Discrete-time Control Barrier Functions for Guaranteed Recursive Feasibility in Nonlinear MPC: An Application to Lane Merging

TL;DR

This paper introduces discrete-time control barrier functions and quasi-variants to ensure recursive feasibility in nonlinear MPC, demonstrated through a lane merging application with improved control input bounds and lower costs.

Contribution

It proposes new DTCBF and qDTCBF certificates that guarantee recursive feasibility in nonlinear MPC under input constraints, with applications to automated driving.

Findings

qDTCBF allows tighter control input bounds

Certificates enable earlier control reactions

Simulation confirms improved feasibility and cost reduction

Abstract

In this paper, we present conditions under which the terminal ingredients, defined by discrete-time control barrier function (DTCBF) certificates, guarantee recursive feasibility in nonlinear MPC. Further, we introduce the notion of quasi-DTCBF (qDTCBF) certificates. Compared to DTCBFs, qDTCBF conditions can be satisfied with tighter control input bounds, which is highly advantageous if only limited actuation is possible. Both certificates encourage an earlier reaction of the control system and result in a lower cumulative MPC cost. The methodology is applied to a lane merging problem in automated driving, in which DTCBF and qDTCBF certificates subject to input constraints form the terminal ingredients to guarantee recursive feasibility of the nonlinear MPC scheme. A simulation study demonstrates the efficacy of the concept.