Chance-Constrained Neural MPC under Uncontrollable Agents via Sequential Convex Programming

TL;DR

The paper tackles safety guarantees for systems interacting with uncontrollable, stochastic agents by combining a neural trajectory predictor with split conformal prediction to yield region specific error bounds, which are integrated into a chance constrained MPC. A two loop iterative sequential convex programming algorithm solves the resulting non convex optimization, with inner SCP for fixed bounds and an outer loop that refines bounds based on the obtained control sequence. The authors establish convergence and local optimality guarantees and validate the approach in a pedestrian–vehicle interaction scenario, achieving high success rates and faster traffic performance. The work advances practical safe planning under distribution shifts by explicitly accounting for coupling between control actions and predicted agent behavior, enabling tighter and more adaptive uncertainty quantification. The approach shows strong potential for real-time safety-critical robotics and autonomous driving applications where uncontrollable agents influence system dynamics.

Abstract

This work investigates the challenge of ensuring safety guarantees under uncontrollable agents whose behaviors are stochastic and depend on both their own and the system's states. We present a neural model predictive control (MPC) framework that predicts the trajectory of the uncontrollable agent using a predictor learned from offline data. To provide probabilistic guarantees on prediction errors, we employ split conformal prediction to construct region-specific, time-dependent uncertainty bounds, which are integrated into the MPC formulation. To solve the resulting non-convex, discontinuous optimization problem, we propose a two-loop iterative sequential convex programming algorithm. The inner loop solves convexified subproblems with fixed error bounds, while the outer loop refines these bounds based on updated control sequences. We establish convergence guarantees under mild regularity conditions and demonstrate the optimality of the algorithm. We illustrate our method with an autonomous driving scenario involving interactive pedestrians. Experimental results demonstrate that our approach achieves superior safety and efficiency compared to baseline methods, with success rates exceeding 99.5\% while maintaining higher average speeds in multi-pedestrian scenarios.

Figures (3)

• Figure 1: Scenario Illustration: given the same initial position, the distribution of a pedestrian's trajectory over the next few steps will change with the car's control signals. As the car approaches more quickly, the pedestrian tends to avoid the car more conservatively.
• Figure 2: Pedestrian trajectory ground truth, and network predictions with error bounds under SCP$^2$ (left) and ACP (right).
• Figure 3: Prediction Error with Bound $\bar{R}_{k=1}$ through a complete zebra crossing task (SCP$^2$ v.s. ACP). SCP$^2$ can correctly predict error bounds (85% coverage) even under rapidly changing multi-agent interaction. The lines are the true prediction errors and the areas are the error bounds.