Enhancing Feasibility and Safety of Nonlinear Model Predictive Control with Discrete-Time Control Barrier Functions

TL;DR

This paper introduces two novel NMPC formulations that integrate control barrier functions and control Lyapunov functions with slack variables to simultaneously improve safety and feasibility in nonlinear control systems.

Contribution

The paper proposes unified NMPC formulations combining CBFs and CLFs with slack variables, enabling concurrent enhancement of safety and feasibility in nonlinear control.

Findings

Theoretical analysis shows improved safety and feasibility tradeoff.

Numerical results validate the effectiveness of the proposed formulations.

Proposed methods outperform existing approaches in safety and feasibility metrics.

Abstract

Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.