Towards X-embodiment safety: A control theory perspective on transferring safety certificates across dynamical systems

TL;DR

The paper addresses the challenge of transferring safety guarantees designed on simple abstract models to more complex, mismatched dynamical systems by introducing a transferred control barrier function (tCBF). The core idea is to shrink the abstract safe set using a margin phi of a simulation function V, yielding a transferred barrier $b_2(x_2) = b_1(\Pi(x_2)) - \phi(V(\Pi(x_2), x_2))$, and enforce safety on the target via a QP-based safety filter. A formal margin condition $\phi'(s)\alpha_V(s) \ge \alpha_b(\phi(s)) + r(s)$ guarantees that safety transfers remain valid under exact, stationary, or approximate pushforward, with a concrete quadrotor example demonstrating collision avoidance under model mismatch. The framework enables offline safety synthesis on tractable abstract models while providing rigorous, real-time safety enforcement for high-dimensional, nonlinear systems. Overall, the work offers a principled path to cross-model safety guarantees in heterogeneous dynamics using simulation-based interfaces and margin-based CBF transfer.

Abstract

Control barrier functions (CBFs) provide a powerful tool for enforcing safety constraints in control systems, but their direct application to complex, high-dimensional dynamics is often challenging. In many settings, safety certificates are more naturally designed for simplified or alternative system models that do not exactly match the dynamics of interest. This paper addresses the problem of transferring safety guarantees between dynamical systems with mismatched dynamics. We propose a transferred control barrier function (tCBF) framework that enables safety constraints defined on one system to be systematically enforced on another system using a simulation function and an explicit margin term. The resulting transferred barrier accounts for model mismatch and induces a safety condition that can be enforced on the target system via a quadratic-program-based safety filter. The proposed approach is general and does not require the two systems to share the same state dimension or dynamics. We demonstrate the effectiveness of the framework on a quadrotor navigation task with the transferred barrier ensuring collision avoidance for the target system, while remaining minimally invasive to a nominal controller. These results highlight the potential of transferred control barrier functions as a general mechanism for enforcing safety across heterogeneous dynamical systems.

Figures (2)

• Figure 1: Instances of the quadrotor trajectory in an obstacle environment. Red spheres denote obstacles, the green curve shows the RRT* path, and the black curve shows the nominal minimum-snap trajectory incurring collisions. Semi-transparent purple spheres indicate the tCBF-QP trajectory.
• Figure 2: (Left) Evolution of the transferred control barrier functions associated with each obstacle. The minimum transferred barrier value is shown by the dashed curve. As the quadrotor approaches obstacles, the transferred barriers decrease and become active near zero, demonstrating enforcement of safety at the concrete system level despite abstraction mismatch. (Right) Minimum obstacle clearance along the trajectory. The true geometric clearance remains strictly positive, confirming collision avoidance. The inflated clearance used in the abstract barrier construction is shown for reference, illustrating the additional safety margin imposed by the transferred CBF.

Theorems & Definitions (17)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Lemma 1
• proof
• Theorem 1
• proof
• Proposition 1
• proof