Improving Feasibility and Safety of Nonlinear MPC with Control Barrier Function via Learning-based Non-Convex Reachable Sets

This paper proposes a learning-based reachability-aware (RA) nonlinear model predictive control (NMPC) framework with discrete control barrier functions (DCBF) to improve safety and feasibility for complex, nonlinear systems, specifically demonstrated on a tractor-trailer system. Traditional NMPC-CBF methods often encounter feasibility issues due to the potential empty intersection between the reachable set and the safe region confined by CBF constraints. Additionally, standard reachability analysis methods rely on oversimplified approximations of reachable sets. To address these challenges, we introduce a novel learning-based approach leveraging sampling-based reachability analysis combined with Alpha Shapes, accurately capturing non-convex reachable sets. A Multi-Layer Perceptron (MLP) neural network is trained offline to efficiently approximate the infeasible reachable region online. By integrating this learned approximation directly into the NMPC’s objective function, the proposed method significantly enhances optimization feasibility without compromising safety guarantees. Numerical experiments validate the approach, demonstrating better constraint handling, and enhanced maneuverability and feasibility compared to conventional convex hull-based RA-NMPC-DCBF and slack variable-based NMPC.