Safety-Critical Control with Uncertainty Quantification using Adaptive Conformal Prediction

TL;DR

The paper tackles safety for robotic systems under unknown and evolving motion noise, where traditional guarantees relying on fixed distributions may fail. It proposes ACP-SBC, a distribution-free framework that couples Adaptive Conformal Prediction with probabilistic Control Barrier Functions inside MPC to quantify online uncertainty and enforce safety with a probabilistic constraint. Theoretical analysis demonstrates convergence of the safety probability to a prescribed level and provides principled guarantees under MPC horizons, while extensive simulations show robustness to distribution shifts and scalability to large multi-robot teams. The proposed approach offers a practical path to provably safe planning and control in real-world, uncertain environments without requiring precise noise models.

Abstract

Safety assurance is critical in the planning and control of robotic systems. For robots operating in the real world, the safety-critical design often needs to explicitly address uncertainties and the pre-computed guarantees often rely on the assumption of the particular distribution of the uncertainty. However, it is difficult to characterize the actual uncertainty distribution beforehand and thus the established safety guarantee may be violated due to possible distribution mismatch. In this paper, we propose a novel safe control framework that provides a high-probability safety guarantee for stochastic dynamical systems following unknown distributions of motion noise. Specifically, this framework adopts adaptive conformal prediction to dynamically quantify the prediction uncertainty from online observations and combines that with the probabilistic extension of the control barrier functions (CBFs) to characterize the uncertainty-aware control constraints. By integrating the constraints in the model predictive control scheme, it allows robots to adaptively capture the true prediction uncertainty online in a distribution-free setting and enjoys formally provable high-probability safety assurance. Simulation results on multi-robot systems with stochastic single-integrator dynamics and unicycle dynamics are provided to demonstrate the effectiveness of our framework.

Figures (5)

• Figure 1: Computation steps for time-lagged ACP. In the current time horizon ($H=3$) starting at time step $k$, the time-lagged error of CBFs can be computed by $E^{\tau}_{B_k} = | \hat{B}_k - B^{\tau}_{k-\tau}|$. Then, $E^{\tau}_{B_k}$, $\tau=1, \dots, H$, are stored in the nonconformity set $\mathfrak{E}$.
• Figure 2: The effect of the parameter in our method (ACP-SBC).
• Figure 3: Distribution-free validation. Normal (Uniform) means that the Gaussian distribution (uniform distribution) is added to the CBFs-based method or our method (ACP-SBC) while mixture means that one of them is randomly added to the stochastic system at each time step.
• Figure 4: Simulation for multi-robot coordination using 30 robots with single integrator dynamics in an obstacle-free environment.
• Figure 5: Simulation with 6 Khepera IV robots with unicycle dynamics for multi-robot coordination in CoppeliaSim with Fig.\ref{['fig:CBFs']} using CBFs-based method and Fig.\ref{['fig:acp-sbc']} using ACP-SBC. It is obvious that collision happens using the CBFs-based method as shown in Fig.\ref{['fig:CBFs']} and the minimum distance shown in Fig.\ref{['fig:minimum distance']} also reveals that the collision, as the plot intersects the reference line, indicating that $h<0$

Theorems & Definitions (10)

• Lemma 1
• Lemma 2
• proof
• Remark 1
• Theorem 1
• proof
• Proposition 1
• proof
• Lemma 3
• Proposition 2