cs.ROFeb 16, 2026

Multimodal Belief-Space Covariance Steering with Active Probing and Influence for Interactive Driving

Authors: Devodita Chakravarty, John Dolan, Yiwei Lyu

Organizations: Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, India · Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA · Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

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Abstract

Autonomous driving in complex traffic requires reasoning under uncertainty. Common approaches rely on prediction-based planning or risk-aware control, but these are typically treated in isolation, limiting their ability to capture the coupled nature of action and inference in interactive settings. This gap becomes especially critical in uncertain scenarios, where simply reacting to predictions can lead to unsafe maneuvers or overly conservative behavior. Our central insight is that safe interaction requires not only estimating human behavior but also shaping it when ambiguity poses risks. To this end, we introduce a hierarchical belief model that structures human behavior across coarse discrete intents and fine motion modes, updated via Bayesian inference for interpretable multi-resolution reasoning. On top of this, we develop an active probing strategy that identifies when multimodal ambiguity in human predictions may compromise safety and plans disambiguating actions that both reveal intent and gently steer human decisions toward safer outcomes. Finally, a runtime risk-evaluation layer based on Conditional Value-at-Risk (CVaR) ensures that all probing actions remain within human risk tolerance during influence. Our simulations in lane-merging and unsignaled intersection scenarios demonstrate that our approach achieves higher success rates and shorter completion times compared to existing methods. These results highlight the benefit of coupling belief inference, probing, and risk monitoring, yielding a principled and interpretable framework for planning under uncertainty.

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Fig. 1 : Overview of the lane-merging interaction between an autonomous ego vehicle and a human-driven vehicle, illustrating the evolution of hierarchical belief updates, CVaR-based risk assessment, control effort, and resulting trajectories from t1t_{1} to t5t_{5} . The progression shows how active probing and Bayesian updates refine intent inference from uncertain to cooperative, while control effort adapts to balance safety and efficiency. Specifically, the hierarchical belief update displays Bayesian updates integrating noisy observations and probing-induced responses, evolving from a uniform intent distribution at t1t_{1} to a concentrated cooperative belief at t5t_{5} . Instead of passively observing, the active probing controller at t2t_{2} demonstrates how probing actions intentionally change the interaction and belief state to reveal latent human intentions. The CVaR risk assessment curve illustrates how risk-aware control adjusts the vehicle’s aggressiveness and conservatism during the interaction by first rising and then falling over time steps. Lastly, the model’s ability to dynamically combine efficiency and safety is demonstrated by the way the adaptive control effort changes in response to inferred risk and intent certainty.
Fig. 2 : Unsignaled four-way intersection. The ego shapes the crossing agent’s belief, leading it to yield.
MetricAP-IHCC-MPCAP-MPOurs
Success Rate82%82\%87%87\%92%92\%96%\mathbf{96\%}
Time to Merge (s)6.80±1.346.80\pm 1.344.72±1.654.72\pm 1.655.25±1.425.25\pm 1.422.03±1.38\mathbf{2.03\pm 1.38}
Gap to Vehicle (m)9.54±3.609.54\pm 3.609.84±2.109.84\pm 2.108.10±2.208.10\pm 2.207.60±2.29\mathbf{7.60\pm 2.29}
Velocity (m/s)8.35±1.068.35\pm 1.067.90±1.087.90\pm 1.088.01±1.178.01\pm 1.178.88±1.02\mathbf{8.88\pm 1.02}
Longitudinal Jerk (m/s 3 )0.31±0.180.31\pm 0.180.28±0.190.28\pm 0.190.21±0.22\mathbf{0.21\pm 0.22}0.22±0.160.22\pm 0.16
Angular Jerk (rad/s 3 )(1.52±1.21) ⁣× ⁣10−2(1.52\pm 1.21)\!\times\!10^{-2}(1.84±1.10) ⁣× ⁣10−2(1.84\pm 1.10)\!\times\!10^{-2}(1.76±1.05) ⁣× ⁣10−2(1.76\pm 1.05)\!\times\!10^{-2}(1.49±0.98) ⁣× ⁣10−2\mathbf{(1.49\pm 0.98)\!\times\!10^{-2}}
TABLE I : Comparison of Performance Metrics for lane merging scenario for 500 simulation runs
MetricAP-IHCC-MPCAP-MPOurs
Success Rate78%78\%84%84\%88%88\%94%\mathbf{94\%}
Time to Cross (s)8.02±2.048.02\pm 2.045.78±1.905.78\pm 1.906.80±2.906.80\pm 2.904.14±1.87\mathbf{4.14\pm 1.87}
Gap to Vehicle (m)6.20±2.106.20\pm 2.106.80±2.006.80\pm 2.006.10±1.906.10\pm 1.905.70±2.00\mathbf{5.70\pm 2.00}
Velocity (m/s)4.56±0.784.56\pm 0.784.73±0.724.73\pm 0.724.84±0.674.84\pm 0.675.11±0.61\mathbf{5.11\pm 0.61}
Longitudinal Jerk (m/s 3 )0.21±0.150.21\pm 0.150.20±0.160.20\pm 0.160.19±0.140.19\pm 0.140.16±0.13\mathbf{0.16\pm 0.13}
Angular Jerk (rad/s 3 )0.18±0.120.18\pm 0.120.15±0.110.15\pm 0.110.12±0.10\mathbf{0.12\pm 0.10}0.14±0.110.14\pm 0.11
TABLE II : Comparison of Performance Metrics for an unsignaled four-way intersection scenario for 500 simulation runs
Fig. 3 : Trajectory comparison across methods for the same lane merge scenario. AP-IH (brown), CC-MPC (pink), and AP-MP (blue) manage to merge but require longer times or more conservative maneuvers, while our method (yellow) merges more quickly and with smoother motion, reflecting the efficiency and risk-aware confidence of our planner.
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