Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers

2026-05-24

AI Summary

Providing efficient and differentiable reachability guarantees for neural network-controlled closed-loop systems under uncertainty remains a significant challenge. This work proposes the first parallelized reachability analysis framework that supports GPU batch processing and automatic differentiation, integrating Taylor model flowpipes with CROWN-style linear bound propagation to enable differentiable computation while preserving affine dependencies. By bridging the gap between formal verification and learning-based planning, the method facilitates reachability-aware sampling-based model predictive control (MPC). Evaluated on non-prehensile manipulation and quadrotor tasks, the approach enables online planning for systems up to 72 dimensions, delivering precise reachability certificates under bounded uncertainty while maintaining real-time performance.

Abstract

Neural network (NN) dynamics models and control policies achieve strong performance in robotics, but providing sound guarantees under uncertainty remains difficult, especially for closed-loop NN systems. Existing reachability tools provide formal over-approximations, yet are often non-differentiable, overly conservative, or too slow for modern learning and online planning pipelines. To address this, we present a parallelizable, differentiable reachability framework in JAX for continuous- and discrete-time systems with analytical and NN-based dynamics and controllers. Our framework combines Taylor-model flowpipe construction with CROWN-style linear bound propagation through a unified representation that preserves affine dependencies while supporting GPU-batched computation and automatic differentiation. Building on this reachability primitive, we develop (i) a certified training method that encourages reachability-friendly dynamics models and controllers, and (ii) a reachability-aware sampling-based MPC scheme with gradient-based refinement. Experiments on non-prehensile manipulation and quadrotor tasks, including hardware and higher-dimensional evaluations (up to 72D), demonstrate practical online planning while maintaining certified reachable-set over-approximations under bounded uncertainty.

Problem

• neural dynamics
• reachability analysis
• certified control
• uncertainty
• closed-loop systems

Innovation

• differentiable reachability
• certified neural control
• Taylor-model flowpipe
• CROWN-style bound propagation
• reachability-aware MPC