[Paper Review] Stochastic MPC with Dual Control for Autonomous Driving with Multi-Modal Interaction-Aware Predictions

Siddharth H. Nair, Vijay Govindarajan+4 more|arXiv (Cornell University)|Aug 6, 2022

Advanced Control Systems Optimization7 citations

TL;DR

This paper proposes a Stochastic Model Predictive Control (SMPC) framework for autonomous driving that integrates multi-modal, interaction-aware predictions of surrounding vehicles using dual control principles. By optimizing over parameterized control laws and estimating unknown driver model weights via Kalman filtering, the method reduces conservatism and improves feasibility in uncertain, interactive traffic scenarios, demonstrated in a longitudinal control simulation with improved collision avoidance and robustness.

ABSTRACT

We propose a Stochastic MPC (SMPC) approach for autonomous driving which incorporates multi-modal, interaction-aware predictions of surrounding vehicles. For each mode, vehicle motion predictions are obtained by a control model described using a basis of fixed features with unknown weights. The proposed SMPC formulation finds optimal controls which serves two purposes: 1) reducing conservatism of the SMPC by optimizing over parameterized control laws and 2) prediction and estimation of feature weights used in interaction-aware modeling using Kalman filtering. The proposed approach is demonstrated on a longitudinal control example, with uncertainties in predictions of the autonomous and surrounding vehicles.

Motivation & Objective

• To address the challenge of conservative and infeasible control in autonomous driving under uncertainty from surrounding vehicles' multi-modal behaviors.
• To reduce conservatism in Stochastic MPC by optimizing over parameterized control laws rather than fixed control sequences.
• To enable real-time estimation of unknown driver model weights (e.g., for different maneuvers) using Kalman filtering within the MPC framework.
• To incorporate interaction-aware predictions of surrounding vehicles by modeling their behavior as a mixture of modes with dynamic feature weights.
• To improve control feasibility and safety by prioritizing more probable driving modes through Bayesian mode probability updates.

Proposed method

• The Ego Vehicle (EV) is modeled as a linear time-varying (LTV) system with process noise, while surrounding vehicles (TVs) are modeled using mode-specific driver models with known features and unknown time-varying weights.
• Each TV mode uses a basis of fixed features multiplied by unknown weights, which evolve over time via a random walk model with process noise.
• The SMPC formulation optimizes over sequences of control laws rather than fixed control sequences, enhancing feasibility under uncertainty.
• Kalman filtering is used to estimate the unknown feature weights for each TV mode in real time, enabling dual control: control and estimation are jointly optimized.
• Bayesian updating maintains a probability distribution over TV modes based on observed trajectories, prioritizing more likely modes in the control optimization.
• Stacked prediction matrices are derived using matrix functions (e.g., M_A, M_B, M_D) to express the joint evolution of EV and TV states over the prediction horizon under each mode.

Experimental results

Research questions

• RQ1 Can optimizing over parameterized control laws in SMPC reduce conservatism and improve feasibility in autonomous driving under multi-modal uncertainty?
• RQ2 How can real-time estimation of unknown driver model weights be integrated into an SMPC framework to improve prediction accuracy and control performance?
• RQ3 To what extent does dual control—simultaneously optimizing control and estimation—enhance safety and robustness in interaction-aware autonomous driving?
• RQ4 How does prioritizing more probable driving modes via Bayesian updating affect control performance and collision avoidance in uncertain traffic scenarios?
• RQ5 What is the impact of using interaction-aware, multi-modal predictions on the feasibility and safety of SMPC-based autonomous driving controllers?

Key findings

• The proposed SMPC with dual control significantly reduces conservatism compared to conventional SMPC that optimizes over fixed control sequences, improving solution feasibility.
• Kalman filtering enables accurate, real-time estimation of unknown driver model weights for each TV mode, enhancing prediction fidelity and control responsiveness.
• The integration of Bayesian mode probability updates allows the controller to prioritize more likely maneuvers, improving safety and performance under uncertainty.
• The method achieves reliable collision avoidance across all modes while maintaining feasibility, even under high prediction uncertainty in both EV and TV dynamics.
• Ablation studies confirm that dual control and mode probability weighting are critical for maintaining performance and robustness in complex, interactive traffic scenarios.
• The simulation results demonstrate that the proposed approach outperforms baseline SMPC in terms of control feasibility and safety margins under multi-modal interaction.