arXiv subjects

Massimiliano de Sa

Publications and source records attributed to Massimiliano de Sa.

6 recordsLinked to original sources

arXiv2026

Constructive Safety-Critical Control for a Class of Underactuated Systems: A Hierarchical Approach

Underactuated systems with nontrivial geometry are abundant in practical robotic problems. However, little is known about constructive safety-critical control design in the presence of underactuation. In this work, we provide a constructive framework for synthesizing safe control architectures and control barrier functions for a class of quadrotor-like underactuated systems. By studying the geometry of their underactuation, we characterize when these systems have natural layered architectures useful for safety-critical control design. Using these architectures, we devise a constructive, hierarchical CBF synthesis procedure and provide conditions under which it succeeds.

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arXiv2026

CBF-RL: Safety Filtering Reinforcement Learning in Training with Control Barrier Functions

Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.

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arXiv2026

SafeSpace: Aggregating Safe Sets from Backup Control Barrier Functions under Input Constraints

Control barrier functions (CBFs) provide a principled framework for enforcing safety in control systems -- yet the certified safe operating region in practice is often conservative, especially under input bounds. In many applications, multiple smaller safe sets can be certified independently, e.g., around distinct equilibria with different stabilizing controllers. This paper proposes a framework for uniting such regions into a single certified safe set using \emph{combinatorial CBFs}. We refine the combinatorial CBF framework by introducing an auxiliary variable that enables logical compositions of individual CBFs. In the proposed framework, we show that such compositions yield a \emph{generalized combinatorial CBF} under a condition termed \emph{conjunctive compatibility}. Building on this result, we extend the framework to enable the aggregation of multiple implicit safe sets generated by the backup CBF framework. We show that the resulting CBF-based quadratic program yields a continuous safety filter over the aggregated safe region. The approach is demonstrated on two spacecraft safety problems, safe attitude control and safe station keeping, where multiple certified safe regions are combined to expand the operational envelope.

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arXiv2026

Topological Obstructions to the Existence of Control Barrier Functions

In 1983, Brockett developed a topological necessary condition for the existence of continuous, asymptotically stabilizing control laws. Building upon recent work on necessary conditions for set stabilization, we develop Brockett-like necessary conditions for the existence of control barrier functions (CBFs). By leveraging the unique geometry of CBF safe sets, we provide simple and self-contained derivations of necessary conditions for the existence of CBFs and their safe, continuous controllers. We demonstrate the application of these conditions to instructive examples and kinematic nonholonomic systems, and discuss their relationship to Brockett's necessary condition.

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arXiv2025

From Bundles to Backstepping: Geometric Control Barrier Functions for Safety-Critical Control on Manifolds

Control barrier functions (CBFs) have a well-established theory in Euclidean spaces, yet still lack general formulations and constructive synthesis tools for systems evolving on manifolds common in robotics and aerospace applications. In this paper, we develop a general theory of geometric CBFs on bundles and, for control-affine systems, recover the standard optimization-based CBF controllers and their smooth analogues. Then, by generalizing kinetic energy-based CBF backstepping to Riemannian manifolds, we provide a constructive CBF synthesis technique for geometric mechanical systems, as well as easily verifiable conditions under which it succeeds. Further, this technique utilizes mechanical structure to avoid computations on higher-order tangent bundles. We demonstrate its application to an underactuated satellite on SO(3).

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arXiv2022

Tethered Power for a Series of Quadcopters: Analysis and Applications

Tethered quadcopters are used for extended flight operations where the power to the system is provided via a tether connected to an external power source. In this work, we consider a system of multiple quadcopters powered by a single tether. We study the design factors that influence the power requirements, such as the electrical resistance of the tether, input voltage, and quadcopters' positions. We present an analysis to predict the required power to be supplied to a series of N tethered quadcopters, with respect to the thrust of each quadcopter which guarantees electrical safety and helps in design optimization. We find that there is a critical boundary of thrusts that cannot be exceeded due to fundamental electrical limitations. We compare the power consumption for one tethered quadcopter and two tethered quadcopters and show that for large quadcopters far enough from the anchor point, a two-quadcopter system consumes lesser power. We show that, for a representative use case of firefighting, a tethered system with two quadcopters consumes 26% less power than a corresponding system with one quadcopter. Finally, we present experiments demonstrating the use of a two-quadcopter tethered system as compared to a one-quadcopter tethered system in a cluttered environment, such as passing through a window and grasping an object over an obstacle.

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