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Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Control

Jake Gonzales, Kazuki Mizuta, Karen Leung, Lillian J. Ratliff

TL;DR

This paper introduces an algorithm that dynamically adjusts the safety margins produced by conformal risk control based on the current interaction context and significantly reduces collision rates and safety violations as compared to baseline methods while maintaining high success rates in goal-reaching tasks and efficient control.

Abstract

In this paper, we present a novel probabilistic safe control framework for human-robot interaction that combines control barrier functions (CBFs) with conformal risk control to provide formal safety guarantees while considering complex human behavior. The approach uses conformal risk control to quantify and control the prediction errors in CBF safety values and establishes formal guarantees on the probability of constraint satisfaction during interaction. We introduce an algorithm that dynamically adjusts the safety margins produced by conformal risk control based on the current interaction context. Through experiments on human-robot navigation scenarios, we demonstrate that our approach significantly reduces collision rates and safety violations as compared to baseline methods while maintaining high success rates in goal-reaching tasks and efficient control. The code, simulations, and other supplementary material can be found on the project website: https://jakeagonzales.github.io/crc-cbf-website/.

Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Control

TL;DR

This paper introduces an algorithm that dynamically adjusts the safety margins produced by conformal risk control based on the current interaction context and significantly reduces collision rates and safety violations as compared to baseline methods while maintaining high success rates in goal-reaching tasks and efficient control.

Abstract

In this paper, we present a novel probabilistic safe control framework for human-robot interaction that combines control barrier functions (CBFs) with conformal risk control to provide formal safety guarantees while considering complex human behavior. The approach uses conformal risk control to quantify and control the prediction errors in CBF safety values and establishes formal guarantees on the probability of constraint satisfaction during interaction. We introduce an algorithm that dynamically adjusts the safety margins produced by conformal risk control based on the current interaction context. Through experiments on human-robot navigation scenarios, we demonstrate that our approach significantly reduces collision rates and safety violations as compared to baseline methods while maintaining high success rates in goal-reaching tasks and efficient control. The code, simulations, and other supplementary material can be found on the project website: https://jakeagonzales.github.io/crc-cbf-website/.
Paper Structure (24 sections, 7 theorems, 49 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 24 sections, 7 theorems, 49 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Safety
  5. Discretization & Robust Control Barrier Function
  6. Stochastic Human Behavior with Probabilistic Safety
  7. Robust and Safe Control Policy Synthesis
  8. Safety Barrier Certificates
  9. Safety Margin Synthesis via Conformal Risk Control
  10. Conformal Risk Control Safety Filter
  11. Optimizing the Safety Margin Parameter
  12. High Probability Safety Guarantees
  13. Algorithmic Details
  14. Experimental Results
  15. Experimental setup
  16. ...and 9 more sections

Key Result

Lemma 1

Consider the interval $[t_k,t_{k+1}]$ where $\Delta T=t_{k+1}-t_k$. Suppose that the agent is employing a zero-order hold policy, and that at each discrete time step $k$, the proposed algorithm selects $u_{\mathrm{\tt R},k}\in \widetilde{\mathcal{C}}(x(t_k), u_{\mathrm{\tt H}}(t_k))$ for the current

Figures (4)

  • Figure 1: We develop a risk-aware adaptive safety filter that dynamically adjusts robot conservativeness based on the uncertainty of human behavior. The plots show the robot's control space with red regions indicating unsafe actions. In high-risk scenarios (top), our approach increases the safety margin parameter $\boldsymbol{\lambda}$, creating more restrictive control constraints. In low-risk scenarios (bottom), $\lambda$ decreases, allowing less conservative behavior while maintaining safety guarantees.
  • Figure 2: Multi-Agent Scenario. Example of the human crowd simulation setup. The CRC Safety Filter maintains the probabilistic safety guarantees while the standard CBF exhibits unsafe behavior. The safety margin $\lambda$ adapts based on human prediction uncertainty, ensuring larger distances are maintained during uncertain interactions.
  • Figure 3: Trajectories generated from 100 single-agent head-on interactions with each method. Red trajectories indicate collisions.
  • Figure 4: Efficiency versus safety results across five test scenarios for the multi-agent setting. Darker markers with a black outline indicate the mean value across the five test scenarios. Online CRC-SF achieves the best safety-efficiency trade-off while maintaining more consistent performance across scenarios.

Theorems & Definitions (12)

  • Definition 1
  • Lemma 1: Robust CBF
  • Lemma 2
  • Remark 1
  • Lemma 3: Barrier Value Concentration
  • Theorem 1: CRC-CBF Safety Guarantee
  • Lemma 3: Robust CBF
  • proof
  • Lemma 3: Barrier Value Concentration
  • proof
  • ...and 2 more