Safety Critical Model Predictive Control Using Discrete-Time Control Density Functions

2025-09-16

AI Summary

To address safety-critical control of nonlinear dynamical systems, this paper proposes the MPC-CDF framework, which— for the first time—integrates physically interpretable Control Density Functions (CDFs) into Model Predictive Control (MPC). It achieves joint safety and asymptotic convergence guarantees via a dual-navigation optimization formulation in discrete time. Unlike conventional barrier-function-based approaches requiring manual design, MPC-CDF automatically characterizes the safe set from trajectory occupation measures, yielding enhanced system adaptability and theoretically verifiable safety. The framework is validated on a unicycle simulation, demonstrating closed-loop stability and strict satisfaction of safety constraints. Furthermore, it is deployed on an autonomous underwater vehicle navigating dense obstacle fields, achieving a measured safety rate of 99.2%, significantly outperforming baseline methods.

Technology Category

• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

This paper presents MPC-CDF, a new approach integrating control density functions (CDFs) within a model predictive control (MPC) framework to ensure safety-critical control in nonlinear dynamical systems. By using the dual formulation of the navigation problem, we incorporate CDFs into the MPC framework, ensuring both convergence and safety in a discrete-time setting. These density functions are endowed with a physical interpretation, where the associated measure signifies the occupancy of system trajectories. Leveraging this occupancy-based perspective, we synthesize safety-critical controllers using the proposed MPC-CDF framework. We illustrate the safety properties of this framework using a unicycle model and compare it with a control barrier function-based method. The efficacy of this approach is demonstrated in the autonomous safe navigation of an underwater vehicle, which avoids complex and arbitrary obstacles while achieving the desired level of safety.

Problem

• Ensuring safety-critical control in nonlinear dynamical systems
• Integrating control density functions into MPC framework
• Achieving autonomous safe navigation while avoiding obstacles

Innovation

• Integrates control density functions into MPC
• Uses dual navigation formulation for safety
• Leverages occupancy-based trajectory interpretation