Risk-Aware Robotics: Tail Risk Measures in Planning, Control, and Verification

TL;DR

This paper surveys risk-aware robotics by focusing on tail risk measures to quantify and manage rare, high-consequence outcomes in planning, control, and verification. It centers on Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and Entropic Value-at-Risk (EVaR), highlighting their coherent properties and dual representations, and situates them within dynamic and distributionally robust frameworks for robotic decision-making. The authors review risk-aware planning (behavior, motion, MPC), safety-critical control (RCBFs), and risk-aware verification (temporal logic, regression of robustness measures), illustrated by subterranean traversability and bipedal walking case studies, plus lane-keeping and quadruped verification experiments. The work identifies practical open problems—computational efficiency, nonlinear dynamics, multi-agent interactions, learning integration, nonstationary data, and compositional verification—that must be addressed to deploy rigorous tail-risk frameworks in real-world autonomous systems. Overall, the survey demonstrates that tail-risk methodologies provide a principled, scalable path to safer, more reliable robotics under uncertainty, with tangible pipelines from planning through verification and real-world validation.

Abstract

The need for a systematic approach to risk assessment has increased in recent years due to the ubiquity of autonomous systems that alter our day-to-day experiences and their need for safety, e.g., for self-driving vehicles, mobile service robots, and bipedal robots. These systems are expected to function safely in unpredictable environments and interact seamlessly with humans, whose behavior is notably challenging to forecast. We present a survey of risk-aware methodologies for autonomous systems. We adopt a contemporary risk-aware approach to mitigate rare and detrimental outcomes by advocating the use of tail risk measures, a concept borrowed from financial literature. This survey will introduce these measures and explain their relevance in the context of robotic systems for planning, control, and verification applications.

Figures (15)

• Figure 1: Visualization of common tail risk measures. The tail risk measures referenced in the article are shown above, applied to the random variable $X$ with distribution function $P$. $X$ could represent any cost random variable, for example - negative distance from an obstacle, distance from a goal, or energy used by the robot. Figure adapted from dixit2022riskaverse.
• Figure 2: An overview of a typical (risk-aware) planning and verification pipeline in an autonomy stack.
• Figure 3: The transition graph of a transient MDP. The goal state $x=x^g$ is cost-free and absorbing.
• Figure 4: Left: Trade-off between the distance traversed by the robot and different risk levels. Right: the trade-off between maximum risk taken along the traversed path and different risk levels. Note that $\beta = 1 - \alpha$. Figure taken from dixit2023step.
• Figure 5: Four instances from a Monte-Carlo simulation illustrate how different choices of risk levels, $1-\beta$, affect the paths taken by the robot. Figure taken from dixit2023step.

Theorems & Definitions (3)

• Remark 1
• Theorem 1
• Theorem 2