SPARC: Prediction-Based Safe Control for Coupled Controllable and Uncontrollable Agents with Conformal Predictions

TL;DR

SPARC tackles safe control for systems operating with uncontrollable agents whose dynamics are coupled and unknown. It combines conformal prediction to produce probabilistic prediction regions for the uncontrollable agent with a control barrier function (CBF) safety filter applied on an augmented joint state, thereby addressing distribution shift due to coupling. The approach yields probabilistic safety guarantees of at least $1-\\alpha$ and demonstrates improved safety in a vehicle-pedestrian scenario compared to a vanilla CBF baseline. This data-driven, coupling-aware framework has practical implications for autonomous driving and human-robot interaction, with potential extensions to perception uncertainty and richer multi-agent settings.

Abstract

We investigate the problem of safe control synthesis for systems operating in environments with uncontrollable agents whose dynamics are unknown but coupled with those of the controlled system. This scenario naturally arises in various applications, such as autonomous driving and human-robot collaboration, where the behavior of uncontrollable agents, like pedestrians, cannot be directly controlled but is influenced by the actions of the autonomous vehicle or robot. In this paper, we present SPARC (Safe Prediction-Based Robust Controller for Coupled Agents), a novel framework designed to ensure safe control in the presence of coupled uncontrollable agents. SPARC leverages conformal prediction to quantify uncertainty in data-driven prediction of agent behavior. Particularly, we introduce a joint distribution-based approach to account for the coupled dynamics of the controlled system and uncontrollable agents. By integrating the control barrier function (CBF) technique, SPARC provides provable safety guarantees at a high confidence level. We illustrate our framework with a case study involving an autonomous driving scenario with walking pedestrians.

Figures (5)

• Figure 1: Instances of coupled dynamics in real-world scenarios can be observed across various datasets. For example, the interactions between traffic participants often exhibit mutual influence. In Fig.\ref{['fig:inD']}, vehicles may decelerate as they encounter bicycles at crosswalks. At the same time bicycles may alter their trajectories to avoid collisions with vehicles, resulting in curved paths.
• Figure 2: SPARC (Our Framework)
• Figure 3: The pedestrian's speed follows an unknown stochastic distribution affected by the state of the vehicle, i.e.,$\Delta Y \sim \mathcal{D}(X,Y)$. The pedestrian starts at a random position on one side of the crosswalk while the vehicle begins at the midpoint of the starting line. Red circles indicate collision volume.
• Figure 4: Nonconformity scores histogram for pedestrian position displacement $(\Delta {Y_{par}},\Delta {Y_{perp}})$ on $D_{cal}$
• Figure 5: The prediction output with conformal prediction region. The plot also includes $\phi(\text{car speed})$ with all other parameters fixed as a noise-free reference ground truth.

Theorems & Definitions (1)

• proof