Integrating Predictive Motion Uncertainties with Distributionally Robust Risk-Aware Control for Safe Robot Navigation in Crowds

TL;DR

This work addresses safe robot navigation in crowds by integrating ML-based human trajectory forecasts into control with distributionally robust chance constraints. It introduces DRCC-MPC, which enforces safety through a distributionally robust CVaR constraint over an ellipsoidal collision-free region and moment-based ambiguity sets for predicted human motion, solved in real time via a GPU-accelerated constrained Cross-Entropy Method. The approach yields interpretable safety parameters through the collision probability $\varepsilon$ and demonstrates safer navigation on real-world pedestrian data compared to strong baselines, with favorable computation times. The contributions offer a practical, robust framework for risk-aware navigation in crowds and set the stage for future work where human behavior reacts to the robot.

Abstract

Ensuring safe navigation in human-populated environments is crucial for autonomous mobile robots. Although recent advances in machine learning offer promising methods to predict human trajectories in crowded areas, it remains unclear how one can safely incorporate these learned models into a control loop due to the uncertain nature of human motion, which can make predictions of these models imprecise. In this work, we address this challenge and introduce a distributionally robust chance-constrained model predictive control (DRCC-MPC) which: (i) adopts a probability of collision as a pre-specified, interpretable risk metric, and (ii) offers robustness against discrepancies between actual human trajectories and their predictions. We consider the risk of collision in the form of a chance constraint, providing an interpretable measure of robot safety. To enable real-time evaluation of chance constraints, we consider conservative approximations of chance constraints in the form of distributionally robust Conditional Value at Risk constraints. The resulting formulation offers computational efficiency as well as robustness with respect to out-of-distribution human motion. With the parallelization of a sampling-based optimization technique, our method operates in real-time, demonstrating successful and safe navigation in a number of case studies with real-world pedestrian data.

Figures (4)

• Figure 1: Trajectory forecasting model enables a robot to estimate the distribution of future human trajectories. In response, the robot modifies its route to reduce the chance of collision.
• Figure 2: VaR and CVaR in a normal distribution with allowable probability $\varepsilon = 0.1$. VaR is a $1-\varepsilon$ quantile of the safety loss and CVaR is the conditional expectation of safety loss over the VaR (blue area).
• Figure 3: For human $i$, collision-free set $\mathcal{X}_{i,free}^k$ is an ellipsoid centered on $\mu_i^k$ which belongs to $\mathcal{X} \backslash \mathcal{X}_{robot}$. We constraint the random human state $x_i^k$ to belong to such a set.
• Figure 4: Sensitivity analysis in Hotel sequence with 100 experiments. As the DRCC-MPC becomes more conservative by reducing $\varepsilon$, the robot tends to keep a larger distance from the humans and decides to take a longer path. On the contrary, RSSAC showed similar behavior for different choices of its risk-sensitivity parameter $\sigma$, showing an inability to display a straightforward interpretation of risk and safety.

Theorems & Definitions (6)

• Definition 1: Chance constraint over a collision-free set
• Definition 2: Value-at-Risk
• Definition 3: Conditional Value-at-Risk
• Theorem 1
• proof
• Corollary 1