AC-SMPC: Differentiable Actor--Critic MPC with State Constraints for Safe and Fast Robot Navigation

This research presents AC-SMPC, a novel actor-critic model predictive control framework designed for safe and efficient robot navigation in confined dynamic environments. The method addresses the challenge of integrating explicit state constraints into learning-based planning by representing robots and obstacles as vertices and half-spaces, locally linearizing nonlinear dynamics, and convexifying collision avoidance constraints into a differentiable MPC layer. An elastic quadratic program is formed using bounded slack variables to handle cases where local constraint approximations cannot be simultaneously satisfied. Simulation tests and experiments demonstrate the framework's ability to adaptively adjust learned policies for multi-robot navigation in narrow spaces while maintaining motion safety and improving efficiency over existing approaches.