Safe Quadrotor Navigation using Composite Control Barrier Functions

TL;DR

The paper tackles safe autonomous navigation of multirotors in unknown, cluttered environments by introducing a Composite Control Barrier Function (CBF) safety filter that aggregates many position constraints into a single $h(\boldsymbol{x})$ for a third-order system. The method builds a high-order CBF via exponential/ECBFs for each obstacle and fuses them with a softmin to form a smooth, single safety constraint, with Lie derivatives $\mathcal{L}_f h$ and $\mathcal{L}_g h$ expressed through obstacle weights $\lambda_i(\boldsymbol{x})$. A key theoretical result shows recursive feasibility: the potentially infeasible set is a zero-volume singular set, ensuring the safety filter remains feasible in almost all practical states. Hardware experiments with onboard LiDAR demonstrate real-time safety on an onboard computer, confirming scalability to thousands of obstacles and robustness against both naïve and adversarial policies, with a safety filter that minimally alters the reference controller to satisfy constraints.

Abstract

This paper introduces a safety filter to ensure collision avoidance for multirotor aerial robots. The proposed formalism leverages a single Composite Control Barrier Function from all position constraints acting on a third-order nonlinear representation of the robot's dynamics. We analyze the recursive feasibility of the safety filter under the composite constraint and demonstrate that the infeasible set is negligible. The proposed method allows computational scalability against thousands of constraints and, thus, complex scenes with numerous obstacles. We experimentally demonstrate its ability to guarantee the safety of a quadrotor with an onboard LiDAR, operating in both indoor and outdoor cluttered environments against both naive and adversarial nominal policies.

Figures (5)

• Figure 1: Left: Coordinate conventions utilized. All equations are expressed in North-East-Down (NED) and Front-Right-Down (FRD) frame. Right: Singular configuration example. A necessary requirement for conflicting constraints in \ref{['OCP']} is that the virtual obstacle (orange) lies on the positive thrust axis (shown in red).
• Figure 2: Aggregated map and path of experiment A. An example of the obstacle map used by the safety filter is highlighted in green. The mission starts at the cyan circle on the right, receiving a constant velocity reference of $1 m/s$ in the positive $X$ direction, shown as a blue arrow. The norm of the intervention (cost of the qp \ref{['OCP']}) is color-coded into the path, highlighting the areas where the safety filter becomes active. Time instances marked A-D are reported in Fig. \ref{['fig:CBF_elektro']} for visualizing the corresponding numerical values.
• Figure 3: Constraint values (top) and velocity error w.r.t. the reference (center) and filter-induced deviation (bottom) during experiment A.
• Figure 4: Aggregated map and path of experiment B. The mission starts at the cyan circle on the right. The quadrotor receives an adversarial velocity reference that actively tries to collide with obstacles. The red arrows depict this reference velocity for some selected time instances, A-D, which are reported in Fig. \ref{['fig:CBF_dragvoll']}.
• Figure 5: Constraint values during experiment B.

Theorems & Definitions (8)

• Definition 1: Control Invariant Set
• Definition 2: Control Barrier Function ames2019control
• Theorem 1
• Lemma 1
• Theorem 2
• Remark 1
• Proposition 1
• proof