, the triangle represents the quadruped, the dotted blue line is its trajectory, the dark red dot marks the obstacle, the light red circle is the user-defined unsafe set $\mathcal{X}_S^C$, and the green solid line is the unsafe set boundary padded with discrete-time safety margin, $\sigma_{\text{DT}}$. The $\phi_\theta$ value is displayed above the quadruped.
• Figure 4: Full trajectories using SIA in Courses 1, 2, and 3.
• Figure 5: Trajectories (solid lines) of $\phi_{0}$ and $\dot\phi_{0}$ for the non-adapted and adapted safety indices from hardware deployment. The segments move from solid circles to crossmarks. Blue lines are for the non-adapted case and the red lines are for the adapted case. Dashed lines denote the CT safe set boundaries.

Theorems & Definitions (1)

• Remark