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

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

cs.ROMar 11, 2026

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

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

Organizations: University of Washington, Department of Electrical and Computer Engineering · University of Washington, Department of Aeronautics and Astronautics

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/.

Figures & tables

Fig. 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.

Panel of Figure 2 — Fig. 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.

Fig. 3 : Trajectories generated from 100 single-agent head-on interactions with each method. Red trajectories indicate collisions.

Multi-Agent Scenario
Method	Coll. (%)↓	Safety Viol.(%)↓	Goal (%)↑	Control Effort↓	Control Smooth.↓
CBF-QP	38.8	81.4	96.4	0.30	0.12
Fixed CRC-SF	10.2	49.0	31.6	0.53	0.23
Online CRC-SF	3.0	53.2	84.8	0.43	0.19
MPPI	34.4	81.2	77.6	0.65	0.46
Single-Agent Scenario

TABLE I : Performance comparison between multi-agent and single-agent human-robot navigation scenarios. The multi-agent results represent averages across five different test configurations (each with distinct initial and goal positions), with each configuration run 100 times. The single-agent results represent averages from 100 head-on simulations.

Panel of Figure 5 — Fig. 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.

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Control Barrier Functions Solved with Hierarchical Quadratic Programming for Safe Physical Human-Robot Interaction

Rui Luo, Jonas Mariager Jakobsen, Wesley Roozing, Federico Califano+1

Robotic Control Control Barrier Functions Constrained Optimization Human-Robot Interaction

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Physical human-robot interaction offers the potential to leverage human intelligence and robot physical capabilities to enable a range of exciting applications, e.g., collaborative robots for rehabilitation. Safety is critical for the successful deployment of this kind of robotic system. In recent years, Control Barrier Function (CBF) has emerged as an effective approach to enforce safety guarantees, which has been widely applied in various applications, from adaptive cruise control to navigation of legged robots. CBFs can be solved in a Quadratic Programming (QP) problem, which can include many CBF-formulated tasks. To manage a large number of safety tasks, a hierarchical CBF has been used to allow hierarchical relaxation of safety tasks to ensure the feasibility of a solution in the presence of conflicting tasks. In this work, we propose to use a CBF-based Hierarchical Quadratic Programming (HQP) framework in physical human-robot interaction to allow us to design both performance tasks (e.g., preserve the desired behavior at the human-robot interaction point) and safety tasks at any level of a hierarchy to balance the safety and the performance in a more flexible way. Extensive experiments were carried out on a real redundant robot to validate the effectiveness, flexibility, and generality of this approach.

Abstract

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